臺灣博碩士論文加值系統

Tu （2000） proposed two modified weighted information criteria, WICu and WICs respectively, to autoregressive models. WICu is essentially equivalent to AICu for small sample sizes and to BIC for large sample sizes. Similarly, WICs is also equivalent to AICu for small sample sizes and to SICc for large sample sizes. We extend these two criteria for order selection in moving average model, autoregressive moving average model, and regressive model. Comparing WICu and WICs with several popular criteria by simulation study. It shows WICu and WICs outperform or at least comparable to WIC. For small sample sizes, WICu and WICs perform as well as AICu and are better than other criteria. And for large sample sizes, WICu and WICs perform as well as BIC and SIC, respectively, and outperform other criteria.

Tu （2000） proposed two modified weighted information criteria, WICu and WICs respectively, to autoregressive models. WICu is essentially equivalent to AICu for small sample sizes and to BIC for large sample sizes. Similarly, WICs is also equivalent to AICu for small sample sizes and to SICc for large sample sizes. We extend these two criteria for order selection in moving average model, autoregressive moving average model, and regressive model. Comparing WICu and WICs with several popular criteria by simulation study. It shows WICu and WICs outperform or at least comparable to WIC. For small sample sizes, WICu and WICs perform as well as AICu and are better than other criteria. And for large sample sizes, WICu and WICs perform as well as BIC and SIC, respectively, and outperform other criteria.

CHAPTER 1 INTRODUCTION 3
1.1 BACKGROUNDS 3
1.2 HISTORY OF MODEL SELECTION CRITERIA 4
1.2.1 The AIC Criterion 6
1.2.2 The AICc Criterion 6
1.2.3 The AICu Criterion 7
1.2.4 The BIC Criterion 7
1.2.5 The SIC Criterion 8
1.2.6 The SICc Criterion 8
1.2.7 The WIC Criterion 8
1.3 SIGNAL-TO-NOISE RATIOS 9
AICc 10
AICu 10
SIC 11
SICc 11
CHAPTER 2 PROPERTIES OF WIC 12
2.1 WIC 12
Property 2.1.1 12
Property 2.1.2 13
Property 2.1.3 13
Property 2.1.4 13
2.2 WICU 14
Property 2.2.1 15
Property 2.2.2 15
2.3 WICS 15
Property 2.3.1 16
Property 2.3.2 16
Property 2.3.3 17
2.4 SIGNAL-TO-NOISE RATIOS OF WICU AND WICS 18
2.4.1 WICu 18
2.4.2 WICs 19
2.4.3 BIC 19
CHAPTER 3 MONTE CARLO SIMULATON 21
3.1 TIME SERIES MODEL 21
3.2 REGRESSION MODEL 42
3.3 NUMERICAL RESULTS OF SIGNAL-TO-NOISE RATIO 48
CHAPTER 4 CONCLUSION 50
4.1 AUTOREGRESSIVE MODELS 50
4.2 MA AND ARMA MODELS 51
4.3 REGRESSION MODELS 52
4.4 SIGNAL-TO-NOISE RATIO 52
4.5 FURTHER STUDY 53
REFERENCES 54

Akaike, H., （1974）. A New Look at The Statistical Model Identification, IEEE Transactions on Automatic Control, 19, 716-723.
Akaike, H., （1978）. A Bayesian Analysis of The Minimum AIC Procedure. Annals of the Institute of Statistical Mathematics, 30, 9-14.
Hannan, E. J., （1980）. The Estimation of The Order of an ARMA Process. The Annals of Statistics, 8, 1071-1081.
Hurvish, C. M, and Tsai, C. L., （1989）. Regression and Time Series Model Selection in Small Samples. Biometrika, 76, 297-307.
McQuarrie, A., Shumway, R. and Tsai, C., L., （1997）. The Model Selection Criterion AICu.. Statistics & Probability Letters, 34, 285-292.
McQuarrie, A., Shumway, R. and Tsai, C., L., （1998）. Regression and Time Series Model Selection. World Scientific Publishing, Singapore.
McQuarrie, A., （1999）. A Small-sample correction for the Schwarz SIC Model Selection Criterion. Statistics & Probability Letters, 44, 89-86.
Priesly, M. B., （1982）. Spectral Analysis and Time Series, vol. 1. Wiley, New York.
Schwarz, G., （1978）. Estimating The Dimension of a Model. Annals of Statistics, 6, 461-464.
Shibata, R., （1980）. Asymptotic Efficient Selection of The Order of the Model for Estimating Parameters of A linear Process. Annals of Statistics, 8, 147-164.
Wu, T. J., and Sepulveda, A. （1998）. The Weighted Average Information Criterion for Order Selection in Time Series and Regression Models. Statistics and Probability Letters, 39, 1-10.
Tu, Y. H., （2000）. Modified WIC for Order Selection in Autoregressive Model. Master Thesis, Department of Statistics, National Cheng Kung University, Tainan, Taiwan.