Adaptive signal processing of asset price dynamics with predictability analysis

In this paper we illustrate the optimal filtering of log returns of commodity prices in which both the mean and volatility are modulated by a hidden Markov chain with finite state space. The optimal estimate of the Markov chain and the parameters of the price model are given in terms of discrete-time recursive filters. We provide an application on a set of high frequency gold price data for the period 1973-2006 and analyse the h-step ahead price predictions against the Diebold-Kilian metric. Within the modelling framework where the mean and volatility are switching regimes, our findings suggest that a two-state hidden Markov model is sufficient to describe the dynamics of the data and the gold price is predictable up to a certain extent in the short term but almost impossible to predict in the long term. The proposed model is also benchmarked with ARCH and GARCH models with respect to price predictability and forecasting errors.

[1]  James D. Hamilton.  Time Series Analysis , 1994 .

[2]  K. Singleton,et al.  Term Structure Dynamics in Theory and Reality , 2002 .

[3]  A. Deaton,et al.  Competitive Storage and Commodity Price Dynamics , 1996, Journal of Political Economy.

[4]  N. Shephard,et al.  Stochastic Volatility: Likelihood Inference And Comparison With Arch Models , 1996 .

[5]  Sam Mirmirani,et al.  Gold Price, Neural Networks and Genetic Algorithm , 2004 .

[6]  Jeffrey S. Rosenthal,et al.  Probability and Statistics: The Science of Uncertainty , 2003 .

[7]  James D. Hamilton.  A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle , 1989 .

[8]  Eduardo S. Schwartz,et al.  Short-Term Variations and Long-Term Dynamics in Commodity Prices , 2000 .

[9]  Robert J. Elliott,et al.  Exact adaptive filters for Markov chains observed in Gaussian noise , 1994, Autom..

[10]  M. Nielsen,et al.  A Regime Switching Long Memory Model for Electricity Prices , 2006 .

[11]  T. Bollerslev,et al.  Generalized autoregressive conditional heteroskedasticity , 1986 .

[12]  Stephen Gray,et al.  Regime switching in foreign exchange rates : Evidence from currency option prices , 2000 .

[13]  Francis X. Diebold,et al.  Measuring Predictability: Theory and Macroeconomic Applications , 1997 .

[14]  Robert J. Elliott,et al.  Financial Signal Processing: A Self Calibrating Model , 2000 .

[15]  John B. Moore,et al.  Hidden Markov Models: Estimation and Control , 1994 .

[16]  D. Cox,et al.  Time series models : in econometrics, finance and other fields , 1997 .

[17]  Mary R. Hardy,et al.  A Regime-Switching Model of Long-Term Stock Returns , 2001 .

[18]  Michele Marchesi,et al.  A hybrid genetic-neural architecture for stock indexes forecasting , 2005, Inf. Sci..

[19]  Tung Liu,et al.  Stock Market Volatility and Regime Shifts in Returns , 1996, Inf. Sci..

[20]  Madalina Olteanu.  A descriptive method to evaluate the number of regimes in a switching autoregressive model , 2006, Neural Networks.

[21]  N. Shephard.  Statistical aspects of ARCH and stochastic volatility , 1996 .

[22]  Phelim P. Boyle,et al.  Pricing exotic options under regime switching , 2007 .

[23]  R. Engle.  Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation , 1982 .

[24]  Timo Teräsvirta,et al.  A Sequential Procedure for Determining the Number of Regimes in a Threshold Autoregressive Model , 2006 .

[25]  Robert J. Elliott,et al.  New finite-dimensional filters for parameter estimation of discrete-time linear Gaussian models , 1999, IEEE Trans. Autom. Control..

[26]  Wen‐ya Chang,et al.  On Dynamic Tax Reform with Regime Switching , 2006 .

[27]  New York Dover,et al.  ON THE CONVERGENCE PROPERTIES OF THE EM ALGORITHM , 1983 .

[28]  Eduardo S. Schwartz.  The stochastic behavior of commodity prices: Implications for valuation and hedging , 1997 .

[29]  Hao Zhou,et al.  Term Structure of Interest Rates with Regime Shifts , 2001 .