臺灣博碩士論文加值系統

參考Engle and Rangel(2008)提出的spline-GARCH，本篇文章提出了新的長期波動度的模型建立與預測方式。我們使用Empirical Mode Decomposition(EMD)方法拆解GDP與CPI的季資料得到數個不同頻率且互相獨立的數列。EMD方法有著簡單且適用於任何非線性、非穩態的好處。此外，我們可以觀察到拆解出的GDP成分與景氣循環間的相關性。於是本篇文章將利用這些成分建立隨總體環境變動而演變的財務市場長期波動度，使得短期波動度能在長期下自然的進行結構轉變。進一步，我們利用此架構預測2008與2009年的99%風險值，結果顯示在加入總體資訊的考量之下，長期風險管理的表現將會因此得到改進。

Generalizing the component GARCH by Engle and Rangel (2008), this paper proposes a new modeling and forecasting strategy for systemic risk both in the short term and long run. By utilizing the orthogonally decomposed stationary regularity series from real quarterly GDP and CPI by EMD (Empirical Mode Decomposition), an empirical adaptive decomposition method that entertains nonlinear and nonstationary time series, we demonstrate the close coupling relationship between long run stock market volatility and the business cycle fluctuations. As these component series preserve the most primary information in the macroeconomic state variables sampled at lower frequencies, the long run component volatility is capable of generating regime shift behaviors in daily volatility without resorting to Markov switching or other regime switching mechanisms. Moreover, prediction of future volatility at various horizons is easy within the framework by taking advantage of the stable cyclical pattern of these orthogonalized macro series. Our empirical applications in hedging and evaluating VaR reveals that incorporating information from lower frequency macroeconomic fundamentals did provide incremental value toward the modeling of long run risks.

中文摘要 i
Abstract ii
Contents iii
List of Figures iv
List of Tables v
I. Introduction 1
II. Model Review 6
A. THE REGIME SWITCHING MODEL WITHOUT LOW-FREQUENCY INFORMATION 6
A.1. GJR-GARCH 7
A.2. Component GARCH model 8
A.3. Markov Regime Switching GARCH 9
B. THE REGIME SWITCHING MODEL WITH LOW FREQUENCY INFORMATION 10
B.1. Spline-GARCH 10
B.2. GARCH-MIDAS 12
III. MODEL SPECIFICATION 13
A. A NEW MODEL: SPLINE-GARCH WITH MACROECONOMIC FUNDAMENTALS 13
B. EMPIRICAL MODE DECOMPOSITION 14
IV. DATA AND EMPIRICAL RESULTS 18
A. DATA 18
B. THE DECOMPOSITION OF MACROECONOMIC VARIABLES 18
C. ESTIMATION RESULTS 25
C.1 Diagnostic check 31
C.2 Goodness of fit 32
V. FORECAST THE TERM STRUCTURE OF VAR 35
VI. CONCLUDING REMARKS 39
REFERENCE 40

Andersen, T.G., and T. Bollerslev, 1998, “Deutsche mark-dollar volatility: Intraday activity patterns, macroeconomic announcements, and longer run Dependencies.” Journal of Finance, 53, pp.219-265.
_____________, T. Bollerslev, F.X. Diebol, and E. Heiko, 2001, "The distribution of realized stock return volatility." Journal of Financial Economics, 61, pp.43-76.
Baillie, R., T. Bollerslev, and H. Mikkelsen, 1996, “Fractionally integrated gen- eralized autoregressive conditional heteroskedasticity.” Journal of Econometrics, 74, pp.3-30.
Barndoroff-Nielsen, O.E., and N. Shephard, 2002, “Econometric analysis of realized volatility and its use in estimating stochastic volatility models.” Journal of the Royal Statistical Society, Series B 64, pp.253-280.
Bollerslev, T., 1986, “Generalized autogressive conditional heteroskedasticity.” Journal of Econometrics, 31, pp.307-327.
Campbell, J., 1991, “A variance decomposition for stock returns.” Economic Journal, 101, pp.101-179.
__________, and R. Shiller, 1988, “The dividend-price ratio and expectations of future dividends and discount factors.” Review of Financial Studies, 1, pp.195-228.
Chernov, M., R. Gallant, E. Ghysels, and G. Tauchen, 2003, “Alternative models for stock price dynamics.” Journal of Econometrics, 116, pp.225-257.
Diebold, F.X. and K. Yilmaz, 2007, “Measuring financial asset return and volatility spillovers, with application to global equity markets.” PIER, working paper, N0. 08-031.
Ding, Z., and C.W.J. Granger, 1996, “Modeling volatility persistence of speculative returns: A new approach” Journal of Econometrics, 73, pp.185-215.
Engle, R.F., 1982, “Autoregressive conditional heteroskedasticity with estimates of the variance of U.K. inflation.” Econometrica, 50, pp.987-1008.
_________, 2009, “The risk that risk will change.” Journal of Investment Management, 7, pp.1-5.
_________, and G. Lee, 1999, “A long run and short run component model of stock return volatility.” in Engle, R. and White, H., Conintegration, Causality, and Forecasting: A festschrift in honor of clive W.J Granger, Oxford University Press, pp.475-97.
_________, and J. Rangel, 2007, “The spline GARCH model for low frequency volatility and its global macroeconomic causes.” The Review of Financial Studies, 21, pp.1187-1222.
_________, E. Ghysels, and B. Sohn, 2009, “Stock market volatility and macroeconomic fundamentals.” working paper
Gallant, A.R., C.-T. Hsu, and G. Tauchen, 1999, “Using daily range data to calibrate volatility diffusions and extract the forward integrated variance.” Review of Economic Statistics, 81, pp.617-631.
Ghysels, E., P. Santa-Clara, and R. Valkanov, 2005, “There is a risk-return tradeoff after all.” Journal of Financial Economics, 76, pp.509-548.
Glosten, L., R. Jagannathan, and D. Runkle, 1993, “Relationship between the expected value and the volatility of the nominal excess return on stocks.” Journal of Finance, 48, pp.1779-1801.
Guidolin, M., and A. Timmermann, 2006, “Term structure of risk under alternative econometric specifications.” Journal of Econometrics, 131, pp.285-308.
Hamilton, J.D., and R. Susmel, 1994, “Autoregressive conditional heteroscedasticity and changes in regime.” Journal of Econometrics, 64, pp.307–333.
___________, and G. Lin, 1996, “Stock Market Volatility and the Business Cycle.” Journal of Applied Econometrics, 11, pp.573-593.
Huang, N.E, Zheng Shen, S.R. Long, M.C. Wu, H.H. Shih, Quanan Zheng, N.C. Yen, C.C. Tung, and H.H. Liu, 1998, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis.” Proc. Roy. Soc. Lond., 454A, pp.903-993.
Nelson, D., 1991, “Conditional heteroskedasticity in asset returns: a new approach.” Econometrica, 59, pp.347-370.
Officer, R., 1973, “The variability of the market factor of New York Stock Exchange.” Journal of Business, 46, pp.434-453.
Sassan Alizadeh, M.W. Brandt, and F.X. Diebold, 2002, “Range-based estimation of stochastic volatility models.” Journal of Finance, 57, pp.1047-1091.
Schwert, G.W., 1989, “Why does stock market volatility change over time?” Journal of Finance, 44, pp.1115-1153.
Wu, Z., N.E. Huang, S.R. Long, and C.-K. Peng, 2007, “On the trend, detrending, and the variability of nonlinear and non-stationary time series.” Proc. Natl. Acad. Sci. USA., 104, pp.14889-14894.