LES ERREURS DE PRÉVISION

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LES ERREURS DE PRÉVISION LES ERREURS DE PRÉVISION e e t t = X = X t t - P - P t t X X 1 X X 2 X X 3 X X 4 X X 5 X X 6 P P 5 P P 6 e e 5 e e 6

description

LES ERREURS DE PRÉVISION. P 5 P 6. X 1 X 2 X 3 X 4 X 5 X 6 …. e 5 e 6. e t = X t - P t. LES ERREURS DE PRÉVISION: UNE SOURCE D’INFORMATION UTILE. Pour l’ajustement des méthodes de prévision et de leurs paramètres Pour l’évaluation des prévisions - PowerPoint PPT Presentation

Transcript of LES ERREURS DE PRÉVISION

  • LES ERREURS DE PRVISIONet = Xt - PtX1X2X3X4 X5 X6P5P6e5e6

  • LES ERREURS DE PRVISION: UNE SOURCE DINFORMATION UTILEPour lajustement des mthodes de prvision et de leurs paramtres

    Pour lvaluation des prvisions

    Pour lestimation de lcart-type de la demande

    Pour la dtermination du stock de scurit

    Pour les intervalles de confiance sur les prvisions

  • EM, EMA ET EMAtMesure du biaisMesure de la distance (amplitude) moyenneentre une prvision et la demanderelle de la priode correspondante

    ]|Expr|[#>`b___}) b'4" *|: ;bP8&c0!"EMA ,]

  • PRVISIONS NON BIAISESPrvisions biaisesCaractristiques desprvisions non biaises- il ny a pas dallure distinctive dans les erreurs de prvision

    - les erreurs sont centres 0

    - il y a peu prs autant de termes derreurs positifs que de ngatifs

    Graph1

    10911050

    10061054.1

    11051049.29

    10341054.861

    10951052.7749

    10811056.99741

    11361059.397669

    11161067.0579021

    11091071.95211189

    11991075.656900701

    12091087.9912106309

    12321100.0920895678

    11911113.282880611

    12391121.0545925499

    12351132.8491332949

    13301143.0642199654

    13421161.7577979689

    13321179.782018172

    13741195.0038163548

    14021212.9034347193

    15041231.8130912474

    15021259.0317821226

    15881283.3286039104

    16071313.7957435194

    16901343.1161691674

    17621377.8045522507

    17571416.2240970256

    18391450.301687323

    18481489.1715185907

    19041525.0543667317

    19751562.9489300585

    20611604.1540370526

    21531649.8386333474

    22131700.1547700126

    22381751.4392930114

    23661800.0953637102

    371856.6858273392

    LES

    a=0.1

    tXtPtet

    190100.00-10.00

    210599.006.00

    39599.60-4.60

    411099.1410.86

    595100.23-5.23

    69099.70-9.70

    710598.736.27

    812099.3620.64

    9120101.4218.58

    10115103.2811.72

    11125104.4520.55

    12115106.518.49

    13115107.367.64

    14125108.1216.88

    15115109.815.19

    16120110.339.67

    17120111.308.70

    18105112.17-7.17

    1990111.45-21.45

    2095109.30-14.30

    21110107.872.13

    2295108.09-13.09

    23105106.78-1.78

    2490106.60-16.60

    25104.94

    LES

    LESA

    b=0.2

    tXtPtetabs(et)EtMtat

    19095.00-5.005.00-5.005.000.40

    210593.0012.0012.00-1.606.400.25

    39596.00-1.001.00-1.485.320.28

    411095.7214.2814.281.677.110.24

    59599.08-4.084.080.526.500.08

    69098.75-8.758.75-1.336.950.19

    710597.077.937.930.527.150.07

    812097.6522.3522.354.8910.190.48

    9120108.3711.6311.636.2410.480.60

    10115115.29-0.290.294.938.440.58

    11125115.129.889.885.928.730.68

    12115121.82-6.826.823.378.350.40

    13115119.07-4.074.071.887.490.25

    14125118.046.966.962.907.380.39

    15115120.77-5.775.771.167.060.16

    16120119.820.180.180.975.690.17

    17120119.850.150.150.804.580.18

    18105119.88-14.8814.88-2.336.640.35

    1990114.65-24.6524.65-6.8010.240.66

    209598.29-3.293.29-6.098.850.69

    2111096.0213.9813.98-2.089.870.21

    229598.97-3.973.97-2.468.690.28

    2310597.857.157.15-0.548.390.06

    249098.30-8.308.30-2.098.370.25

    2596.23

    LESA

    demande

    prvisions

    priodes

    demande et prvisions

    LETS

    priodes

    valeurs de at

    LESAIS

    a=0.5

    g=0.5

    b=0.5

    tXtStbtItPt

    13620.9526

    23851.0132

    34321.1368

    4341380.00009.75000.8974

    5382395.372212.56110.9594371.2882

    6409405.810811.49991.0105413.3009

    7498427.683116.68611.1506474.4164

    8387437.815113.40900.8907398.7629

    9473472.119123.85650.9806432.9066

    10513501.820426.77891.0164501.1874

    11582517.205121.08181.1380608.2211

    12474535.240819.55870.8881479.4261

    13544.0560

    14583.7738

    15675.8498

    16544.8383

    LESAIS

    demande

    prvisions

    priodes

    demande

    LETO2

    a=0.5L=4

    b=0.5X bar=380

    tXtStItPt

    13620.9526

    23851.0132

    34321.1368

    4341380.00000.8974

    5382390.49720.9654362.0000

    6409397.09281.0216395.6354

    7445394.26401.1328451.4318

    8335383.78890.8851353.8000

    9360378.33870.9585370.5235

    10375372.71001.0139386.5002

    11440380.57031.1445422.1924

    12355390.82240.8967336.8512

    13374.5963

    14396.2385

    15447.2813

    16350.4628

    LETO2

    demande

    prvisions

    priodes

    demande

    LETO1

    a=0.3

    XtS'tS''tStbtPt

    110911091109110910

    21006106610831048-8

    31105107710821073-21040

    41034106410761052-51071

    51095107410761072-11047

    6108110761076107601071

    7113610941081110751076

    8111611001087111461112

    9110911031092111451120

    101199113211041160121119

    111209115511191191151172

    121232117811371219181206

    131191118211501214141237

    141239119911651233151227

    151235121011781241131248

    161330124611991293201255

    171342127512211328231313

    181332129212431341211351

    191374131712651368221362

    201402134212881396231390

    211504139113191463311420

    221502142413501498321493

    231588147313871559371529

    241607151314251602381596

    251640

    261677

    271715

    LETO1

    observations

    S't

    S''t

    prvisions

    priodes

    demande

    MMP

    a=0.3

    g=0.4

    tXtStbtPt

    110911091.0010.00

    211011101.0010.001101.00

    311051109.209.281111.00

    410341093.14-0.861118.48

    510951093.09-0.531092.28

    610811089.09-1.921092.56

    711361101.823.941087.18

    811161108.835.171105.76

    911091112.504.571114.00

    1011991141.6514.401117.07

    1112091171.9320.751156.05

    1212321204.4825.471192.69

    1311911218.2720.801229.95

    1412391239.0420.791239.06

    1512351252.3817.811259.83

    1613301288.1424.991270.19

    1713421321.7828.451313.12

    1813321344.7726.261350.24

    1913741371.9226.621371.03

    2014021399.5827.031398.54

    2115041449.8336.321426.61

    2215021490.9138.221486.15

    2315881546.7945.291529.13

    2416071596.5547.081592.08

    251643.63

    261690.71

    271737.79

    MMP

    Erreurs

    w1=0.5w1=0.1

    w2=0.3w2=0.2

    w3=0.2w3=0.3

    w4=0.4

    tXtPtPt

    190

    2105

    395

    411097.00

    595104.5097.50

    69099.50102.00

    710595.5099.00

    812098.50101.00

    9120109.5098.00

    10115117.00103.50

    11125117.50113.50

    12115121.00119.50

    13115118.00119.00

    14125117.00118.00

    15115120.00120.00

    16120118.00117.00

    17120119.50118.50

    18105119.00120.50

    1990112.50116.50

    2095100.50114.00

    2111095.50107.00

    2295101.5099.00

    2310599.5096.00

    2490103.00100.50

    2595.50102.50

    Erreurs

    Feuil1

    a=0.1

    tXtPtetabs(et)

    110911050.00

    210061054.1048.1048.1

    311051049.29-55.7155.71

    410341054.8620.8620.86

    510951052.77-42.2342.23

    610811057.00-24.0024.00

    711361059.40-76.6076.60

    811161067.06-48.9448.94

    911091071.95-37.0537.05

    1011991075.66-123.34123.34

    1112091087.99-121.01121.01

    1212321100.09-131.91131.91

    1311911113.28-77.7277.72

    1412391121.05-117.95117.95

    1512351132.85-102.15102.15

    1613301143.06-186.94186.94

    1713421161.76-180.24180.24

    1813321179.78-152.22152.22

    1913741195.00-179.00179.00

    2014021212.90-189.10189.10

    2115041231.81-272.19272.19

    2215021259.03-242.97242.97

    2315881283.33-304.67304.67

    2416071313.80-293.20293.20

    2516901343.12-346.88346.88

    2617621377.80-384.20384.20

    2717571416.22-340.78340.78

    2818391450.30-388.70388.70

    2918481489.17-358.83358.83

    3019041525.05-378.95378.95

    3119751562.95-412.05412.05

    3220611604.15-456.85456.85

    3321531649.84-503.16503.16

    3422131700.15-512.85512.85

    3522381751.44-486.56486.56

    3623661800.10-565.90565.90

    371856.69

    -229.31233.25

    EMEMA

    Feuil1

    MM

    moisdemande

    Aug-971115

    sept.-971125

    oct.-971115

    nov.-971120

    dc.-971120

    jan.-981105

    fv.-981090

    Mar-981095

    Apr-981110

    May-981095

    Jun-981105

    juil.-981090

    MM

    demande

    mois

    demande

    Demande mensuelle

    MM3MM5MM7

    tXtPtPtPt

    190

    2105

    395

    411096.67

    595103.33

    690100.0099.00

    710598.3399.00

    812096.6799.0098.57

    9120105.00104.00102.86

    10115115.00106.00105.00

    11125118.33110.00107.86

    12115120.00117.00110.00

    13115118.33119.00112.86

    14125118.33118.00116.43

    15115118.33119.00119.29

    16120118.33119.00118.57

    17120120.00118.00118.57

    18105118.33119.00119.29

    1990115.00117.00116.43

    2095105.00110.00112.86

    2111096.67106.00110.00

    229598.33104.00107.86

    23105100.0099.00105.00

    2490103.3399.00102.86

    2596.6799.0098.57

    moy.=107.08

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

  • LE PMEAUne mesure relative

  • EM, EMA, EMAt et PMEA: ex. 1.14EM = -0,083 EMA = 4,07 PMEA = 5,15%a = 0,2

    Calcul des valeurs de EM, EMA, EMAt et PMEA

    mois

    Demande (Xt)

    Prvisions (Pt)

    et

    |et|

    |et|/Xt

    EMAt

    1

    75

    80,0

    -5,0

    5,0

    0,0667

    5,00

    2

    86

    79,0

    7,0

    7,0

    0,0814

    5,40

    3

    84

    80,4

    3,6

    3,6

    0,0429

    5,04

    4

    78

    81,1

    -3,1

    3,1

    0,0397

    4,65

    5

    83

    80,5

    2,5

    2,5

    0,0301

    4,22

    6

    72

    81,0

    -9,0

    9,0

    0,1250

    5,18

    7

    81

    79,2

    1,8

    1,8

    0,0222

    4,50

    8

    79

    79,6

    -0,6

    0,6

    0,0076

    3,72

    9

    75

    79,4

    -4,4

    4,4

    0,0587

    3,86

    10

    77

    78,6

    -1,6

    1,6

    0,0208

    3,41

    11

    77

    78,2

    -1,2

    1,2

    0,0156

    2,96

    12

    84

    78,0

    9,0

    9,0

    0,1071

    4,17

    Somme

    -1

    48,8

    0,6178

  • LE PMEA AJUSTUne sous-estimation dela demande a un plusgrand impact quunesurestimation quivalenteSi Pt = 50Si Pt = 200Xt = 100

  • LA STATISTIQUE U DE THEILU = 1

    U < 1

    U > 1Plus la valeur de U est basse, mieux cest ...

    ]|Expr|[#>`b___})%# b'4" *|: ;bP8&c0!"U ,]

  • LA STATISTIQUE U: ex. 1.16U = 0,9248

    t

    Xt

    Pt

    et

    (et+1/Xt)2

    [(Xt+1-Xt)/Xt]2

    1

    90

    95,00

    -5,00

    0,0178

    0,0278

    2

    105

    93,00

    12,00

    0,0001

    0,0091

    3

    95

    96,00

    -1,00

    0,0226

    0,0249

    4

    110

    95,72

    14,28

    0,0014

    0,0186

    5

    95

    99,08

    -4,08

    0,0085

    0,0028

    6

    90

    98,75

    -8,75

    0,0078

    0,0278

    7

    105

    97,07

    7,93

    0,0453

    0,0204

    8

    120

    97,65

    22,35

    0,0094

    0,0000

    9

    120

    108,37

    11,63

    0,0000

    0,0017

    10

    115

    115,29

    -0,29

    0,0074

    0,0076

    11

    125

    115,12

    9,88

    0,0030

    0,0064

    12

    115

    121,82

    -6,82

    0,0013

    0,0000

    13

    115

    119,07

    -4,07

    0,0037

    0,0076

    14

    125

    118,04

    6,96

    0,0021

    0,0064

    15

    115

    120,77

    -5,77

    0,0000

    0,0019

    16

    120

    119,82

    0,18

    0,0000

    0,0000

    17

    120

    119,85

    0,15

    0,0154

    0,0156

    18

    105

    119,88

    -14,88

    0,0551

    0,0204

    19

    90

    114,65

    -24,65

    0,0013

    0,0031

    20

    95

    98,29

    -3,29

    0,0217

    0,0249

    21

    110

    96,02

    13,98

    0,0013

    0,0186

    22

    95

    98,97

    -3,97

    0,0057

    0,0111

    23

    105

    97,85

    7,15

    0,0062

    0,0204

    24

    90

    98,30

    -8,30

    Somme

    0,2369

    0,2770

  • EMQ ET EMQtPour lestimation de lcart-type

  • ESTIMATION DE LCART-TYPEDeux faons destimer lcart-type des erreurs de prvision

  • EMQ, EMQt et ET: ex. 1.17EMQ = 107,43

    ET = 10,59

    ET24 = 10,16

    t

    Xt

    Pt

    et

    et2

    EQMt

    1

    90

    95,00

    -5,00

    25,00

    25,00

    2

    105

    93,00

    12,00

    144,00

    36,90

    3

    95

    96,00

    -1,00

    1,00

    33,31

    4

    110

    95,72

    14,28

    203,92

    50,37

    5

    95

    99,08

    -4,08

    16,65

    47,00

    6

    90

    98,75

    -8,75

    76,56

    49,95

    7

    105

    97,07

    7,93

    62,88

    51,25

    8

    120

    97,65

    22,35

    499,52

    96,08

    9

    120

    108,37

    11,63

    135,26

    99,99

    10

    115

    115,29

    -0,29

    0,08

    90,00

    11

    125

    115,12

    9,88

    97,61

    90,76

    12

    115

    121,82

    -6,82

    46,51

    86,34

    13

    115

    119,07

    -4,07

    16,56

    79,36

    14

    125

    118,04

    6,96

    48,44

    76,27

    15

    115

    120,77

    -5,77

    33,29

    71,97

    16

    120

    119,82

    0,18

    0,03

    64,78

    17

    120

    119,85

    0,15

    0,02

    58,30

    18

    105

    119,88

    -14,88

    221,41

    74,61

    19

    90

    114,65

    -24,65

    607,62

    127,91

    20

    95

    98,29

    -3,29

    10,82

    116,21

    21

    110

    96,02

    13,98

    195,44

    124,13

    22

    95

    98,97

    -3,97

    15,76

    113,29

    23

    105

    97,85

    7,15

    51,12

    107,08

    24

    90

    98,30

    -8,30

    68,89

    103,26

    Somme

    2 578,43

  • LE POURCENTAGE DE PRVISIONS RUSSIESri = 1 si E est vrai et ri = 0 si E est faux

    E: un vnement prdfini

  • PPR: ex. 1.18PPR = 62,5%

    t

    Xt

    Pt

    et

    Xt 8%

    Xt + 8%

    rt

    1

    90

    95,00

    -5,00

    82,80

    97,20

    1

    2

    105

    93,00

    12,00

    96,60

    113,40

    0

    3

    95

    96,00

    -1,00

    87,40

    102,60

    1

    4

    110

    95,72

    14,28

    101,20

    118,80

    0

    5

    95

    99,08

    -4,08

    87,40

    102,60

    1

    6

    90

    98,75

    -8,75

    82,80

    97,20

    0

    7

    105

    97,07

    7,93

    96,60

    113,40

    1

    8

    120

    97,65

    22,35

    110,40

    129,60

    0

    9

    120

    108,37

    11,63

    110,40

    129,60

    0

    10

    115

    115,29

    -0,29

    105,80

    124,20

    1

    11

    125

    115,12

    9,88

    115,00

    135,00

    1

    12

    115

    121,82

    -6,82

    105,80

    124,20

    1

    13

    115

    119,07

    -4,07

    105,80

    124,20

    1

    14

    125

    118,04

    6,96

    115,00

    135,00

    1

    15

    115

    120,77

    -5,77

    105,80

    124,20

    1

    16

    120

    119,82

    0,18

    110,40

    129,60

    1

    17

    120

    119,85

    0,15

    110,40

    129,60

    1

    18

    105

    119,88

    -14,88

    96,60

    113,40

    0

    19

    90

    114,65

    -24,65

    82,80

    97,20

    0

    20

    95

    98,29

    -3,29

    87,40

    102,60

    1

    21

    110

    96,02

    13,98

    101,20

    118,80

    0

    22

    95

    98,97

    -3,97

    87,40

    102,60

    1

    23

    105

    97,85

    7,15

    96,60

    113,40

    1

    24

    90

    98,30

    -8,30

    82,80

    97,20

    0

    Somme

    15

  • LA DTERMINATION DE LA LONGUEUR DUN CYCLE SAISONNIERPar inspection visuelle

    Graph1

    362

    385

    432

    341

    382

    409

    498

    387

    473

    513

    582

    474

    L = 4

    priode

    demande

    Feuil2

    iXtMM(12) centre 7MM(12) centre 6MM(12) centreRatios saisonniersIndices sais.

    10.7494

    20.8452

    30.9569

    41540

    51.1724

    61.2777629.83RAPPORT DTAILL

    71.3728629.83628.25629.041.16

    81.2759628.25644.50636.381.19Statistiques de la rgression

    91.1643644.50650.67647.580.99Coefficient de dtermination multiple0.9978859236

    101643650.67666.00658.330.98Coefficient de dtermination R^20.9957763165

    110.9641666.00671.42668.710.96Coefficient de dtermination R^20.9956520905

    120.8588671.42681.17676.290.87Erreur-type7.11060783

    130.7475681.17692.42686.790.69Observations36

    140.8647692.42707.67700.040.92

    150.9643707.67729.08718.380.90ANALYSE DE VARIANCE

    161724729.08737.75733.420.99Degr de libertSomme des carrsMoyenne des carrsFValeur critique de F

    171.1789737.75745.67741.711.06Rgression1405287.11117021405287.111170218015.84552399170

    181.2894745.67759.17752.421.19Rsidus341719.065286193950.5607437116

    191.3863759.17769.25764.211.13Total35407006.176456404

    201.2942769.25775.33772.291.22

    211.1900775.33782.67779.001.16CoefficientsErreur-typeStatistique tProbabilitLI 95%LS 95%

    221747782.67792.75787.710.95Constante561.40047547553.0358405356184.92423066720555.2309092704567.5700416805

    230.9736792.75810.17801.460.92Variable X 110.21376555130.114080447389.531254453409.981926341110.4456047615

    240.8750810.17815.33812.750.92

    250.7596815.33833.58824.460.72

    260.8720833.58840.83837.210.86

    270.9731840.83840.58840.710.87

    281845840.58859.17849.880.99

    291.1998859.17873.33866.251.15

    301.2956873.33873.33873.331.09

    311.31082873.33879.25876.291.231.1737793135

    321.21029879.25882.00880.631.171.1936425676

    331.1897882.00889.17885.581.011.0537138125

    341970889.17903.42896.291.081.0024221353

    350.9906903.42909.17906.291.000.9588561802

    360.8750909.17929.42919.290.820.8693619579

    370.7667929.42942.58936.000.710.7090424605

    380.8753942.58956.75949.670.790.8590471629

    390.9817956.75976.17966.460.850.8699783919

    4011016976.17979.00977.581.041.0069073333

    411.11067979.00982.58980.791.091.1012498324

    421.21199982.58988.92985.751.221.1663868926

    431.31240988.921000.5923941799

    441.211991010.8061597312

    451.111301021.0199252824

    46110041031.2336908337

    470.99491041.447456385

    480.88261051.6612219362Prvisions

    491061.8749874875912.2006954033

    501072.0887530388932.6940493593

    511082.302518591089.7783428024

    521092.51628414131203.1333747647

    531102.73004969261286.2098759915

    541112.94381524381306.3504273707

    551123.15758079511340.6486985871

    561133.37134634641194.2490423489

    571143.58511189761146.3550297673

    581153.79887744891106.3271843261

    591164.01264300011011.9483103964

    601174.2264085514832.5763818707

    MM(12) complte, t=T-L/2, , T

    prvisions dsaisonnalises

    Feuil2

    demande

    MM(12) centre 7

    MM(12) centre 6

    MM(12) centre

    prvisions

    Feuil3

    priodedemande

    1362

    2385

    3432

    4341

    5382

    6409

    7498

    8387

    9473

    10513

    11582

    12474

    Feuil3

    L = 4

    priode

    demande

  • LONGUEUR DUN CYCLE SAISONNIER: LAUTOCORRLATIONCorrlation entre une sriedobservations et ces mmesobservations dcales de kpriodesk: ordre de lautocorrlation-1 rk 1rk = -1 ou rk = 1autocorrlation parfaite

    rk = 0autocorrlation nulle

  • CYCLE DE LONGUEUR LSi les observations sont affectes par la prsence dun cycle saisonnier,lautocorrlation dordre L sera, parmi toutes les autres autocorrlations,la plus importante.Gnralement, les autocorrlations dodre k=1, , 12 sont calculespuisque la plupart du temps, la longueur des cycles saisonniers est dauplus 12 priodes.

  • AUTOCORRLATION: ex. 1.19-0,2669rk -0,3581-0,22160,6072

    priode

    demande

    k=1

    k=2

    k=3

    k=4

    1

    362

    2

    385

    362

    3

    432

    385

    362

    4

    341

    432

    385

    362

    5

    382

    341

    432

    385

    362

    6

    409

    382

    341

    432

    385

    7

    445

    409

    382

    341

    432

    8

    335

    445

    409

    382

    341

    9

    360

    335

    445

    409

    382

    10

    375

    360

    335

    445

    409

    11

    440

    375

    360

    335

    445

    12

    355

    440

    375

    360

    335

  • GRAPHIQUE DES AUTOCORRLATIONS-0,2669 -0,3581-0,22160,6072

    _974525618.xls

    Graph1

    -0.2668829524

    -0.3581085888

    -0.2215549147

    0.6072483911

    ordre k des autocorrlations

    rk

    Feuil7

    priodedemandek=1k=2k=3k=4r1r2r3r4err. Car.

    1362532.84

    23853621.920.01

    3432385362-3.91-1082.992201.17

    4341432385362-2068.243.671017.591943.34

    5382341432385362135.92-144.660.2671.179.51

    6409382341432385-73.74-1054.331122.09-1.99572.01

    74454093823414321433.01-184.74-2641.332811.093590.01

    8335445409382341-3000.83-1197.83154.422207.842508.34

    93603354454093821256.26-1502.91-599.9177.34629.17

    10375360335445409252.92505.01-604.16-241.16101.67

    11440375360335445-553.74-1377.49-2750.413290.423015.84

    12355440375360335-1652.08303.34754.591506.67905.01

    sommes-4272.51-5732.93-3546.859721.3916008.92

    moyenne385.08

    somme car.16008.92rk-0.2669-0.3581-0.22160.6072

    Feuil7

    ordre k des autocorrlations

    rk

    Feuil6

    exemple 5.18

    tXtPtetXt 8%Xt + 8%rt

    19095-582.80102.601

    2105931296.60100.440

    39596-187.40103.681

    411095.7214.28101.20103.380

    59599.08-4.0887.40107.011

    69098.75-8.7582.80106.651

    710597.077.9396.60104.841

    812097.6522.35110.40105.460

    9120108.3711.63110.40117.040

    10115115.29-0.29105.80124.511

    11125115.129.88115.00124.331

    12115121.82-6.82105.80131.571

    13115119.07-4.07105.80128.601

    14125118.046.96115.00127.481

    15115120.77-5.77105.80130.431

    16120119.820.18110.40129.411

    17120119.850.15110.40129.441

    18105119.88-14.8896.60129.471

    1990114.65-24.6582.80123.821

    209598.29-3.2987.40106.151

    2111096.0213.98101.20103.700

    229598.97-3.9787.40106.891

    2310597.857.1596.60105.681

    249098.3-8.382.80106.161

    Feuil5

    exemple 5.16 et 5.17a=0.1

    tXtPtet(et+1/Xt)^2((Xt+1-Xt)/Xt)^2et^2EQMt

    19095-50.01780.027825.0025.00

    210593120.00010.0091144.0036.90

    39596-10.02260.02491.0033.31

    411095.7214.280.00140.0186203.9250.37

    59599.08-4.080.00850.002816.6547.00

    69098.75-8.750.00780.027876.5649.95

    710597.077.930.04530.020462.8851.25

    812097.6522.350.00940.0000499.5296.08

    9120108.3711.630.00000.0017135.2699.99

    10115115.29-0.290.00740.00760.0890.00

    11125115.129.880.00300.006497.6190.76

    12115121.82-6.820.00130.000046.5186.34

    13115119.07-4.070.00370.007616.5679.36

    14125118.046.960.00210.006448.4476.27

    15115120.77-5.770.00000.001933.2971.97

    16120119.820.180.00000.00000.0364.78

    17120119.850.150.01540.01560.0258.30

    18105119.88-14.880.05510.0204221.4174.61

    1990114.65-24.650.00130.0031607.62127.91

    209598.29-3.290.02170.024910.82116.21

    2111096.0213.980.00130.0186195.44124.13

    229598.97-3.970.00570.011115.76113.29

    2310597.857.150.00620.020451.12107.08

    249098.3-8.368.89103.26

    Total0.23690.27702578.43

    U=0.9247620447EQM=107.43

    Feuil4

    Exemple 5.14

    a=0.2

    moisDemande (Xt)Prvisions (Pt)et|et|EMAt|et|/Xt

    17580-555.000.0667

    28679775.400.0814

    38480.43.63.65.040.0429

    47881.1-3.13.14.650.0397

    58380.52.52.54.220.0301

    67281-995.180.1250

    78179.21.81.84.500.0222

    87979.6-0.60.63.720.0076

    97579.4-4.44.43.860.0587

    107778.6-1.61.63.410.0208

    117778.2-1.21.22.960.0156

    128478994.170.1071

    Somme-148.8

    Feuil1

    a=0.2Diffrenciation d'ordre 1

    priodedemandeX'tP'tX''t

    11091

    21006-85-85.00

    3110599-85.00184

    41034-71-48.20-170

    5109561-52.76132

    61081-14-30.01-75

    7113655-26.8169

    81116-20-10.45-75

    91109-7-12.3613

    10119990-11.2897

    111209108.97-80

    121232239.1813

    131191-4111.94-64

    141239481.3589

    151235-410.68-52

    161330957.7599

    1713421225.20-83

    181332-1022.56-22

    1913744216.0552

    2014022821.24-14

    21150410222.5974

    221502-238.47-104

    2315888630.3888

    2416071941.50-67

    2537.00

    Feuil1

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    demande

    priode

    demande

    Feuil2

    a=0.1Diffrenciation d'ordre 1 et 2

    priodedemandeX'tX''tP''tP'tPt

    11091

    21006-85

    31105991840.00

    41034-71-17018.40

    5109561132-0.44

    61081-14-7512.80

    7113655694.02

    81116-20-7510.52

    91109-7131.97

    10119990973.07

    11120910-8012.46

    12123223133.22

    131191-41-644.20

    1412394889-2.62

    151235-4-526.54

    16133095990.69

    17134212-8310.52

    181332-10-221.17

    1913744252-1.15

    20140228-144.16

    211504102742.35

    221502-2-1049.51

    2315888688-1.84

    24160719-677.15

    25-0.2718.731625.73

    26-0.2718.461643.92

    27-0.2718.191661.58

    28-0.2717.921678.69

    Feuil2

    1091

    1006

    1105

    1034

    1095

    1081

    1136

    1116

    1109

    1199

    1209

    1232

    1191

    1239

    1235

    1330

    1342

    1332

    1374

    1402

    1504

    1502

    1588

    1607

    demande

    priode

    demande

    Feuil3

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    priodes

    X't

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    priodes

    X''t

    Dcomposition par dsaisonnalisation

    priodedemandeMM(4)RtIt

    1362

    2385

    3432

    4341380.000.8974

    5382385.000.9922

    6409391.001.0460

    7445394.251.1287

    8335392.750.8530

    9360387.250.92960.9609

    10375378.750.99011.0181

    11440377.501.16561.1471

    12355382.500.92810.8928

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    srie originale

    srie dsaisonnalise

    priodes

    demande

  • LA STATISTIQUE DE DURBIN-WATSONPour sassurer que les erreurs de prvision sont indpendantesLa valeur de D-W doittre prs de 2 ...

  • TEST DE SIGNIFICATIVIT DE LA STATISTIQUE DE DURBIN-WATSONValeurs lues dans letableau 1.33, p. 102selon le nombre T determes derreur si dU < D-W < 4-dU, D-W nest pas significativement diffrent de 2; si D-W < dL ou D-W > 4-dL, D-W est significativement diffrent de 2; si dL < D-W < dU ou 4-dU < D-W < 4-dL, on ne peut conclure.

  • STATISTIQUE DE DURBIN-WATSON: ex. 1.20D-W = 0,5319T = 16dL = ?dU = ?Conclusion: ?

    t

    et

    (et - et-1)2

    (et)2

    1

    -63,82

    4 072,99

    2

    -56,44

    54,46

    3 185,47

    3

    -14,79

    1 734,72

    218,74

    4

    -9,31

    30,03

    86,68

    5

    7,62

    286,62

    58,06

    6

    12,86

    27,46

    165,38

    7

    29,57

    279,22

    874,38

    8

    34,61

    25,40

    1 197,85

    9

    -27,85

    3 901,25

    775,62

    10

    -20,06

    60,68

    402,40

    11

    -17,06

    9,00

    291,04

    12

    -17,35

    0,08

    301,02

    13

    8,38

    662,03

    70,22

    14

    13,55

    26,73

    183,60

    15

    23,19

    92,93

    537,78

    16

    41,87

    348,94

    1 753,10

    Somme

    7 539,58

    14 174,36

  • GRAPHIQUE DES ERREURS DE PRVISION: ex. 1.20Les erreurs ne sont pas centres 0 et elles ne sont pas distribuesalatoirement

    Graph1

    -63.82

    -56.44

    -14.79

    -9.31

    7.62

    12.86

    29.57

    34.61

    -27.85

    -20.06

    -17.06

    -17.35

    8.38

    13.55

    23.19

    41.87

    priodes

    erreurs de prvision

    Feuil1

    1-63.82

    2-56.44

    3-14.79

    4-9.31

    57.62

    612.86

    729.57

    834.61

    9-27.85

    10-20.06

    11-17.06

    12-17.35

    138.38

    1413.55

    1523.19

    1641.87

    Feuil1

    priodes

    erreurs de prvision

    Feuil2

    Feuil3

  • SIGNAL DALERTEPour la dtection dun changement dans la structure des observations

    Graph1

    90

    105

    95

    110

    95

    90

    105

    120

    120

    115

    125

    115

    115

    125

    115

    120

    120

    105

    90

    95

    110

    95

    105

    90

    25

    priodes

    observations

    LES

    a=0.1

    tXtPtet

    190100.00-10.00

    210599.006.00

    39599.60-4.60

    411099.1410.86

    595100.23-5.23

    69099.70-9.70

    710598.736.27

    812099.3620.64

    9120101.4218.58

    10115103.2811.72

    11125104.4520.55

    12115106.518.49

    13115107.367.64

    14125108.1216.88

    15115109.815.19

    16120110.339.67

    17120111.308.70

    18105112.17-7.17

    1990111.45-21.45

    2095109.30-14.30

    21110107.872.13

    2295108.09-13.09

    23105106.78-1.78

    2490106.60-16.60

    25104.94

    LES

    priodes

    observations

    LESA

    b=0.2

    tXtPtetabs(et)EtMtat

    19095.00-5.005.00-5.005.000.40

    210593.0012.0012.00-1.606.400.25

    39596.00-1.001.00-1.485.320.28

    411095.7214.2814.281.677.110.24

    59599.08-4.084.080.526.500.08

    69098.75-8.758.75-1.336.950.19

    710597.077.937.930.527.150.07

    812097.6522.3522.354.8910.190.48

    9120108.3711.6311.636.2410.480.60

    10115115.29-0.290.294.938.440.58

    11125115.129.889.885.928.730.68

    12115121.82-6.826.823.378.350.40

    13115119.07-4.074.071.887.490.25

    14125118.046.966.962.907.380.39

    15115120.77-5.775.771.167.060.16

    16120119.820.180.180.975.690.17

    17120119.850.150.150.804.580.18

    18105119.88-14.8814.88-2.336.640.35

    1990114.65-24.6524.65-6.8010.240.66

    209598.29-3.293.29-6.098.850.69

    2111096.0213.9813.98-2.089.870.21

    229598.97-3.973.97-2.468.690.28

    2310597.857.157.15-0.548.390.06

    249098.30-8.308.30-2.098.370.25

    2596.23

    LESA

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    demande

    prvisions

    priodes

    demande et prvisions

    LETS

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    priodes

    valeurs de at

    LESAIS

    a=0.5

    g=0.5

    b=0.5

    tXtStbtItPt

    13620.9526

    23851.0132

    34321.1368

    4341380.00009.75000.8974

    5382395.372212.56110.9594371.2882

    6409405.810811.49991.0105413.3009

    7498427.683116.68611.1506474.4164

    8387437.815113.40900.8907398.7629

    9473472.119123.85650.9806432.9066

    10513501.820426.77891.0164501.1874

    11582517.205121.08181.1380608.2211

    12474535.240819.55870.8881479.4261

    13544.0560

    14583.7738

    15675.8498

    16544.8383

    LESAIS

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    demande

    prvisions

    priodes

    demande

    LETO2

    a=0.5L=4

    b=0.5X bar=380

    tXtStItPt

    13620.9526

    23851.0132

    34321.1368

    4341380.00000.8974

    5382390.49720.9654362.0000

    6409397.09281.0216395.6354

    7445394.26401.1328451.4318

    8335383.78890.8851353.8000

    9360378.33870.9585370.5235

    10375372.71001.0139386.5002

    11440380.57031.1445422.1924

    12355390.82240.8967336.8512

    13374.5963

    14396.2385

    15447.2813

    16350.4628

    LETO2

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    demande

    prvisions

    priodes

    demande

    LETO1

    a=0.3

    XtS'tS''tStbtPt

    110911091109110910

    21006106610831048-8

    31105107710821073-21040

    41034106410761052-51071

    51095107410761072-11047

    6108110761076107601071

    7113610941081110751076

    8111611001087111461112

    9110911031092111451120

    101199113211041160121119

    111209115511191191151172

    121232117811371219181206

    131191118211501214141237

    141239119911651233151227

    151235121011781241131248

    161330124611991293201255

    171342127512211328231313

    181332129212431341211351

    191374131712651368221362

    201402134212881396231390

    211504139113191463311420

    221502142413501498321493

    231588147313871559371529

    241607151314251602381596

    251640

    261677

    271715

    LETO1

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    observations

    S't

    S''t

    prvisions

    priodes

    demande

    MMP

    a=0.3

    g=0.4

    tXtStbtPt

    110911091.0010.00

    211011101.0010.001101.00

    311051109.209.281111.00

    410341093.14-0.861118.48

    510951093.09-0.531092.28

    610811089.09-1.921092.56

    711361101.823.941087.18

    811161108.835.171105.76

    911091112.504.571114.00

    1011991141.6514.401117.07

    1112091171.9320.751156.05

    1212321204.4825.471192.69

    1311911218.2720.801229.95

    1412391239.0420.791239.06

    1512351252.3817.811259.83

    1613301288.1424.991270.19

    1713421321.7828.451313.12

    1813321344.7726.261350.24

    1913741371.9226.621371.03

    2014021399.5827.031398.54

    2115041449.8336.321426.61

    2215021490.9138.221486.15

    2315881546.7945.291529.13

    2416071596.5547.081592.08

    251643.63

    261690.71

    271737.79

    MMP

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    Erreurs

    w1=0.5w1=0.1

    w2=0.3w2=0.2

    w3=0.2w3=0.3

    w4=0.4

    tXtPtPt

    190

    2105

    395

    411097.00

    595104.5097.50

    69099.50102.00

    710595.5099.00

    812098.50101.00

    9120109.5098.00

    10115117.00103.50

    11125117.50113.50

    12115121.00119.50

    13115118.00119.00

    14125117.00118.00

    15115120.00120.00

    16120118.00117.00

    17120119.50118.50

    18105119.00120.50

    1990112.50116.50

    2095100.50114.00

    2111095.50107.00

    2295101.5099.00

    2310599.5096.00

    2490103.00100.50

    2595.50102.50

    Erreurs

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    Feuil1

    a=0.1

    tXtPtetabs(et)

    110911050.00

    210061054.1048.1048.1

    311051049.29-55.7155.71

    410341054.8620.8620.86

    510951052.77-42.2342.23

    610811057.00-24.0024.00

    711361059.40-76.6076.60

    811161067.06-48.9448.94

    911091071.95-37.0537.05

    1011991075.66-123.34123.34

    1112091087.99-121.01121.01

    1212321100.09-131.91131.91

    1311911113.28-77.7277.72

    1412391121.05-117.95117.95

    1512351132.85-102.15102.15

    1613301143.06-186.94186.94

    1713421161.76-180.24180.24

    1813321179.78-152.22152.22

    1913741195.00-179.00179.00

    2014021212.90-189.10189.10

    2115041231.81-272.19272.19

    2215021259.03-242.97242.97

    2315881283.33-304.67304.67

    2416071313.80-293.20293.20

    2516901343.12-346.88346.88

    2617621377.80-384.20384.20

    2717571416.22-340.78340.78

    2818391450.30-388.70388.70

    2918481489.17-358.83358.83

    3019041525.05-378.95378.95

    3119751562.95-412.05412.05

    3220611604.15-456.85456.85

    3321531649.84-503.16503.16

    3422131700.15-512.85512.85

    3522381751.44-486.56486.56

    3623661800.10-565.90565.90

    371856.69

    -229.31233.25

    EMEMA

    Feuil1

    MM

    moisdemande

    Aug-971115

    sept.-971125

    oct.-971115

    nov.-971120

    dc.-971120

    jan.-981105

    fv.-981090

    Mar-981095

    Apr-981110

    May-981095

    Jun-981105

    juil.-981090

    MM

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    demande

    mois

    demande

    Demande mensuelle

    MM3MM5MM7

    tXtPtPtPt

    190

    2105

    395

    411096.67

    595103.33

    690100.0099.00

    710598.3399.00

    812096.6799.0098.57

    9120105.00104.00102.86

    10115115.00106.00105.00

    11125118.33110.00107.86

    12115120.00117.00110.00

    13115118.33119.00112.86

    14125118.33118.00116.43

    15115118.33119.00119.29

    16120118.33119.00118.57

    17120120.00118.00118.57

    18105118.33119.00119.29

    1990115.00117.00116.43

    2095105.00110.00112.86

    2111096.67106.00110.00

    229598.33104.00107.86

    23105100.0099.00105.00

    2490103.3399.00102.86

    2596.6799.0098.57

    moy.=107.08

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

  • SIGNAL TSValeur critique: TS* = 4Si |TSt| > TS* ...

    ]|Expr|[#>`b___})%# b'4$(!" *|: ;bP8&c0!"TS}^t_ ,]

  • SIGNAL DE TRIGGSAt = |Et / Mt|

    Et = bet + (1-b)Et-1

    Mt = b|et| + (1-b)Mt-1

    0 < b < 1LES adaptatif ...La valeur de SAt indique des erreurs de prvision non alatoires avec:

    une probabilit de 95% si la valeur de SAt excde 0,51 pour une constante de lissage b=0,1; une probabilit de 95% si la valeur de SAt excde 0,74 pour une constante de lissage b=0,2

  • SIGNAL DALERTE: ex. 1.21Les signauxdtectent unchangementde structure

    t

    Xt

    Pt

    et

    |et|

    EMAt

    Et

    Mt

    et

    TSt

    SAt

    1

    90

    95,00

    -5,00

    5

    5,00

    -5,00

    5,00

    -5

    -1,00

    -1,00

    2

    105

    93,00

    12,00

    12

    5,70

    -1,60

    6,40

    7

    1,23

    -0,25

    3

    95

    96,00

    -1,00

    1

    5,23

    -1,48

    5,32

    6

    1,15

    -0,28

    4

    110

    95,72

    14,28

    14,28

    6,14

    1,67

    7,11

    20,28

    3,31

    0,24

    5

    95

    99,08

    -4,08

    4,08

    5,93

    0,52

    6,51

    16,2

    2,73

    0,08

    6

    90

    98,75

    -8,75

    8,75

    6,21

    -1,33

    6,95

    7,45

    1,20

    -0,19

    7

    105

    97,07

    7,93

    7,93

    6,38

    0,52

    7,15

    15,38

    2,41

    0,07

    8

    120

    97,65

    22,35

    22,35

    7,98

    4,89

    10,19

    37,73

    4,73

    0,48

    9

    120

    108,37

    11,63

    11,63

    8,35

    6,23

    10,48

    49,36

    5,91

    0,60

    10

    115

    115,29

    -0,29

    0,29

    7,54

    4,93

    8,44

    49,07

    6,51

    0,58

    11

    125

    115,12

    9,88

    9,88

    7,77

    5,92

    8,73

    58,95

    7,58

    0,68

    12

    115

    121,82

    -6,82

    6,82

    7,68

    3,37

    8,35

    52,13

    6,79

    0,40

    13

    115

    119,07

    -4,07

    4,07

    7,32

    1,88

    7,49

    48,06

    6,57

    0,25

    14

    125

    118,04

    6,96

    6,96

    7,28

    2,90

    7,38

    55,02

    7,56

    0,39

    15

    115

    120,77

    -5,77

    5,77

    7,13

    1,17

    7,06

    49,25

    6,91

    0,16

    16

    120

    119,82

    0,18

    0,18

    6,44

    0,97

    5,69

    49,43

    7,68

    0,17

    17

    120

    119,85

    0,15

    0,15

    5,81

    0,80

    4,58

    49,58

    8,54

    0,18

    18

    105

    119,88

    -14,88

    14,88

    6,71

    -2,33

    6,64

    34,7

    5,17

    -0,35

    19

    90

    114,65

    -24,65

    24,65

    8,51

    -6,80

    10,24

    10,05

    1,18

    -0,66

    20

    95

    98,29

    -3,29

    3,29

    7,99

    -6,09

    8,85

    6,76

    0,85

    -0,69

    21

    110

    96,02

    13,98

    13,98

    8,59

    -2,08

    9,88

    20,74

    2,42

    -0,21

    22

    95

    98,97

    -3,97

    3,97

    8,12

    -2,46

    8,70

    16,77

    2,06

    -0,28

    23

    105

    97,85

    7,15

    7,15

    8,03

    -0,54

    8,39

    23,92

    2,98

    -0,06

    24

    90

    98,30

    -8,30

    8,3

    8,05

    -2,09

    8,37

    15,62

    1,94

    -0,25

  • CHANGEMENT DE STRUCTURE: GRAPHIQUEAugmentation du niveau moyen de 20% partir de la priode 8

    Graph1

    90

    105

    95

    110

    95

    90

    105

    120

    120

    115

    125

    115

    115

    125

    115

    120

    120

    105

    90

    95

    110

    95

    105

    90

    25

    priodes

    observations

    LES

    a=0.1

    tXtPtet

    190100.00-10.00

    210599.006.00

    39599.60-4.60

    411099.1410.86

    595100.23-5.23

    69099.70-9.70

    710598.736.27

    812099.3620.64

    9120101.4218.58

    10115103.2811.72

    11125104.4520.55

    12115106.518.49

    13115107.367.64

    14125108.1216.88

    15115109.815.19

    16120110.339.67

    17120111.308.70

    18105112.17-7.17

    1990111.45-21.45

    2095109.30-14.30

    21110107.872.13

    2295108.09-13.09

    23105106.78-1.78

    2490106.60-16.60

    25104.94

    LES

    priodes

    observations

    LESA

    b=0.2

    tXtPtetabs(et)EtMtat

    19095.00-5.005.00-5.005.000.40

    210593.0012.0012.00-1.606.400.25

    39596.00-1.001.00-1.485.320.28

    411095.7214.2814.281.677.110.24

    59599.08-4.084.080.526.500.08

    69098.75-8.758.75-1.336.950.19

    710597.077.937.930.527.150.07

    812097.6522.3522.354.8910.190.48

    9120108.3711.6311.636.2410.480.60

    10115115.29-0.290.294.938.440.58

    11125115.129.889.885.928.730.68

    12115121.82-6.826.823.378.350.40

    13115119.07-4.074.071.887.490.25

    14125118.046.966.962.907.380.39

    15115120.77-5.775.771.167.060.16

    16120119.820.180.180.975.690.17

    17120119.850.150.150.804.580.18

    18105119.88-14.8814.88-2.336.640.35

    1990114.65-24.6524.65-6.8010.240.66

    209598.29-3.293.29-6.098.850.69

    2111096.0213.9813.98-2.089.870.21

    229598.97-3.973.97-2.468.690.28

    2310597.857.157.15-0.548.390.06

    249098.30-8.308.30-2.098.370.25

    2596.23

    LESA

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    demande

    prvisions

    priodes

    demande et prvisions

    LETS

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    priodes

    valeurs de at

    LESAIS

    a=0.5

    g=0.5

    b=0.5

    tXtStbtItPt

    13620.9526

    23851.0132

    34321.1368

    4341380.00009.75000.8974

    5382395.372212.56110.9594371.2882

    6409405.810811.49991.0105413.3009

    7498427.683116.68611.1506474.4164

    8387437.815113.40900.8907398.7629

    9473472.119123.85650.9806432.9066

    10513501.820426.77891.0164501.1874

    11582517.205121.08181.1380608.2211

    12474535.240819.55870.8881479.4261

    13544.0560

    14583.7738

    15675.8498

    16544.8383

    LESAIS

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    demande

    prvisions

    priodes

    demande

    LETO2

    a=0.5L=4

    b=0.5X bar=380

    tXtStItPt

    13620.9526

    23851.0132

    34321.1368

    4341380.00000.8974

    5382390.49720.9654362.0000

    6409397.09281.0216395.6354

    7445394.26401.1328451.4318

    8335383.78890.8851353.8000

    9360378.33870.9585370.5235

    10375372.71001.0139386.5002

    11440380.57031.1445422.1924

    12355390.82240.8967336.8512

    13374.5963

    14396.2385

    15447.2813

    16350.4628

    LETO2

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    demande

    prvisions

    priodes

    demande

    LETO1

    a=0.3

    XtS'tS''tStbtPt

    110911091109110910

    21006106610831048-8

    31105107710821073-21040

    41034106410761052-51071

    51095107410761072-11047

    6108110761076107601071

    7113610941081110751076

    8111611001087111461112

    9110911031092111451120

    101199113211041160121119

    111209115511191191151172

    121232117811371219181206

    131191118211501214141237

    141239119911651233151227

    151235121011781241131248

    161330124611991293201255

    171342127512211328231313

    181332129212431341211351

    191374131712651368221362

    201402134212881396231390

    211504139113191463311420

    221502142413501498321493

    231588147313871559371529

    241607151314251602381596

    251640

    261677

    271715

    LETO1

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    observations

    S't

    S''t

    prvisions

    priodes

    demande

    MMP

    a=0.3

    g=0.4

    tXtStbtPt

    110911091.0010.00

    211011101.0010.001101.00

    311051109.209.281111.00

    410341093.14-0.861118.48

    510951093.09-0.531092.28

    610811089.09-1.921092.56

    711361101.823.941087.18

    811161108.835.171105.76

    911091112.504.571114.00

    1011991141.6514.401117.07

    1112091171.9320.751156.05

    1212321204.4825.471192.69

    1311911218.2720.801229.95

    1412391239.0420.791239.06

    1512351252.3817.811259.83

    1613301288.1424.991270.19

    1713421321.7828.451313.12

    1813321344.7726.261350.24

    1913741371.9226.621371.03

    2014021399.5827.031398.54

    2115041449.8336.321426.61

    2215021490.9138.221486.15

    2315881546.7945.291529.13

    2416071596.5547.081592.08

    251643.63

    261690.71

    271737.79

    MMP

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    Erreurs

    w1=0.5w1=0.1

    w2=0.3w2=0.2

    w3=0.2w3=0.3

    w4=0.4

    tXtPtPt

    190

    2105

    395

    411097.00

    595104.5097.50

    69099.50102.00

    710595.5099.00

    812098.50101.00

    9120109.5098.00

    10115117.00103.50

    11125117.50113.50

    12115121.00119.50

    13115118.00119.00

    14125117.00118.00

    15115120.00120.00

    16120118.00117.00

    17120119.50118.50

    18105119.00120.50

    1990112.50116.50

    2095100.50114.00

    2111095.50107.00

    2295101.5099.00

    2310599.5096.00

    2490103.00100.50

    2595.50102.50

    Erreurs

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    Feuil1

    a=0.1

    tXtPtetabs(et)

    110911050.00

    210061054.1048.1048.1

    311051049.29-55.7155.71

    410341054.8620.8620.86

    510951052.77-42.2342.23

    610811057.00-24.0024.00

    711361059.40-76.6076.60

    811161067.06-48.9448.94

    911091071.95-37.0537.05

    1011991075.66-123.34123.34

    1112091087.99-121.01121.01

    1212321100.09-131.91131.91

    1311911113.28-77.7277.72

    1412391121.05-117.95117.95

    1512351132.85-102.15102.15

    1613301143.06-186.94186.94

    1713421161.76-180.24180.24

    1813321179.78-152.22152.22

    1913741195.00-179.00179.00

    2014021212.90-189.10189.10

    2115041231.81-272.19272.19

    2215021259.03-242.97242.97

    2315881283.33-304.67304.67

    2416071313.80-293.20293.20

    2516901343.12-346.88346.88

    2617621377.80-384.20384.20

    2717571416.22-340.78340.78

    2818391450.30-388.70388.70

    2918481489.17-358.83358.83

    3019041525.05-378.95378.95

    3119751562.95-412.05412.05

    3220611604.15-456.85456.85

    3321531649.84-503.16503.16

    3422131700.15-512.85512.85

    3522381751.44-486.56486.56

    3623661800.10-565.90565.90

    371856.69

    -229.31233.25

    EMEMA

    Feuil1

    MM

    moisdemande

    Aug-971115

    sept.-971125

    oct.-971115

    nov.-971120

    dc.-971120

    jan.-981105

    fv.-981090

    Mar-981095

    Apr-981110

    May-981095

    Jun-981105

    juil.-981090

    MM

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    demande

    mois

    demande

    Demande mensuelle

    MM3MM5MM7

    tXtPtPtPt

    190

    2105

    395

    411096.67

    595103.33

    690100.0099.00

    710598.3399.00

    812096.6799.0098.57

    9120105.00104.00102.86

    10115115.00106.00105.00

    11125118.33110.00107.86

    12115120.00117.00110.00

    13115118.33119.00112.86

    14125118.33118.00116.43

    15115118.33119.00119.29

    16120118.33119.00118.57

    17120120.00118.00118.57

    18105118.33119.00119.29

    1990115.00117.00116.43

    2095105.00110.00112.86

    2111096.67106.00110.00

    229598.33104.00107.86

    23105100.0099.00105.00

    2490103.3399.00102.86

    2596.6799.0098.57

    moy.=107.08

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

  • SLECTION DUNE MTHODE DE PRVISION POUR UN PRODUIT SANS HISTORIQUEPrvoir la demande des produits sans historique en se basant uniquement sur des tudes de march;

    Utiliser, comme donnes historiques, une srie de consommation dont le niveau moyen de la demande et son comportement sont semblables;

    Demander aux vendeurs des produits concerns de fournir leurs propres prvisions.

  • LIEN ENTRE LES ERREURS DE PRVISION ET LA DISTRIBUTION DE LA DEMANDELa distribution des erreurs de prvision sert, sous certaines conditions, estimer lcart-type de la demande des produits correspondants:- prvisions non biaises;- erreurs de prvisions distribues alatoirement autour de 0;- la meilleure mthode de prvision possible a t utilise.Conditions:

    _974619502.xls

    Graph2

    13.3333333333

    -8.3333333333

    -10

    6.6666666667

    23.3333333333

    15

    0

    6.6666666667

    -5

    -3.3333333333

    6.6666666667

    -3.3333333333

    1.6666666667

    0

    -13.3333333333

    -25

    -10

    13.3333333333

    -3.3333333333

    5

    -13.3333333333

    priode

    erreurs de prvision

    Feuil9

    exemple 5.22

    0.20.30.1

    tXtmm(3)mm(4)LES(0,2)LES(0,3)LEA(0,1)e mm(3)e mm(4)e (0,2)e (0,3)e (0,1)EtMtatabs(e mm(3))abs(e mm(4))abs(e (0,2))abs(e (0,3))abs(e (0,1))% e mm(3)% e mm(4)% e (0,2)% e (0,3)% e (0,1)

    19090.0090.0090.000.000.000.000.000.000.20

    210590.0090.0090.0015.0015.0015.001.501.501.00

    39593.0094.50105.002.000.50-10.000.352.350.15

    411096.6793.4094.65103.5113.3316.6015.356.490.962.760.35

    595103.33100.0096.7299.26105.77-8.33-5.00-1.72-4.26-10.77-0.213.560.06

    690100.00101.2596.3897.98105.14-10.00-11.25-6.38-7.98-15.14-1.704.720.36

    710598.3397.5095.1095.5899.686.677.509.909.425.32-1.004.780.21

    812096.67100.0097.0898.41100.7923.3320.0022.9221.5919.211.026.220.16

    9120105.00102.50101.66104.89103.9415.0017.5018.3415.1116.062.527.210.35

    10115115.00108.75105.33109.42109.560.006.259.675.585.442.827.030.40

    11125118.33115.00107.27111.09111.746.6710.0017.7313.9113.263.867.650.50

    12115120.00120.00110.81115.27118.43-5.00-5.004.19-0.27-3.433.137.230.43

    13115118.33118.75111.65115.19116.94-3.33-3.753.35-0.19-1.942.626.700.393.333.753.350.191.940.02900.03260.02910.00160.0169

    14125118.33117.50112.32115.13116.186.677.5012.689.878.823.246.910.476.677.5012.689.878.820.05330.06000.10140.07900.0705

    15115118.33120.00114.86118.09120.32-3.33-5.000.14-3.09-5.322.396.750.353.335.000.143.095.320.02900.04350.00130.02690.0462

    16120118.33117.50114.88117.16118.441.672.505.122.841.562.306.230.371.672.505.122.841.560.01390.02080.04260.02360.0130

    17120120.00118.75115.91118.01119.020.001.254.091.990.982.175.710.380.001.254.091.990.980.00000.01040.03410.01650.0082

    18105118.33120.00116.73118.61119.39-13.33-15.00-11.73-13.61-14.390.526.580.0813.3315.0011.7313.6114.390.12700.14290.11170.12960.1371

    1990115.00115.00114.38114.53118.26-25.00-25.00-24.38-24.53-28.26-2.368.750.2725.0025.0024.3824.5328.260.27780.27780.27090.27250.3140

    2095105.00108.75109.50107.17110.63-10.00-13.75-14.50-12.17-15.63-3.699.430.3910.0013.7514.5012.1715.630.10530.14470.15270.12810.1645

    2111096.67102.50106.60103.52104.5213.337.503.406.485.48-2.779.040.3113.337.503.406.485.480.12120.06820.03090.05890.0498

    229598.33100.00107.28105.46106.20-3.33-5.00-12.28-10.46-11.20-3.619.260.393.335.0012.2810.4611.200.03510.05260.12930.11010.1179

    23105100.0097.50104.83102.32101.835.007.500.172.683.17-2.948.650.345.007.500.172.683.170.04760.07140.00170.02550.0302

    2490103.33101.25104.86103.13102.90-13.33-11.25-14.86-13.13-12.90-3.939.070.4313.3311.2514.8613.1312.900.14810.12500.16510.14590.1434

    Pour les priodes 13 24EM-3.75-4.38-4.07-4.44-5.80

    EMA8.198.758.898.429.14

    PMEA8.238.758.928.499.27

    Feuil9

    priode

    erreurs de prvision

    Feuil8

    exemple 5.21b=0.2pour Et et Mt

    a=0.1pour EMAt

    tXtPtet|et|EMAtEtMtsomme(et)TStSAt

    19095-555.00-5.005.00-5-1.00-1.00

    21059312125.70-1.606.4071.23-0.25

    39596-115.23-1.485.3261.15-0.28

    411095.7214.2814.286.141.677.1120.283.310.24

    59599.08-4.084.085.930.526.5116.22.730.08

    69098.75-8.758.756.21-1.336.957.451.20-0.19

    710597.077.937.936.380.527.1515.382.410.07

    812097.6522.3522.357.984.8910.1937.734.730.48

    9120108.3711.6311.638.356.2310.4849.365.910.60

    10115115.29-0.290.297.544.938.4449.076.510.58

    11125115.129.889.887.775.928.7358.957.580.68

    12115121.82-6.826.827.683.378.3552.136.790.40

    13115119.07-4.074.077.321.887.4948.066.570.25

    14125118.046.966.967.282.907.3855.027.560.39

    15115120.77-5.775.777.131.177.0649.256.910.16

    16120119.820.180.186.440.975.6949.437.680.17

    17120119.850.150.155.810.804.5849.588.540.18

    18105119.88-14.8814.886.71-2.336.6434.75.17-0.35

    1990114.65-24.6524.658.51-6.8010.2410.051.18-0.66

    209598.29-3.293.297.99-6.098.856.760.85-0.69

    2111096.0213.9813.988.59-2.089.8820.742.42-0.21

    229598.97-3.973.978.12-2.468.7016.772.06-0.28

    2310597.857.157.158.03-0.548.3923.922.98-0.06

    249098.3-8.38.38.05-2.098.3715.621.94-0.25

    Feuil7

    Exemple 5.19

    priodedemandek=1k=2k=3k=4r1r2r3r4err. Car.

    1362532.84

    23853621.920.01

    3432385362-3.91-1082.992201.17

    4341432385362-2068.243.671017.591943.34

    5382341432385362135.92-144.660.2671.179.51

    6409382341432385-73.74-1054.331122.09-1.99572.01

    74454093823414321433.01-184.74-2641.332811.093590.01

    8335445409382341-3000.83-1197.83154.422207.842508.34

    93603354454093821256.26-1502.91-599.9177.34629.17

    10375360335445409252.92505.01-604.16-241.16101.67

    11440375360335445-553.74-1377.49-2750.413290.423015.84

    12355440375360335-1652.08303.34754.591506.67905.01

    sommes-4272.51-5732.93-3546.859721.3916008.92

    moyenne385.08

    somme car.16008.92rk-0.2669-0.3581-0.22160.6072

    Feuil7

    ordre k des autocorrlations

    rk

    Feuil6

    exemple 5.18

    tXtPtetXt 8%Xt + 8%rt

    19095-582.80102.601

    2105931296.60100.440

    39596-187.40103.681

    411095.7214.28101.20103.380

    59599.08-4.0887.40107.011

    69098.75-8.7582.80106.651

    710597.077.9396.60104.841

    812097.6522.35110.40105.460

    9120108.3711.63110.40117.040

    10115115.29-0.29105.80124.511

    11125115.129.88115.00124.331

    12115121.82-6.82105.80131.571

    13115119.07-4.07105.80128.601

    14125118.046.96115.00127.481

    15115120.77-5.77105.80130.431

    16120119.820.18110.40129.411

    17120119.850.15110.40129.441

    18105119.88-14.8896.60129.471

    1990114.65-24.6582.80123.821

    209598.29-3.2987.40106.151

    2111096.0213.98101.20103.700

    229598.97-3.9787.40106.891

    2310597.857.1596.60105.681

    249098.3-8.382.80106.161

    Feuil5

    exemple 5.16 et 5.17a=0.1

    tXtPtet(et+1/Xt)^2((Xt+1-Xt)/Xt)^2et^2EQMt

    19095-50.01780.027825.0025.00

    210593120.00010.0091144.0036.90

    39596-10.02260.02491.0033.31

    411095.7214.280.00140.0186203.9250.37

    59599.08-4.080.00850.002816.6547.00

    69098.75-8.750.00780.027876.5649.95

    710597.077.930.04530.020462.8851.25

    812097.6522.350.00940.0000499.5296.08

    9120108.3711.630.00000.0017135.2699.99

    10115115.29-0.290.00740.00760.0890.00

    11125115.129.880.00300.006497.6190.76

    12115121.82-6.820.00130.000046.5186.34

    13115119.07-4.070.00370.007616.5679.36

    14125118.046.960.00210.006448.4476.27

    15115120.77-5.770.00000.001933.2971.97

    16120119.820.180.00000.00000.0364.78

    17120119.850.150.01540.01560.0258.30

    18105119.88-14.880.05510.0204221.4174.61

    1990114.65-24.650.00130.0031607.62127.91

    209598.29-3.290.02170.024910.82116.21

    2111096.0213.980.00130.0186195.44124.13

    229598.97-3.970.00570.011115.76113.29

    2310597.857.150.00620.020451.12107.08

    249098.3-8.368.89103.26

    Total0.23690.27702578.43

    U=0.9247620447EQM=107.43

    Feuil5

    priode

    erreurs de prvision

    Feuil4

    Exemple 5.14

    a=0.2

    moisDemande (Xt)Prvisions (Pt)et|et|EMAt|et|/Xt

    17580-555.000.0667

    28679775.400.0814

    38480.43.63.65.040.0429

    47881.1-3.13.14.650.0397

    58380.52.52.54.220.0301

    67281-995.180.1250

    78179.21.81.84.500.0222

    87979.6-0.60.63.720.0076

    97579.4-4.44.43.860.0587

    107778.6-1.61.63.410.0208

    117778.2-1.21.22.960.0156

    128478994.170.1071

    Somme-148.8

    Feuil1

    a=0.2Diffrenciation d'ordre 1exemple 5.11

    priodedemandeX'tP'tX''tk=1r1SC

    1109126068.7934027778

    21006-85-85.00109139792.751736111160741.7100694444

    3110599-85.00184100636342.335069444421743.9600694444

    41034-71-48.20-170110532213.501736111147724.0434027777

    5109561-52.76132103434398.085069444424793.1267361111

    61081-14-30.01-75109526997.543402777829397.9600694444

    7113655-26.8169108119967.751736111113562.5434027778

    81116-20-10.45-75113615891.710069444418620.8767361111

    91109-7-12.3613111619576.085069444420580.2934027778

    10119990-11.289711097669.04340277782857.7934027778

    111209108.97-8011992323.21006944441888.6267361111

    121232239.18131209889.0850694444418.5434027778

    131191-4111.94-6412321257.33506944443777.1267361111

    141239481.35891191827.1267361111181.1267361111

    151235-410.68-521239234.9600694444304.7934027778

    161330957.75991235-1353.74826388896012.7100694445

    1713421225.20-8313306943.21006944458017.7100694445

    181332-1022.56-2213427122.29340277786326.8767361111

    1913744216.055213329667.626736111114772.3767361111

    2014022821.24-14137418175.543402777822362.7100694445

    21150410222.5974140237615.960069444563273.2100694445

    221502-238.47-104150462770.126736111162271.0434027778

    2315888630.3888150283731.6267361112112588.210069444

    2416071941.50-671588118963.501736111125699.793402778

    2537.00

    somme582016.664930556667917.164930556

    moyenne1252.4583333333

    r1=0.871390489

    Feuil1

    demande

    priode

    demande

    Feuil2

    a=0.1Diffrenciation d'ordre 1 et 2

    priodedemandeX'tX''tP''tP'tPt

    11091

    21006-85

    31105991840.00

    41034-71-17018.40

    5109561132-0.44

    61081-14-7512.80

    7113655694.02

    81116-20-7510.52

    91109-7131.97

    10119990973.07

    11120910-8012.46

    12123223133.22

    131191-41-644.20

    1412394889-2.62

    151235-4-526.54

    16133095990.69

    17134212-8310.52

    181332-10-221.17

    1913744252-1.15

    20140228-144.16

    211504102742.35

    221502-2-1049.51

    2315888688-1.84

    24160719-677.15

    25-0.2718.731625.73

    26-0.2718.461643.92

    27-0.2718.191661.58

    28-0.2717.921678.69

    Feuil2

    1091

    1006

    1105

    1034

    1095

    1081

    1136

    1116

    1109

    1199

    1209

    1232

    1191

    1239

    1235

    1330

    1342

    1332

    1374

    1402

    1504

    1502

    1588

    1607

    demande

    priode

    demande

    Feuil3

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    priodes

    X't

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    priodes

    X''t

    Dcomposition par dsaisonnalisation

    priodedemandeMM(4)RtIt

    1362

    2385

    3432

    4341380.000.8974

    5382385.000.9922

    6409391.001.0460

    7445394.251.1287

    8335392.750.8530

    9360387.250.92960.9609

    10375378.750.99011.0181

    11440377.501.16561.1471

    12355382.500.92810.8928

    srie originale

    srie dsaisonnalise

    priodes

    demande

  • DISTRIBUTION DE LA DEMANDEET = 1,25 EMA ou ETt = 1,25 EMAtForme de la distributionFast moversSlow moversNormalePoisson

    Demande moyenne pour une priode t: Pt

    cart-type de la demande pour une priode t:

    ou

  • INTERVALLES DE CONFIANCE POUR LES PRVISIONSCas o la distribution des erreurs de prvision est connue:

    - distribution Normale- distribution de Poisson

    Cas o la distribution des erreurs de prvision est inconnue:

    - ingalit de Chebychev- ingalit de Camp-Meidel

    Cas pour la rgression linaire

    - la valeur de la variable indpendante a dj t observe- la valeur de la variable indpendante na jamais t observe

  • INTERVALLES DE CONFIANCE PARTIR DE LA DISTRIBUTION NORMALEPt Za/2 s Xt Pt + Za/2 ss = ET

    Z/2

    0,001

    3,100

    0,005

    2,575

    0,010

    2,327

    0,025

    1,960

    0,050

    1,645

    0,075

    1,439

    0,100

    1,281

  • INTERVALLES DE CONFIANCE PARTIR DE LA DISTRIBUTION DE POISONP(Xt = x | l) = (e-l lx) / x!P(Xt xinf | l) 1 - a/2P(Xt xsup | l) a/2xinf Xt xsup

  • INGALIT DE CHEBYCHEV

  • INGALIT DE CAMP-MEIDEL

  • INTERVALLES DE CONFIANCE: exemples ...Intervalle 90%, EQM = 1 750 et Pt = 400Ingalit de ChebychevIngalit de Camp-Meideln = 12

  • INTERVALLES DE CONFIANCE: exemples ...Intervalle 90%, EQM = 1 750 et Pt = 400Distribution Normalen = 12

    Z/2

    0,001

    3,100

    0,005

    2,575

    0,010

    2,327

    0,025

    1,960

    0,050

    1,645

    0,075

    1,439

    0,100

    1,281

  • INTERVALLES DE CONFIANCE: exemples ...Slow mover avec l = 10, intervalle 90%?Tableau, p. 227

  • INTERVALLES POUR RGRESSION: VALEUR DE X DJ OBSERVE

    = 6 490

  • INTERVALLES POUR RGRESSION: VALEUR DE X JAMAIS OBSERVE

  • INTERVALLES POUR RGRESSION: ex. 1.24a1 425 Y13 1 573

    = 788,27 + 0,0158(45 000) = 1 499 units

    = 6 490

  • INTERVALLES POUR RGRESSION: ex. 1.24b1 305 Y13 1 693

    ]|Expr|[#>`b___})0# b'4" *|: ;bP8&c0!"s"!Symbol^:!&c0 .B: &c0!" ,]:! s