GARCH ; : GARCH GARCH

Transkript

1 * : GARCH GARCH GARCH ; ; : GARCH : F831 : A ( ) Hamilton (1989) Engel Hamilton (1990) Klaassen(2002) Bergman Hansson (2005) Bollen (2000) Wilfling (2009) : ; * : (08JC790089) (2009R0079) 60 /2010.1

2 (1999) GARCH Granger (2003) (2005) GARCH EGARCH ( ) (STAR) : GARCH GARCH ( Markov Regime Switching GARCH MRS-GARCH) 2005 ; (2007) 31 (SETAR) (2007) GARCH (2008) ( ) (TAR) ; 2008 GARCH 2. GDP GARCH /2010.1

3 3. ; ( ) GARCH {r t }(t=12...t) GARCH (11) : k 4. r t = 覬 + 00 Σ 覬 r +ε l0 t-l t ε t = 姨 h t v t l = l h t Ω t-l =ω 0 +α 0 ε 2 +β h t-l 0 t-1 (1) 覬 l0 ; v t ; Ω t-l t-1 ; ω 0 0 α 0 0 β : s t =i(i=01;t=12...t) i μ it h it MRS- GARCH Gray (1996) Klaassen (2002) : k r t =μ it +ε t = 覬 0i + Σ 覬 r +ε li t-l t l = 1 6. ε t = 姨 h it v t i=01 (2) ; v t : h it =ω i +α i ε 2 t-l+β i h t-l i=01 (3) ; s t : P= p 00 p 1 01 p 10 p 11 1 (4) 7. p i0 +p i1 =1 p ij (ij=01) s t-l =i s t =j 62 /2010.1

4 (p 00 p 11 ) (2) ~ (4) 3 : (ex ante) Ljung-Box 5 10 (smoothed) t-1 Pr (s t Ω t-1 ) (filtering) Pr (s t Ω t ); t Pr (s t Ω T ) ( 1 ) 2005 Hamilton (1989) Pr (s t =0 Ω T ) >0.5 ; ( 1 ) 0.018% GARCH MRS-GARCH ( ) ( ( ) r t =100 GARCH 2 (lnex t -lnex t-1 ) r t EX t t % 1 ARCH GARCH 1 GARCH GARCH (IGARCH) (0.003) (0.003) (0.170) (0.388) LB (5) LB (10) LB2 (5) LB2 (10) [0.325] [0.212] [0.000] [0.000] : ; ; LB (q) LB 2 (q) q Ljung-Box 2 GARCH % 63 /2010.1

5 2 GARCH MRS-GARCH 准 ( ) * (0.002) ** 准 (0.004) * ω ( ) ( ) * ω ( ) * α (0.017) * (0.029) α (0.021) *** β (0.017) * (0.023) β (0.017) * p (0.007) * p (0.003) * LnL LB 2 (5) [0.471] [0.746] LB 2 (10) [0.437] [0.726] 2 MRS-GARCH Klaassen (2002) ( ) ( 0) ARCH (α 0 ) GARCH (β 0 ) ( 1) ARCH (α 1 ) GARCH (β 1 ) GARCH t 1 t+1 MSE t+5 ( ) : * ** *** 1% 5% 10% ; LnL ; t % t+2 GARCH GARCH GARCH (11) MRS-GARCH ( 2) GARCH GARCH Ljung-Box GARCH Ljung-Box GARCH GARCH GARCH GARCH GARCH GARCH (Lamoureux 638 Lastrapes1990) GARCH 300 ( ( ) ) (MSEMSE= (ε 2 -h t t )2 /n) 2 64 /2010.1

6 p p (( ) -1 ) ~ (( ) -1 ) ~ ~ p 01 (0.0142) p 10 (0.0097) ~ ~ ~ ~ ~ ~ ~ ~ ( ) 2 ( ) ( ) ( 0 ) MRS-GARCH ; ( 1 ) 2006 : (2009) (2009) % 0.15% /2010.1

7 ; GARCH GARCH GARCH GARCH GARCH 2008 GARCH ; /2010.1

8 : ( : ) : [1]. [J] (4). [2]. GARCH [J] (5). [3]. TAR [J] (9). [4]. [J] (2). [5]. GARCH [J] (3). [6]. [J] (1). [7]. [J] (6). [8]. [J] (9). [9]. STAR [J] (5). [10]. : [J] (10). [11] Bergman U.M. and Hansson J. Real Exchange Rates and Switching Regimes [J]. Journal of International Money and Finance (1) :121~138. [12] Bollen N.P.B. Gray S.F. and Whaley R.F. Regime Switching in Foreign Exchange Rates: Evidence from Currency Option Prices [J]. Journal of Econometrics (1-2) : 239~276. [13] Engel C. and Hamilton J.D. Long Swings in the Dollar: Are They in the Data and Do Markets Know It [J]. American Economic Review (4) :689~713. [14] Gray S.F. Modeling the Conditional Distribution of Interest Rates as a Regime- switching Process [J]. Journal of Financial Economics 1996 (42) : 27~62. [15] Hamilton J.D. A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle [J]. Econometrica (2) : 357~384. [16] Klaassen F. Improving GARCH Volatility Forecasts with Regime-switching GARCH [J]. Empirical Economics 2002 (27) : 363~394. [17] Lamoureux C. G. and Lastrapes W. D. Persistence in Variance Structural Change and the GARCH Model [J]. Journal of Business and Economic Statistics 1990 (8) : 225~234. [18] Wilfing B. Volatility Regime-switching in European Exchange Rates prior to Monetary Unifcation [J]. Journal of International Money and Finance 2009 (28) : 240~270. Abstract: In this paper single-regime and regime-switching GARCH models are used to analyze the characteristics of the volatility of the RMB exchange rate after 2005 Exchange Rate Reform. The results show that the regime -switching GARCH model in fitness and forecast is superior to single-regime GARCH model. Furthermore the RMB exchange rate presents staggered high-low volatility regimes. The characteristics of the RMB exchange rate under the different regimes are different: there are volatility clustering and persistence in high-volatility regime and homoskedasticity in low-volatility regime. We also find that the duration of low-volatility regime is shorter than that of high-volatility regime and the RMB exchange rate switches more easily from low-volatility regime to high-volatility regime. Finally different regimes at different stages and their transitions are closely related to domestic and foreign economic and political factors. Keywords: RMB Exchange Rate; Volatility; GARCH; Regime-switching 67 /2010.1