本研究使用含外生多變數為門檻值之TAR模型，分析並預測103年到105年的台股指數。建構多變量之門檻自迴歸模式較傳統以時變或自變數自動控制值更能反映出時間數列結構改變的過程與趨勢。這對於模式分析與預測有更優的解釋能力。且含外生多變數為門檻值之多變量門檻模式的可適用範圍很廣，尤其是當時間數列中的結構改變的現象，來自於外在多個變數衝擊，或非線性現象。此時加入多個外生變數作為考量，更能精準分析資料和做預測。我們以台股指數為例，實證結果顯示，我們所提出之模型，較傳統預測方法有更高之準確度。

In this research, we use exogenous multi-variables as threshold values to construct a threshold autoregressive model in order to analysis and forecast TAIEX index between 103 years and 105 years. Constructing the threshold autoregressive model with multi-variables is better to reflect the process and trend of the change in time series structure than traditional model. This provides the better explanatory ability for model analysis and forecast. Also, the threshold autoregressive model with multi-variables containing exogenous multi-variables can apply more range, especially, as the structure change in time series due to the exogenous multi-variables shock. Through adding more exogenous variables, one can analyze data and forecast accurately. In this paper, the empirical results of TAIEX index shows that the threshold autoregressive model with multi-variables containing exogenous multi-variables is more precise than the traditional way.

1. 吳柏林 (1995)。時間數列分析導論，華泰書局，台北。
2. 楊奕農 (2009)。時間序列分析：經濟與財務上的應用，雙葉書廊，台北。
3. 林茂文 (1992)。時間序列分析與預測，華泰書局，台北。
4. Tong H. and Lim K. S. (1980), Threshold Autoregressive, Limit Cycles and Cyclical Data (with Discussion), Journal of the Royal Statistical Society. Series B, Vol.42, No.3, pp245-292.
5. Subba Rao T. and Gabr M. (1980), A test for linearity of stationary time series analysis, Journal of Time Series Analysis, Vol.1, No1, pp145-158.
6. Black, F. (1986), Noise, Journal of Finance, Vol.41, pp529-543.
7. D Domian, D Louton (1997), A threshold autoregressive analysis of stock. returns and real economic activity, International Review of Economics and Finance, Vol.6, pp197-179.
8. J. D. Byers and D. A. Peel (1995), Evidence on volatility spillovers in the interwar floating exchange rate period based on high/low prices, Applied Economics Letters, Taylor and Francis Journals, Vol.2, No.10, pp394-396.
9. Bai Jushan and Pierre Perron (2003), Computation and Analysis of Multiple Structural-Change Models, Journal of Applied Econometrics, Vol.18, No.1, pp1-22.
10. Tsay, R.S. (1989), Testing and Modeling Threshold Autoregressive Processes, Journal of the American Statistical Association, Vol.84, No.405, pp231-240.
11. Tsay, R.S. (1998), Testing and modeling multivariate threshold models, Journal of American Statistical Association, Vol.93, pp1188-1202.
12. Thomakos, D. and Guerard Jr, J. (2004). Naïve, ARIMA, nonparametric, transfer function and VAR models: A comparison of forecasting performance, International Journal of Forecasting, Vol.20, pp53-67.
13. Haggan V. and Ozaki T. (1980), Amplitude-dependent Exponential AR Model Fitting for Non-linear Random Vibrations, in Time Series, (O. D. Anderson ed.), North-Holland, Amsterdam.
14. Hansen, B.E. (1994), Autoregressive Condition Density Estimation, International Economic Review, Vol.35, pp705-730.
15. Hansen, B.E. (1999), Threshold effects in non-dynamic panels: Estimation, testing and inference, Journal of Econometrics, Vol.93, pp345-368.
16. Hansen, B.E. (1999), Testing for Linearity, Journal of Economic Surveys, Vol.13, No.5, pp551-576.
17. Hansen, B.E. (2000), Sample splitting and threshold estimation, Econometrics, Vol.68, pp575-603.
18. Kumar K and Wu B (2001), Detection of change points in time series analysis with fuzzy statistics, International Journal of Systems Science, Vol.32, No.9, pp1185-1192.
19. Akaike, H. (1973), Information theory and an extension of maximum likelihood principle, Second International Symposium on Information Theory, Vol.1, pp267-281.
20. Sharma S. (1996), Applied Multivariate Techniques, John Wiley & Sons. New York, USA.
21. Oscar, B.R. (2004), Searching for Threshold Effects in the Evolution of Budget Deficits: An Application to the Spanish Case, Economics Letters, Vol.82, pp239-243.
22. Sephton, P.S. (2003), Spatial Market Arbitrage and Threshold Cointegration, American, Journal of Agricultural Economics, Vol.85, pp1041-1046.