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系統識別號 U0026-2007201711445600
論文名稱(中文) 對區間值時間序列模型的探討
論文名稱(英文) Study on the Interval Time Series Model
校院名稱 成功大學
系所名稱(中) 統計學系
系所名稱(英) Department of Statistics
學年度 105
學期 2
出版年 106
研究生(中文) 王維敬
研究生(英文) Wei-Ching Wang
學號 r26041029
學位類別 碩士
語文別 英文
論文頁數 28頁
口試委員 指導教授-林良靖
口試委員-陳瑞彬
口試委員-黃士峰
中文關鍵字 異質變異性  區間值的時間序列  STAR模型 
英文關鍵字 Heteroscedasticity  interval time series  STAR model 
學科別分類
中文摘要 在金融經濟學中,許多的模型及分析是以當天的收盤價為基準建立的,甚至有些是以更低頻率的資料,像是周或月資料為基準,這樣會造成像是當日最高價和最低價這些有價值的資訊沒被考慮到,在此研究中,我們將最高及最低價視作區間值的觀測值,並利用符號資料的方法去處理他們。在建立區間值的時間序列時,最為困難的莫過於如何避免最大值及最小值互相交叉,大部分的文獻是透過將區間值的時間序列更改為區間的中心及半徑來處理這個問題,但是因為對於誤差項為常態的假設,半徑並無法確定一定為正值,而Teles和Brito於2015年提出space-time autoregressive (STAR)模型,STAR模型雖然可以確保在做預測時上界值會比下界值還要大,但是在生成資料時卻不然。在這篇研究中,我們結合了STAR模型及多維度的GARCH處理財務資料的異質變異性;另外,我們亦提出了heteroscedastic auto-inter regressive (HAIR)模型,此模型直接利用了符號資料的概念且同時考慮了隨時間變化的干擾項。在模型比較上,我們考慮了以2016年S&P500指數為基準之實證向的實驗,並提供了我們所有提及之模型的比較。在實證資料分析上,我們則探討了每個模型在樣本間和樣本外的行為及表現。
英文摘要 In financial economics, a large number of analysis and models were developed based on the daily closing prices, or even at lower frequencies such as weekly or monthly. It may discard some valuable intra-daily information such as the highest and lowest prices. We may regard the highest and lowest prices as an interval valued observations and use some symbolic data methodologies to deal with them. When modelling the interval time series, the most difficulty is to avoid the maximum and minimum values to be crossed with each other. Most of literatures deal this problem by changing the interval time series to be the center and radius of the intervals. Nevertheless, due to the normal assumption for the innovation term, the radius processes may not ensure to be positive. Alternatively, Teles and Brito (2015) proposed the
space-time autoregressive (STAR) models. STAR model can exactly ensure the predicted upper values to be larger than lower values but can not in generating simulated data. In this paper, we combine the STAR model with multivariate GARCH to deal with the heteroscedasticity of financial data. Alternatively, we propose a model which directly uses the concept of symbolic data and considers the time varying noise terms simultaneously, namely heteroscedastic auto-inter regressive (HAIR) model. In model comparison, we consider a practically oriented experiment based on 2016 S&P500 index and provide the comparisons of models we mentioned. In real data analysis, we investigate the in-sample and out-of-sample behavior for each model.
論文目次 摘要i
Abstract ii
誌謝iii
Table of Contents iv
List of Tables v
List of Figures vi
Chapter 1. Introduction 1
Chapter 2. Literature Review 4
2.1 Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Vector Autoregression (VAR) Model for Xt . . . . . . . . . . . . . . . . . . 4
2.3 Vector Autoregression Model for Yt . . . . . . . . . . . . . . . . . . . . . . 5
2.4 Space-Time Autoregression Models for Interval Time Series . . . . . . . . . 6
2.4.1 Parameter Estimation in STAR Models . . . . . . . . . . . . . . . . . 7
2.5 CCC GARCH Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Chapter 3. STAR-GARCH and HAIR Model 9
3.1 STAR Model+Multivariate GARCH . . . . . . . . . . . . . . . . . . . . . . 9
3.1.1 Modified Three-Stage Least Squares . . . . . . . . . . . . . . . . . . 10
3.2 Heteroscedastic Auto-Interval-Regressive (HAIR) Model . . . . . . . . . . . 10
Chapter 4. Model Comparison 12
Chapter 5. Real Data Analysis 14
5.1 In-sample Investigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
5.2 Out-of-Sample: Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Chapter 6. Conclusion and Future Work 16
References 17
Appendix A 19
Appendix B 27
參考文獻 1. Arroyo, J., González-Rivera, G., and Matè, C. (2010). Forecasting with Interval and Histogram Data: Some Financial Applications. Handbook of Empirical Economics
and Finance, 247-279.
2. Arroyo, J., González-Rivera, G., and Matè, C. (2011). Smoothing methods for histogramvalued time series: An application to value-at-risk. Statistical Analysis and Data Mining, 4(2), 216-228.
3. Berndt, E.R., Hall, B.H., and Hall, R.E. (1974). Estimation and inference in nonlinear structural models. Annals of Economic and Social Measurement, 3(4), 653-665.
4. Billard, L., and Diday, E. (2003). From the statistics of data to the statistics of knowledge: symbolic data analysis. Journal of the American Statistical Association, 98(462), 470-487.
5. Billard, L., and Diday, E. (2006). Symbolic Data Analysis: Conceptual Statistics and Data Mining. 1st ed. Chichester: Wiley & Sons.
6. Blanco, A., Colubi, A., Corral, N., and Gonzalez-Rodriguez, G. (2008). On a linear independence test for interval-valued random sets. Soft Methods for Handling Variability and Imprecision. Advances in Soft Computing, 111-117.
7. Bollerslev, T. (1990). Modelling the Coherence in Short-Run Nominal Exchange Rates: A Multivariate Generalized ARCH Model. The Review of Economics and Statistics, 498-505.
8. Brito, P. (2007). Modelling and analysing interval data. Advances in Data Analysis, 197-208.
9. González-Rodríguez, G., Blanco, Á., Corral, N., and Colubi, A. (2007). Least squares estimation of linear regression models for convex compact random sets. Advances in Data Analysis and Classification, 1(1), 67-81.
10. Gonzalez-Rivera, G., Lee, T.-H., and Mishra, S. (2008). Jumps in cross‐sectional rank and expected returns: a mixture model. Journal of Applied Econometrics, 23(5), 585-606.
11. Rodrigues, P. M., and Salish, N. (2011). Modeling and forecasting interval time series with Threshold models: An application to S&P500 Index returns. Banco De Portugal, Economics and Research Department.
12. Teles, P., and Brito, P. (2015). Modeling Interval Time Series with Space–Time Processes. Communications in Statistics-Theory and Methods, 44(17), 3599-3627.
13. Zellner, A., and Theil, H. (1962). Three-stage least squares: simultaneous estimation of simultaneous equations. Econometrica, 54-78.
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