ARFIMA - GARCH F31, C19, C52, C22 :JEL

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1 * GJR APGARCH ARFIMA F31, C19, C52, C22 JEL GARCH *

2 EMH 1 Efficient Market Hypothesis EMH 2 Mees & Rogoff

3 VAR ARMA iid 1 Martingale process 2 Random walk 3 Barkoulas et al 4 Auto Regressive Moving Average 5 Vector Auto Regressive 6 Independent and Identically Distributed

4 ARCH ARCH TGARCH ACF APGARCH EGARCH 1 Auto Regressive Conditional Heteroscedasticity 2 Long memory model 3 Fractional integration FI 4 Granger & Joyeux 5 Autocorrelation function 6 Jin Xiu & Yao Jin 7 GARCH 8 Threshold GARCH 9 The Exponential GARCH 10 Asymetric power GARCH

5 ARDL GPH ARFIMA ARFIMA 1 Auto Regressive Distributed Lag 2 Yin Wong Cheung 3 Geweke Porter Hundak 4 Auto Regressive Fractional Integrated Moving Average 5 Exact maximum likelihood 6 Approximate maximum likelihood

6 EGARCH 1 Semiparametric fractional estimation method 3 Saatcloglu 2 5 Exponential GARCH currency substitution 4 6 Nelson 7 Rahman and Serletis 8 Aloy et al

7 d FELW ESTAR OX w 1 L t d x t x t d 1 d L d dd L 1 dl L 2! w t d x t 1 L d 0 1 Feasible Exact Local Whittle 2 Shimotsu and Philips 3 Exponential Smooth Transition AutoRegressive

8 w t d i x t x i 1 x i x i d KPSS PP ADF ADF pp Kpss ARFIMA p d PACF ACF 1 Peters 2 Partial Auto Correlation Function

9 q ARMA N ARFIMA3,d,1 ARFIMA3,d,1 MLE NLS d MPL ARFIMA5,d,1 d MLE MPL NLS < < 05 ARIMA ARFIMA 1 Maximum likelihood 2 Maximum phylogeny likelihood 3 Non conditional least square 4

10 ARIMA5,1,1 ARIMA Q AIC ARIMA5,1,1 ARFIMA3,029,1 ARIMA ARFIMA ARFIMA3,029, = EGARCH TARCH GARCH ARCH 1 ARFIMA

11 >0 <0 ARCHp 2 1 q t i t i i h w 1 Auto Regressive Conditional Heteroscedasticity ARCH 2 Engle 3 Clusters 4 Engel and Ng

12 ARMA t t ht = q p 2 t i t i j t j i 1 j 1 h w h APGARCH ARMA EGARCH TGRCH = TGARCH E = GJR h = TARCH < Glosten 2 Jaganathan 3 Runkle 4 Threshold

13 1 0 <0 2 1 t t 1 TARCH 2 d t 1 t 1 EGARCH ln h ln h t t 1 t t 1 ht 1 ht 1 EGARCH EGARCH t 1 2 t 1 h t 1 05 t 1 t 1 05 h t APARCHp,q 1 Leverage effect

14 w q t i t i i t i j t j i 1 j 1 < <1 ARCH q p t w i t i ist i t i j t j i 1 j 1 p > GJR 2 i S t TGARCH GJR = =0 t GJR 1 Ding, Granger, and Engle 2 Glosten, Jagannathan & Runkle 3 Zakoian

15 ARFIMA3,029,1 OxMetrics6 JBera 1 Skewness 2 Excess Kurtosis

16 QQ 1 Quantile Quantile Plot

17 AC PAC QStat Prob Q { } Testing for error ARCH from lags 1 to 1 F 1, 341 OxMetrics6 Pvalue

18 ARFIMA3,0,29,1 PACF ACF APGARCH GJR EGARCH

19 APGARCH t 1 Nelson and Cao

20 Ske Kur JB GARCH EGARCH cstv GJR cstv APGARCH OxMetrics6

21 APGARCH GJR Gamma APGARCH Delta

22 OX MPL MLE NLS APGARCH GJR ARFIMA ANFIS NNARX ARIMA

23 1 Arghyrou M, A Gregorio, M Pourpourides, 2009, Exchange Rate Uncertainty and Deviations from Purchasing Power Parity Evidence from the G7 Area, Cardiff Business School, Economics Section in Its Series, Cardiff Economics Working Papers, Number E Aloy, M Boutahar, M, Gente, K PeguinFeissolle, A 2011, Purchasing Power Parity and the Long Memory Properties of Real Exchange Rate Does One Size Fit All?, Economic Modelling, 28, pp Baillie, R and T Bollerslev 1989, Fractional Differencing Modeling and Forecasting of Eurocurrency Deposit Rates, Journal of Financial Reserch, 203, pp Barkoulas, J T Baum, C F Caglayan, M Chakraborty, A 2000, Persistent Dependent in Foreign Exchange Rates? A Reexamination, Boston College Department of Economics 5 Barkoulas, J, W Labys, and J Onochie 1999, Long Memory in Future Price, The Financial Review, 34, pp Bobeica, G and E Bojesteanu 2008, Long Memory in Volatility, An Investigation on the Central and Eastern Europen Exchange Rate, European Resrarch Studies Journal, 4, pp Booth G G, F R Kaen and P E Koveos 1982, RS Analysis of Foreign Exchange Markets Under Two International Monetary Regims, Jornal of Montary Economics, 10, pp Bulut, C, H Levent korap, C Saatcioglu,2007, Does Currency Substitution Affect Exchange Rate Uncertainty? The Case of Turkey, Munich Personal Repec Archive 9 Cheung, Y W 1993, Long Memory in ForeignExchange Rates, Journal of Business and Economic Statistics, 11, pp Ding Z,Granger WJ, and Engle RF 1993, A Long Memory Property of Stock Market Returns and a New Model, Journal of Empirical Finance1, pp 83106

24 11 Engel, C and J D Hamilton 1990, Long Swings in the Dollar Are They in the Date and Do Markets Know It?, American Review, 80, pp Glosten, L R R Jagannathan and D Runkle 1993, On the Relation Between the Expected Value and the Volatility of the Nominal Excess Return on Stocks, Journal of Finance, Vol 48, No 5, pp Kuan, CM and T Liu 1995, Forecasting Exchange Rates Feedforward and Recurrent Neural Network, Journal of Applied Econometrics, 10, pp Marcel Aloy, Mohamed Boutahar, Karine Gente, Anne Peguin Feissolle 2011, Purchasing Power Parity and the Long Memory Properties of Real Exchange Rates Does One Size Fit All?, Halshs , Version 1 15 Meese, R A and A K Rose 1991, An Empirical of Nonlinearities in Models of Exchange Rate Determination, Review of Economic Studies, 80, pp Morana, C and A Beltratti 2004, Structural Change and Long Range Dependence in Volatility of Exchange Rate Either, Neither or Both?, Journal of Empirical Finance, 11, pp Peters EE1999, Chaos and Order in the Capital Markets, Frst ed, Economics Science Press Beijing 18 Rahman, S, A Serletis 2009, The Effects of Exchange Rate Uncertainty on Exports, Journal of Macroeconomics, pp Schnabl, G 2008, Exchange Rate Volatility and Growth in Small Open Economies at the EMU Periphery, Economic System, pp Wojtowicz, T, H Gurgul 2009, Long Memory of Volatility Measures in Time Series, Badania operacyjne I decizje, pp Zakoian J M, 1994, Threshold Heteroscedastic Models, Journal of Economic Dynamics and Control, Vol 18, pp

Conditional Heteroscedasticity

1 Conditional Heteroscedasticity May 30, 2010 Junhui Qian 1 Introduction ARMA(p,q) models dictate that the conditional mean of a time series depends on past observations of the time series and the past