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Analyzing Canadian Lynx Population Data: Statistical Models and Comparative Study

This report, presented by 張淑慧 and 陳雅蕙, explores time plot analysis including ACF and PACF, AR(11) Model by Tong (1977), Deterministic Trend Model by Campbell & Walker (1977), and SETAR(2;7,2) by Tong (1983). It compares ACF and PACF patterns, models' performance, and residual characteristics to white noise. The study also evaluates the variance of fitted residuals, sample moments, ACF patterns, and model ratings for the Lynx data.

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Analyzing Canadian Lynx Population Data: Statistical Models and Comparative Study

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  1. Canadian Lynx (1821-1934) 報告者: 張淑慧、陳雅蕙

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

  3. Introduction ACF PACF

  4. Introduction

  5. Introduction

  6. Introduction ACF PACF

  7. AR model AR(11)

  8. AR model • The fitted model is given by

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

  10. Deterministic Trend Model ACF PACF

  11. Deterministic Trend Model • SIN-COS(9.5) model:

  12. Deterministic Trend Model ACF PACF

  13. Deterministic Trend Model AR(2)

  14. Deterministic Trend Model • The fitted model is given by

  15. AR model • 殘差的ACF 和PACF 大致符合 white noices 的特性 PACF ACF

  16. SETAR • SETAR(2;7,2) model:

  17. AR model • 殘差的 ACF 和 PACF 符合 white noices 的特性 PACF ACF

  18. Comparative • Variance of fitted residuals (at) for the models fitted to the lynx data • Sample moments of the lynx data and simulated data of models

  19. Comparative SETAR(2;7,2) • Sample ACF for the lynx data and the various models. SIN-COS(9.5) AR11 lynx model

  20. Comparative • The rating of the models fitted to the lynx data

  21. 謝 謝 大 家

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