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 報酬與風險一直是投資市場中首重的要點，投資人希望能對未來值有所預測以便作出較佳的投資決策，本文希望透過預測區間的建立，對於欲觀測之未來值得到較為妥適的預測能力。以往以拔靴法建構之預測模型，皆假設以特定模型階數進行之，然而特定階數的選擇若沒有透過適當模型過程便可能產生錯誤推論，是以本文針對Thombs and Schucany(1990)提出建構單一模型AR(p)預測區間的演算法中，給定候選模型及權重(Akaike,1978、1979)，以非參數拔靴法(nonparametric bootstrap)提出模型平均的概念來建構本文探討未來報酬之預測區間模型。比較特定階數AR模型與模型平均法在以拔靴法建構預測區間時，是否模型平均法可得到相對穩健的結果；並分別以數值模擬及台灣股票市場中七檔不同類股之股票來分析AR(p)單一模型及模型平均法在不同樣本數及預測期數下的平均覆蓋機率及平均區間長度。結果顯示：樣本數與預測期數之不同，對模型平均法建立預測區間並沒有太大的影響，其結果仍與真實模型相似，顯示模型平均法之穩定性，且模型平均法相較於特定階數AR(p)模型法上，具較佳之模擬結果。
 The risks and rewards of the two major issues are often the primary attention points in the investment market, the investors hope to predict future values in order to make better investment decisions, this paper is by constructing a prediction interval can be more appropriate predictive capability for the future value we want to observations. In the past, use of the bootstrap method to construct the prediction model are assuming that the specific order model, but the choice of the specific order without going through an appropriate model of the process may generate an error inference, therefore, according to Thombs and Schucany (1990) proposed to construct a single model AR (p) prediction interval algorithm, given the candidate model and the weight (the Akaike, 1978,1979), using non-parametric bootstrap method proposed the concept of model averaging to construct this paper discusses the prediction interval model for future reward. Specific order of the AR model and model averaging in the bootstrap method to construct the prediction interval, whether the model averaging can be obtained relatively stable results; and analysis average coverage probability and the average interval length of the single model of the AR (p) and model averaging under different sample size and prediction phases in the numerical simulation and seven different file stocks of the Taiwan stock market. The results showed that: when different number of samples and prediction phases, the model averaging method to construct the prediction interval does not have a significant impact, and the results are still similar to the real model, showing the stability of the model averaging, and model averaging compared to the specific order of the AR (p) model method with a better simulation results.
 目錄第一章 緒論........................................................1 第一節 研究背景與動機...........................................1 第二節 研究目的.................................................3 第三節 研究流程.................................................3第二章 文獻探討....................................................5第一節 拔靴法（Bootstrap）......................................5第二節 自我迴歸模型（Autoregressive Models）.......................6第三節 AR拔靴法預測區間.......................................7第三章 AR模型平均演算法............................................9第四章 數值模擬與實例分析..........................................11第一節 數值模擬分析............................................11第二節 實例分析................................................13第五章 結論........................................................25參考文獻...........................................................26圖目錄圖1.1：研究流程圖...................................................4圖4.1：台積電股價週報酬率以AR模型及模型平均法建構之預測區間........15圖4.2：鴻海股價週報酬率以AR模型及模型平均法建構之預測區間..........16圖4.3：裕隆股價週報酬率以AR模型及模型平均法建構之預測區間..........17圖4.4：台泥股價週報酬率以AR模型及模型平均法建構之預測區間..........18圖4.5：台塑股價週報酬率以AR模型及模型平均法建構之預測區間..........19圖4.6：國泰金股價週報酬率以AR模型及模型平均法建構之預測區間........20圖4.7：長榮股價週報酬率以AR模型及模型平均法建構之預測區間..........21表目錄表4.1：AR(2)模型預測期數1期時預測區間之數值模擬分析................12表4.2：AR(2)模型預測期數3期時預測區間之數值模擬分析................13表4.3：七檔個股週報酬率之敘述統計表................................14表4.4：七檔個股之平均報酬率及預測區................................22表4.5：七檔個股在特定階數及模型平均法下之MSE值.....................24
 參考文獻一、中文部份1.李孟真（2009），以區塊拔靴法在財務時間序列模型下建構預測區間，銘傳大學應用統計資訊學系碩士班碩士論文。2.李昀寰（2005），隨機波動模型下自助法之應用，國立中央大學，統計研究所博士論文。3.周心怡（2004），拔靴法（Bootstrap）之探討及其應用，國立中央大學，統計研究所碩士論文。4.楊奕農（2009），時間序列分析，雙葉書廊有限公司。 二、英文部份1.Akaike, H. (1978). “A Bayesian analysis of the minimum AIC procedure.” Annals of the Institute of Statistical Mathematics, Vol.30, pp.9-14.2.Akaike, H. (1979). “A Bayesian extension of the minimum AIC procedure of Autoregressive model fitting.” Biometrika, Vol.66, pp.237 -242.3.Bollerslev, T. (1986). “Generalized autoregressive conditional heteroscedasticity.” Journal of Econometrics, Vol.31, pp.307-327.4.Bollerslev, T. (1987). “A conditionally heteroskedastic time series model for speculative prices and rates of return.” Review of Economics and Statistic, Vol. 72, pp.408-505.5.Bollerslev, T., Chou, R. Y., and Kroner, K. F. (1992). “ARCH modeling in finance: a selective review of the theory and empirical evidence.” Econometrics, Vol.52, pp.5-59.6.Box, G. E. P., and Jenkins, G. M. (1976). Time Series Analysis: Forecasting and Control, Holden-Day: San Francisco.7.Cao, R., Febrero-Bande, M., González-Manteiga, W., Prada-Sánchez J. M., and García-Jurado, I. (1997). “Saving computer time in constructing cons-istent bootstrap prediction intervals for autoregressive processes.” Communi-cations in Statistics (Simulation and Computation), Vol.26, pp.961-978.8.Efron, B. (1979). “Bootstrap methods：Another look at the jackknife.” The Annals of Statistics, Vol.7, pp.1-26.9.Efron, B. (1981). The jackknife, the bootstrap, and other resampling plans.SIAM, Philadelphia.10.Efron, B. (1987). “Better bootstrap confidence intervals.” Journal of the American Statistical Association, Vol.82, pp.171-185.11.Efron, B., Tibshirani, R.J. (1993). An introduction to the bootstrap. Chapman& Hall, New York.12.Enders, W. (2004). Applied Economertric Time Series. New York: John Willey& Sons, Inc.13.Engle, R. F. (1982). “Autoregressive conditional heteroscedasticity with est-imates of the variance of United Kingdom inflation.” Econometrics, Vol.50, pp.987-1008.14.Hall, P. (1985). “Resampling a coverage pattern.” Stochastic Processes Applications, Vol.20, pp.231-246.15.Kunsch, H. R. (1989). “The jackknife and the bootstrap for general statio-nary observations.” The Annals of Statistics, Vol.17, pp.1217-1241.16.Miguel, J. A. and Olave, P. (1999a). “Bootstrapping forecast intervals in ARCH models.” Test, Vol.8, pp.345-364.17.Miguel, J. A. and Olave, P. (1999b). “Forecast intervals in ARCH models:Bootstrap versus parametric methods.” Applied Economics Letters, Vol.6, pp.323-327.18.Thombs, L. A. and Schucany, W. R. (1990). “Bootstrap prediction interva-ls for autoregression.” Journal of the American Statistical Association, Vol.85,pp.486-492.19.Wall, K. D., and Stoffer, D. S. (2002). “A state space model to bootstrap-ping conditional forecasts in ARMA models.” Journal of Time Series Ana-lysis, Vol.23, pp.733-751.
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 1 拔靴法(Bootstrap)之探討及其應用 2 以區塊拔靴法在財務時間序列模型下建構預測區間 3 在自我迴歸模型下以預測均方誤差準則建構預測區間 4 平穩型時間序列自我迴歸模型預測誤差研究

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