Canadian Lynx 18211934 Outline q Time plotACFPACF q

Canadian Lynx (18211934) 報告者: 張淑慧、陳雅蕙

Outline q Time plot、ACF、PACF q AR(11) Model (c. f. Tong, 1977) q Deterministic Trend Model (c. f. Campbell & Walker, 1977) q SETAR(2; 7, 2) (c. f. Tong, 1983) q Comparative

Introduction ACF PACF

Introduction

Introduction q

Introduction q ACF PACF

AR model k AIC(k) k 1 -239. 89 6 -321. 17 11 -334. 90 16 -329. 23 2 -319. 00 7 -324. 68 12 -334. 13 17 -327. 24 3 -319. 59 8 -324. 16 13 -333. 35 18 -327. 44 4 -322. 93 9 -323. 49 14 -331. 50 19 -325. 85 5 -322. 58 10 -325. 13 15 -329. 55 20 -324. 43 AR(11) AIC(k) k AIC(k)

AR model q The fitted model is given by

AR model q Fit 模型後殘差的ACF 及PACF 的確符合white noice 的性質 ACF PACF

Deterministic Trend Model ACF PACF

Deterministic Trend Model q SIN-COS(9. 5) model:

Deterministic Trend Model q ACF PACF

Deterministic Trend Model q k AIC(k) k 1 -16. 86 6 -30. 34 11 -30. 36 16 -29. 11 2 -35. 93 7 -27. 60 12 -33. 84 17 -28. 14 3 -35. 26 8 -25. 48 13 -31. 33 18 -25. 97 4 -35. 55 9 -25. 91 14 -28. 49 19 -26. 76 5 -32. 31 10 -24. 96 15 -26. 07 20 -24. 28 AR(2) AIC(k) k AIC(k)

Deterministic Trend Model q The fitted model is given by

AR model q 殘差的ACF 和PACF 大致符合 white noices 的特性 ACF PACF

SETAR q SETAR(2; 7, 2) model:

AR model q 殘差的 ACF 和 PACF 符合 white noices 的特性 ACF PACF

Comparative q Variance of fitted residuals (at) for the models fitted to the lynx data Var(at) AR(11) SIN-COS(9. 5) SETAR(2; 7, 2) 0. 0437 0. 04136 0. 036 q Sample moments of the lynx data and simulated data of models 2 nd 3 rd 4 th Mean Variance moment 2. 90 0. 31 8. 74 27. 11 86. 21 2. 91 SIN-COS(9. 5) 2. 90 SETAR(2; 7, 2) 2. 88 0. 31 0. 38 8. 77 8. 72 27. 28 27. 09 27. 23 87. 38 86. 72 87. 46 Lynx Data AR(11)

Comparative q Sample ACF for the lynx data and the various models. AR 11 SIN-COS(9. 5) SETAR(2; 7, 2) lynx model

Comparative q The rating of the models fitted to the lynx data Var(et) Moments ACF Total AR(11) 3 2 1 6 SIN-COS(9. 5) 2 1 2 5 SETAR(2; 7, 2) 1 2 3 6