臺灣博碩士論文加值系統

CARR(Conditional Autoregressive Range)模型在固定的時間區間對於資產價量的變幅(range)提供一個動態模式。然而採用變幅做為波動性之代理變數仍隱含一些問題，包括變幅對於離群值具高度敏感性，以及採用變幅做為波動性代理變數之CARR模型，所估計出的波動性可能高估實現波動性的變異程度。因此本研究基於適度規避離群值的衝擊與適當刻畫波動性的動態行程此兩目的，針對變幅採取穩健性的衡量方式，意即採用內分位數變幅(interquantile range)做為衡量波動性的代理變數，並與CARR模型做一適切搭配，試圖獲取較佳的樣本內與樣本外之預測結果。本研究主要研究對象為期貨之時間序列，包括NY Light Crude(CL)、Dow Futures(DJ)、Nasdaq 100 Futures(ND)、NY Natural Gas(NG)以及S&P 500 Futures(SP)，而在預測能力的衡量指標上，樣本內採用Mincer-Zarnowitz(MZ)迴歸式，樣本外採用二次損失函數、比例損失函數以及t檢定做為主要衡量指標。實證結果顯示，在樣本資料為實現波動性之波動程度較大且包含數值較大之離群值的資料型態下，如NY Light Crude及NY Natural Gas，內分位數變幅之CARR模型將優於標準變幅之CARR模型。在樣本資料為實現波動性之波動程度較小且離群值較小的資料型態下，如Dow Futures、Nasdaq 100 Futures及S&P 500 Futures，內分位數低估了實現波動性之波動程度，因此標準變幅之CARR模型在預測能力的表現上，優於多數的內分位數變幅之CARR模型。另外，除了樣本Nasdaq 100 Futures外，另外四種期貨資料之樣本內與樣本外預測結果具一致性。

The conditional autoregressive range (CARR) model was proposed a dynamic model for the high/low range of asset prices within fixed time intervals. However, adopting range as the proxy of volatility has some problems. Firstly, range is highly sensitive to outliers. In addition, the CARR model with range will probably overestimate the variance of realized volatility. Based on the purpose of avoiding the effects of outliers and that of properly characterizing the dynamic structure of volatility, we utilize the robust measure of range. In other words, we adopt interquantile range as the proxy of volatility and compare the forecasting performance of the CARR model with either interquantile range or standard range. The forecasting performance measures include Mincer-Zarnowitz (MZ) regression in in-sample forecasts, quadratic loss functions, proportional loss functions and t test in out-of-sample forecasts. The samples include NY Light Crude (CL)、Dow Futures (DJ)、Nasdaq 100 Futures (ND)、NY Natural Gas (NG) and S&P 500 Futures(SP). The empirical results reveal that in the sample which has more volatile realized volatility and many extreme outliers, like NY Light Crude (CL) and NY Natural Gas (NG), the CARR model with interquantile range outperforms the CARR model with standard range, in terms of both in-sample forecasts and out-of-sample forecasts. On the contrary, in the sample which has less volatile realized volatility and small outliers, like Dow Futures (DJ), Nasdaq 100 Futures (ND) and S&P 500 Futures (SP), the results are opposite.

中文摘要 I
ABSTRACT II
謝辭 III
目錄 IV
表目錄 VI
圖目錄 VII
一、前言 1
二、文獻探討 3
2.1 變幅估計值 3
2.2 波動性模型與報酬率 3
2.3 波動性模型與變幅 4
2.4 離群值與極端值理論 5
三、研究方法 7
3.1 CARR模型 7
3.2 內分位數變幅 10
3.3 實現波動性之選取 11
3.4 樣本內預測 14
3.5 樣本外預測 15
3.1.1 預測值計算方式 15
3.1.2 損失函數(loss function) 15
3.1.3 t檢定 16
四、資料分析 18
4.1 資料選取 18
4.2 實現波動性 19
4.3 內分位數變幅之敘述性統計量 20
4.3.1 CL、NG內分位數變幅之敘述性統計量 20
4.3.2 DJ、ND、SP內分位數變幅之敘述性統計量 21
五、實證分析 23
5.1 參數估計 23
5.1.1 CL、NG之參數估計 23
5.1.2 DJ、ND、SP之參數估計 23
5.2 樣本內預測結果 25
5.2.1 CL、NG之樣本內預測結果 25
5.2.2 DJ、ND、SP之樣本內預測結果 26
5.3 樣本外預測結果 28
5.3.1 CL、NG之樣本外預測結果 28
5.3.2 DJ、ND、SP之樣本外預測結果 29
六、結論 31
參考文獻 33

1. 周雨田, 巫春洲, 劉炳麟 (2004), “動態波動模型預測能力之比較與實證,” 財務金融學刊.
2. 林孟樺 (2005), “Forecast volatility from threshold heteroscedastic range models,” 逢甲大學統計與精算所碩士論文.
3. Alizadeh, S., M.W. Brandt and F.X. Diebold (2002), “Range-based estimation of stochastic volatility models,” Journal of Finance, 57, 1047-1092.
4. Andersen, T. and T. Bollerslev (1998), “Answering the skeptics: yes, standard volatility models do provide accurate forecasts,” International Economic Review, 39, 885-905.
5. Beckers, S. (1983), “Variances of security price returns based on high, low, and closing prices,” The Journal of Business, 56(1), 97-112.
6. Bernanke, B. and M. Gertler (1999), “Monetary policy and asset price volatility,” Economic Review - Federal Reserve Bank of Kansas City, 84(4), 17-51
7. Bollersleve, T. (1986), “Generalized Autoregressive Conditional Heteroskedasticity, ”Journal of Econometrics, 31, 307-327.
8. Bollerslev, T., R. Chou, and K. Kroner (1992), “ARCH modeling in finance: a review of the theory and empirical evidence,” Journal of Econometrics, 52, 5-59.
9. Bollerslev, T., R. Engle and D. Nelson (1994), “ARCH models,” In Handbook of Econometrics, IV, 2959-3038, ed. Engle, R.F. and McFadden, D.C., Amsterdam: North-Holland.
10. Brandt, M.W. and C.S. Jones (2006), “Volatility forecasting with range-based EGARCH models,” Journal of Business and Economic Statistics, 24(4), 470.
11. Chou, R. (2005a), “Forecasting financial volatilities with extreme values: the Conditional AutoRegressive Range (CARR) Model,” Journal of Money Credit and Banking, 37(3), 561-582.
12. Chou, R. (2005b), “Modeling the asymmetry of stock movements using price ranges,” Advances in Econometrics, forthcoming.
13. Chou, R., N. Liu and C.C. Wu (2005), “Forecasting correlation and covariance with a range-based dynamic conditional correlation model”, working paper.
14. Ding, Z., C.W.J Granger and R. Engle, “A long memory property of stock market returns and a new model,” Journal of Empirical Finance, 1, 83-106.
15. Engle, R. (1982), “Autoregressive conditional heteroscedasticity with estimates of the variance of U.K. inflation,” Econometrica, 50, 987-1008.
16. Engle, R. and J. Russell (1998), “Autoregressive conditional duration: a new model for irregular spaced transaction data,” Econometrica, 66, 1127-1162.
17. Engle, R. (2002), “Dynamic Conditional Correlation: A simple class of multivariate generalized autoregressive conditional heteroscedasticity models,” Journal of Business and Economic Statistics, 12, 339-350.
18. Hansen, P.R., A. Lunde and J.M. Nason (2003), “Choosing the best volatility models: the model confidence set approach,” Oxford Bulletin of Economics and Statistics, 65, 839-861.
19. Hansen, P.R. and A. Lunde (2005), “Consistent ranking of volatility models,” Journal of Econometrics, forthcoming.
20. Hansen, P.R. and A. Lunde (2005), “A forecast comparison of volatility models: does anything beat a GARCH(1,1)?” Journal of Applied Econometrics, 20, 873-889.
21. Harvey, C.R. and R.E. Whaley (1992), “Market volatility prediction and the efficiency of the S&P 100 index option market,” Journal of Financial Economics, 1, 43-73.
22. Hentschel, L. (1995), “All in the family. Nesting symmetric and asymmetric GARCH models,” Journal of Financial Economics, 39, 71-104.
23. Hol, E. and S.J. Koopman (2002), “Stock index volatility forecasting with high frequency data,” Manuscript, Free University Amsterdam.
24. Hull, J. and A. White (1987), “The pricing of options on assets with stochastic volatilities,” Journal of Finance, 42, 281-300.
25. Lin, Ji-Chai and M. Rozeff (1994), “Variance, return, and high-low price spreads,” Journal of Financial Research, 17, 301-319.
26. Lopez, J.A. (2001), “Evaluating the predictive accuracy of volatility models,” Journal of Forecasting, 20, 87-109.
27. Mandelbrot, B. (1963), “The Variation of Certain Speculative Prices,” Journal of Business, 36, 394-419.
28. Parkinson, M. (1980), “The extreme value method for estimating the variance of the rate of return,” Journal of Business, 53, 61-65.
29. Pagan, A.R. and G.W. Schwert (1990), “Alternative models for conditional stock volatility,” Journal of Econometrics, 45, 267-290.
30. Wiggins, J.B. (1991), “Empirical tests of the bias and efficiency of the extreme-value variance estimator of common stocks,” The Journal of Business, 64(3), 417-432.