臺灣博碩士論文加值系統

非線性時間序列模型之建立與選取於近幾年來已成為一熱門課題.然而由於種種經濟或社會現象呈現出來的特徵是有週期性,又如當政府政策性的改變或是類似物價變動等經濟因素帶來的干擾,常會造成其結構逐漸向上或是向下移動,此一現象在本論文中將被定義為一轉型期或是轉折區間.
雖然於無母數統計中對轉折點問題有深入探討,但它所探討的對象為一組互相獨立的觀察值.本論文將針對一時間序列資料是否存在轉型區間作深入的探討.文中提出三種轉折區間認定的程序步驟,並藉由模擬出來的五種時間序列資料來比較這幾種方法的表現.最後並以來華觀光旅客及匯率兩組資料進行實證分析.

Many papers have been presented on the study of change points detection. Nonetheless, we would like to point out that in dealing with the time series with switching regimes, we should also take the characteristics of change periods into account. Because many patterns of change structure in time series exhibit a certain kind of duration, those phenomena should not be treated as a mere sudden turning at a certain time.
In this paper, we propose procedures about change periods detection for nonlinear time series. One of the detecting statistical methods is an application of fuzzy classification and generalization of Inclan and Tiao’s result. Moreover, we develop the genetic-based searching procedure, which is based on the concepts of leading genetic model. Simulation results show that the performance of these procedures is efficient and successful. Finally, two empirical applications about change periods detection for Taiwan monthly visitors arrival and exchange rate are demonstrated.

Cover
Contens
Chapter 1 Introduction
1.1 Motivations
1.2 Literatures Review of Change Points Detection
Chapter 2 Identification of Change Periods
2.1 Reviews of Change-point Detection
2.2 Statistics for Centered Cumulative Sums of Squares
2.3 Rules for Classification
Chapter 3 Clustering with Fuzzy Statistics
3.1 Fuzzy Statistics
3.2 Using Fuzzy Entropy
Chapter 4 Genetic-based Searching
4.1 Genetic Algorithms
4.2 Revised Forward Selection of Leading Genetic Models
4.3 Genetic-based Searching for Change Periods
Chapter 5 Simulation Studies
5.1 Models Simulation
5.2 The Application of Revised CUSUM Algorithm
5.3 The Application of Genetic-based Searching
Chapter 6 Empirical Examples
6.1 Application to Taiwan Monthly Visitors Arrival
6.2 Application to Taiwan Monthly Exchange Rates
Chapter 7 Conclusions
References

Bagshaw, M. and Johnson, R. A. (1977) Sequential procedures for detecting parameter changes in a time series model. Journal of the American Statistical Association, 72(359), 593-597.
Balke, N. S. (1993). Detecting level shifts in time series. Journal of Business and Economic Statistics, 11(1), 81-92.
Barry, D. and J. A. Hartigan (1993). A Bayesian analysis for change point problems. Journal of the American Statistical Association, 88(421), 309-319.
Basseville, M. and Benveniste, A. (1983) Sequential detection of abrupt changes in spectral characteristics of digital signals. IEEE Trans. On Inf. Theory. 20, 709-723.
Bezdek, J. C. (1973) Fuzzy mathematics in pattern classification. Ph. D. thesis, Cornell University, Ithaca, N. Y.
Bhattacharya, P. K. and Frierson, F. Jr. (1981) A nonparametic control chart for detecting smll disorders. Ann. Statist. 9, 544-554.
Brodsky, B. E. and Darkhovsky, B. S. (1993) Nonparametric methods in change-point problems. Kluwer Academic Publishers.
Brown, R. L., Durbin, J. and Evans, J. M. (1975) Techniques for testing the constancy of regression relationships over time. Journal of the Royal Statistical Society, B. 37, 149-192.
Box, G. E. P. and Tiao, G. C. (1965) A change in level of a nonstationary time series. Biometrika 52, 181-192.
Chernoff, H. and Zacks, S. (1964) Estimating the current mean of a normal distribution which is subject to changes in time. Ann. Math. Statist. 35, 999-1028.
Davis, L. D., ed. (1991) Handbook of genetic algorithms. Van Nostrand Reinhold.
Dufour, J. M. (1982) Recursive stability analysis of linear regression relationships: An exploratory methodology. Journal of Econometrics. 19,31-76.
Dufour, J. M. and Ghysels, E. (1996) Editors’ introduction: Recent developments in the econometrics of structural change. Journal of Econometrics. 70, 1-8.
Gardner, L. A. (1969) On detecting changes in the mean of normal variables. Ann. Math. Statist. 40, 116-126.
Gath, I. and Geva, A. (1989) Fuzzy clustering for the estimation of the parameters of the components of mixtures of normal distributions. Patt. Recog. Lett. 9, 77-86.
Girshick, M. A. and Rubin, H. (1952) A Bayes approach to a quality control model. Ann. Math. Statist. 23, 114-125.
Hinkly, D. V. (1970) Inference about the change point in a sequence of random variables. Biometrika 57, 1-17.
Hinkly, D. V. (1971) Inference about the change point from cumulative sum test. Biometrika 58, 509-523.
Holland, J. H. (1975) Adaptation in natural and artificial systems. University of Michigan Press.(Second edition: MIT Press, 1992).
Hsu, D. A. (1977) Tests for variance shifts at an unknown time point. Appl. Statist. 26, 279-284.
Hsu, D. A. (1979) Detecting shifts of parameter in gamma sequences, with applications to stock price and air traffic flow analysis. J. Amer. Statist. Assoc. 74, 31-40.
Hsu, D. A. (1982) A Bayesian robust detection of shift in the risk structure of stock market returns. J. Amer. Statist. Assoc. 77, 29-39.
Inclan, C. & Tiao, G. C. (1994). Use of Cumulative Sums of Squares for Retrospective Detection of Changes of Variance. Journal of the American Statistical Association, 89(427), 913-924.
Kander, A. and Zacks, S. (1966) Test procedure for poible changes in parameters of statistical distributions occurring at unknown time points. Ann. Math. Statist. 37, 1196-1210.
Kao, C. & Ross, S. L. (1995). A Cusum test in the linear regression model with serially correlated disturbances. Econometric Reviews. 14(3), 331-346.
Kligiene, N. I. (1973) Solution of problem about changes in unknown parameters of an autoregressive sequence. Litov. Math. Sborn. 2, 217-228. (Russian)
Lipeika, A. (1977) Detection of change point moments for an autoregressive sequence, in Stat. Probl. Upr., 24, Inst. Math. Cybern., Lithuan. Acad. Of Sciences, 27-71.(Russian)
McLachlan, G. J. and Basford, K. E. (1988) Mixture models, Marcel Dekker.
Menzefricke, U. (1981) Presented a Bayesian analysis of a change at an unknown time point.
Mottl, V. V. and Muchnik, I. B. (1980) Identification algorithm for the flow of random events. Avtom. Telemekj. 9, 74-80. (Russian)
Nikiforov, I. V. (1983) Sequential detection of changes in characteristics of time series. Nauka, Moscow. (Russian)
Page, E. S. (1954) Continuous inspection schemes, Biometrika 1, 100-115.
Page, E. S. (1955) A test for change in a parameter occurring at an unknown point. Biometrika 42, 523-537.
Page, E. S. (1957) Problem in which a change in a parameter occurs at an unknown point. Biometrika 44, 248-252.
Sastri, T., Flores, B., Valdes, J. (1989) Detecting points of change in time series. Compu. Open Res. 16, 271-293.
Telksnys, L. A. (1969) On application of optimal Bayes algorithm of teaching to determination of moments of changes in properties of random signals. Avtom. Telemekh. 6, 52-58. (Russian)
Tsay, R. S. (1986). Nonlinearity tests for time series. Biometrics. 73,461-6.
Tsay, R. S. (1990). Testing and modeling threshold autoregressive processes. Journal of the American Statistical Association. 84 ,231-240.
Wosley, K. J. (1986) Confidence regions and tests for a change-point in a sequence of exponential family random variables. Biometrika 73, 91-104.
Wu, B., Chen, M. H. (1999). Use of fuzzy technique in change periods detection of nonlinear time series. Applied Mathematics and Computation. 99, 241-254.
Wu, B. & Hwang, J. (1995). On fuzzy identification of nonlinear time series. Taiwan Economic Association, Annual Conference Proceedings. 169-19.
Zadeh, L. A. (1965) Fuzzy sets, Inf. Control. 8, 338-353.