A Trend-Switching Financial Time Series Model with Level-Duration Dependence

The financial time series model that can capture the nonlinearity and asymmetry of stochastic process has been paid close attention for a long time. However, it is still open to completely overcome the difficult problem that motivates our researches in this paper. An asymmetric and nonlinear model with the change of local trend depending on local high-low turning point process is first proposed in this paper. As the point process can be decomposed into the two different processes, a high-low level process and an up-down duration process, we then establish the so-called trend-switching model which depends on both level and duration (Trend-LD). The proposed model can predict efficiently the direction and magnitude of the local trend of a time series by incorporating the local high-low turning point information. The numerical results on six indices in world stock markets show that the proposed Trend-LD model is suitable for fitting the market data and able to outperform the traditional random walk model.

[1]  L. Bauwens,et al.  The Logarithmic Acd Model: An Application to the Bid-Ask Quote Process of Three NYSE Stocks , 2000 .

[2]  S. Manganelli.  Duration, Volume and Volatility Impact of Trades , 2002, SSRN Electronic Journal.

[3]  R. Brown.  XXVII. A brief account of microscopical observations made in the months of June, July and August 1827, on the particles contained in the pollen of plants; and on the general existence of active molecules in organic and inorganic bodies , 1828 .

[4]  Jun Cai.  A Markov Model of Switching-Regime ARCH , 1994 .

[5]  James D. Hamilton.  Specification testing in Markov-switching time-series models , 1996 .

[6]  R. Tsay.  Analysis of Financial Time Series: Tsay/Financial Time Series 3E , 2010 .

[7]  F. Fabozzi,et al.  An autoregressive conditional duration model of credit‐risk contagion , 2005 .

[8]  D. Kugiumtzis.  Local prediction of turning points of oscillating time series. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  Michael W. Brandt,et al.  Range-Based Estimation of Stochastic Volatility Models , 2001 .

[10]  Thomas H. McCurdy,et al.  Duration-Dependent Transitions in a Markov Model of U.S. GNP Growth , 1994 .

[11]  Arthur F. Burns,et al.  Measuring Business Cycles. , 1946 .

[12]  S. Beckers,et al.  Variances of Security Price Returns Based on High , 1983 .

[13]  Robert F. Engle,et al.  The Econometrics of Ultra-High Frequency Data , 1996 .

[14]  F. Diebold,et al.  Comparing Predictive Accuracy , 1994, Business Cycles.

[15]  Joann Jasiak,et al.  Persistence in Intertrade Durations , 1999 .

[16]  Rayleigh.  The Problem of the Random Walk , 1905, Nature.

[17]  Joachim Grammig,et al.  Modeling the interdependence of volatility and inter-transaction duration processes , 2002 .

[18]  Effects of NYMEX trading on IPE Brent Crude futures markets: a duration analysis , 2004 .

[19]  Andrew Ang,et al.  Regime Switches in Interest Rates , 1998 .

[20]  P. Mazur.  On the theory of brownian motion , 1959 .

[21]  Ruey S. Tsay,et al.  A nonlinear autoregressive conditional duration model with applications to financial transaction data , 2001 .

[22]  Ruey S. Tsay,et al.  Analysis of Financial Time Series , 2005 .

[23]  Robert F. Engle,et al.  Forecasting the frequency of changes in quoted foreign exchange prices with the autoregressive conditional duration model , 1997 .

[24]  Chang‐Jin Kim,et al.  Dynamic linear models with Markov-switching , 1994 .

[25]  R. Chou,et al.  Forecasting Financial Volatilities with Extreme Values: The Conditional Autoregressive Range (CARR) Model , 2005 .

[26]  W. E. Wecker,et al.  Predicting the Turning Points of a Time Series , 1979 .

[27]  Joachim Grammig,et al.  Non-monotonic hazard functions and the autoregressive conditional duration model , 2000 .

[28]  F. Canova.  Detrending and business cycle facts , 1998 .

[29]  C. Granger,et al.  Co-integration and error correction: representation, estimation and testing , 1987 .

[30]  Alan T. K. Wan,et al.  A High-Low Model of Daily Stock Price Ranges , 2008, SSRN Electronic Journal.

[31]  G. Uhlenbeck,et al.  On the Theory of the Brownian Motion , 1930 .

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

[33]  R. Folk,et al.  Poisson‐Voronoi核形成と成長変形における分域構造の時間発展:一次元と三次元の結果 , 2008 .

[34]  R. Chou,et al.  Modeling the Asymmetry of Stock Movements Using Price Ranges , 2006 .

[35]  A. Sinha,et al.  The Impact of Time Duration between Trades on the Price of Treasury Note Futures Contracts , 2004 .

[36]  Troy A. Davig.  Regime-switching debt and taxation , 2004 .

[37]  D. Osborn,et al.  Business Cycles for G7 and European Countries , 1997 .

[38]  T. Teräsvirta.  Specification, Estimation, and Evaluation of Smooth Transition Autoregressive Models , 1994 .

[39]  Eduardo S. Schwartz,et al.  Investment Under Uncertainty. , 1994 .

[40]  Keith H. Black.  International Asset Allocation with Regime Shifts , 2003 .

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

[42]  Jeffrey R. Russell,et al.  Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data , 1998 .

[43]  Timo Teräsvirta,et al.  Modelling Economic Relationships with Smooth Transition Regressions , 1996 .

[44]  L. Bauwens,et al.  The stochastic conditional duration model: a latent variable model for the analysis of financial durations , 2004 .

[45]  Howell Tong,et al.  Non-Linear Time Series , 1990 .

[46]  H. Tong,et al.  Threshold Autoregression, Limit Cycles and Cyclical Data , 1980 .