臺灣博碩士論文加值系統

近年來有許多文獻發現，一個穩定的時間序列，若有偶發的結構性改變(regime switching)時，就會產生類似長距相關(long memory)的現象。因此我們的研究目的是建構一些檢定方法來分離這兩種模型。建構的過程有兩個步驟。首先，原始資料先透過一個high-pass filter的轉換，去除資料中與局部變化無關的部分。然後，再利用轉換後資料的樣本峰度、最大值或偵測離群值的統計量，來檢定是否有mean switching 的現象。藉由蒙地卡羅模擬法驗證所提出的統計量在小樣本之下其檢定力不錯。並以尼羅河的資料及外匯交易資料作為實例驗證。

Recent studies have found that regime switching model with rare shift is easily confused with long memory in terms of the behavior of autocorrelations. In this study, our goal is to distinguish regime switching models from long memory models. Several semi-parametric procedures are developed for testing long memory against structure change. The proposed tests are derived based on the transformed data after applying a high pass filter. A simulation study is conducted to investigate the performance of proposed tests. Nile River data and foreign exchange rate data are used for illustrations.

1 Introduction 1
2 The Models 2
2.1 Long Memory Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.2 Regime Switching Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2.1 Mean-plus-Noise Model . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2.2 Markov-switching Model . . . . . . . . . . . . . . . . . . . . . . . . . 5
3 Hypothesis and Testing Procedures 10
3.1 High Pass Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.2 Testing Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2.1 Maximum and Kurtosis . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2.2 Regression for Outlier Detection . . . . . . . . . . . . . . . . . . . . . 18
4 Simulation Study 21
4.1 Empirical Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.2 Power Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.3 Jump Position Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
5 Illustrative Examples 41
5.1 Nile River Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
5.2 Foreign Exchange Rate Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
6 Discussion and Conclusion 47
Reference 49

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Beran, J. (1994), Statistics for Long-Memory Processes, Chapman & Hall: New York.
Bos, C.S., Franses, P.H. and Ooms, M. (1999), Long memory and level shifts: re-analyzing inflation rates, Empirical Economics, 24, 427-449.
Breidt, F.J. and Hsu, N.-J. (2002), A class of nearly long-memory time series models,
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Daubechies, I. (1988), Orthonormal bases of compactly supported wavelets, Communications on Pure and Applied Mathematics, 41, 909-996.
Diebold, F.X. and Inoue, A. (2001), Long memory and regime switching, Journal of Econometrics, 105, 131-159.
Engle, R.F. and Smith, A.D. (1999), Stochastic permanent breaks, Review of Economics and Statistics, 81, 553-574.
Granger, C.W.J. and Ding, Z. (1996), Varieties of long memory models, Journal of Econometrics, 73, 61-78.
Granger, C.W.J. and Hyung, N. (1999), Occasional structure breaks and long memory, UCSD discussion paper 99-14.
Granger, C.W.J. and Ter¨asvirta, T. (1999), A simple nonlinear time series model with misleading linear properties, Economics Letters, 62, 161-165.
Balke, N.S. and Fomby, T.B. (1989), Shifting trends, segmented trends, and infrequent permanent shocks, Journal of Monetary Economics, 28, 61-85.
Beran, J. (1994), Statistics for Long-Memory Processes, Chapman & Hall: New York.
Bos, C.S., Franses, P.H. and Ooms, M. (1999), Long memory and level shifts: re-analyzing inflation rates, Empirical Economics, 24, 427-449.
Breidt, F.J. and Hsu, N.-J. (2002), A class of nearly long-memory time series models, International Journal of Forecasting, in press.
Brockwell, P.J. and Davis, R.A. (1991), Time Series: Theory and Methods, 2nd edition, Springer: New York.
Chen, C. and Tiao, G.C. (1990), Random level-shift time series models, ARIMA approximations, and level-shift detection, Journal of Business and Economic Statistics, 8, 83-97.
Daubechies, I. (1988), Orthonormal bases of compactly supported wavelets, Communications on Pure and Applied Mathematics, 41, 909-996.
Diebold, F.X. and Inoue, A. (2001), Long memory and regime switching, Journal of Econometrics, 105, 131-159.
Engle, R.F. and Smith, A.D. (1999), Stochastic permanent breaks, Review of Economics and Statistics, 81, 553-574.
Granger, C.W.J. and Ding, Z. (1996), Varieties of long memory models, Journal of Econometrics, 73, 61-78.
Granger, C.W.J. and Hyung, N. (1999), Occasional structure breaks and long memory, UCSD discussion paper 99-14.
Granger, C.W.J. and Ter¨asvirta, T. (1999), A simple nonlinear time series model with misleading linear properties, Economics Letters, 62, 161-165.