Bayesian analysis of multiple thresholds autoregressive model

Bayesian analysis of threshold autoregressive (TAR) model with various possible thresholds is considered. A method of Bayesian stochastic search selection is introduced to identify a threshold-dependent sequence with highest probability. All model parameters are computed by a hybrid Markov chain Monte Carlo method, which combines Metropolis–Hastings algorithm and Gibbs sampler. The main innovation of the method introduced here is to estimate the TAR model without assuming the fixed number of threshold values, thus is more flexible and useful. Simulation experiments and a real data example lend further support to the proposed approach.

[1]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .

[2]  Ruey S. Tsay,et al.  Testing and Modeling Threshold Autoregressive Processes , 1989 .

[3]  Bayesian Model Selection for Heteroskedastic Models , 2008 .

[4]  Ruey S. Tsay,et al.  Analysis of Financial Time Series: Tsay/Analysis of Financial Time Series , 2005 .

[5]  Cathy W. S. Chen,et al.  A Bayesian threshold nonlinearity test for financial time series , 2005 .

[6]  Howell Tong,et al.  TESTING FOR A LINEAR MA MODEL AGAINST THRESHOLD MA MODELS , 2005 .

[7]  Hung Man Tong,et al.  Threshold models in non-linear time series analysis. Lecture notes in statistics, No.21 , 1983 .

[8]  R. McCulloch,et al.  Bayesian Inference and Prediction for Mean and Variance Shifts in Autoregressive Time Series , 1993 .

[9]  Mohamed A. Ismail,et al.  Bayesian inference for threshold moving average models , 2003 .

[10]  Donald Geman,et al.  Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images , 1984 .

[11]  Chris Brooks,et al.  Can we explain the dynamics of the UK FTSE 100 stock and stock index futures markets? , 2002 .

[12]  S. Chib,et al.  Understanding the Metropolis-Hastings Algorithm , 1995 .

[13]  A Bayesian analysis of generalized threshold autoregressive models , 1998 .

[14]  Diana Adler.  Non Linear Time Series A Dynamical System Approach , 2016 .

[15]  K. Chan,et al.  Testing for threshold autoregression , 1990 .

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

[17]  Howell Tong,et al.  Ergodicity and invertibility of threshold moving-average models , 2007 .

[18]  P. Morettin.  BAYESIAN ANALYSIS OF THRESHOLD AUTOREGRESSIVE MOVING AVERAGE MODELS , 2002 .

[19]  B. Hansen.  Threshold autoregression in economics , 2011 .

[20]  H. Tong.  On a threshold model , 1978 .

[21]  Cathy W. S. Chen,et al.  BAYESIAN INFERENCE OF THRESHOLD AUTOREGRESSIVE MODELS , 1995 .

[22]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[23]  John Geweke,et al.  BAYESIAN THRESHOLD AUTOREGRESSIVE MODELS FOR NONLINEAR TIME SERIES , 1993 .

[24]  É. Moulines,et al.  Least‐squares Estimation of an Unknown Number of Shifts in a Time Series , 2000 .

[25]  Cathy W. S. Chen,et al.  Bayesian Estimation for Parsimonious Threshold Autoregressive Models in R , 2009 .

[26]  Cathy W. S. Chen,et al.  Falling and explosive, dormant, and rising markets via multiple-regime financial time series models , 2010 .