A Bayesian Time Series Model of Multiple Structural Changes in Level, Trend, and Variance

We consider a deterministically trending dynamic time series model in which multiple structural changes in level, trend, and error variance are modeled explicitly and the number, but not the timing, of the changes is known. Estimation of the model is made possible by the use of the Gibbs sampler. The determination of the number of structural breaks and the form of structural change is considered as a problem of model selection, and we compare the use of marginal likelihoods, posterior odds ratios, and Schwarz's Bayesian model-selection criterion to select the most appropriate model from the data. We evaluate the efficacy of the Bayesian approach using a small Monte Carlo experiment. As empirical examples, we investigate structural changes in the U.S. ex post real interest rate and in a long time series of U.S. real gross domestic product.

[1]  P. Ferreira.  A Bayesian Analysis of a Switching Regression Model: Known Number of Regimes , 1975 .

[2]  L. Broemeling,et al.  Some Bayesian Inferences for a Changing Linear Model , 1980 .

[3]  Adrian F. M. Smith.  Change-Point problems: approaches and applications , 1980 .

[4]  N. B. Booth,et al.  A Bayesian approach to retrospective identification of change-points , 1982 .

[5]  Donald Holbert,et al.  A Bayesian analysis of a switching linear model , 1982 .

[6]  S. Zacks.  SURVEY OF CLASSICAL AND BAYESIAN APPROACHES TO THE CHANGE-POINT PROBLEM: FIXED SAMPLE AND SEQUENTIAL PROCEDURES OF TESTING AND ESTIMATION11Research supported in part by ONR Contracts N00014-75-0725 at The George Washington University and N00014-81-K-0407 at SUNY-Binghamton. , 1983 .

[7]  Frederic S. Mishkin,et al.  What Does the Term Structure Tell Us About Future Inflation? , 1988 .

[8]  P. Krishnaiah,et al.  19 Review about estimation of change points , 1988 .

[9]  Yi-Ching Yao.  Estimating the number of change-points via Schwarz' criterion , 1988 .

[10]  J. Richard,et al.  Econometrics and Structural Change. , 1988 .

[11]  Lawrence J. Christiano,et al.  Searching for a Break in Gnp , 1988 .

[12]  Lucrezia Reichlin,et al.  Segmented trends and non-stationary time series , 1989 .

[13]  A long-run view of the European monetary system , 1991 .

[14]  P. Perron,et al.  The Great Crash, The Oil Price Shock And The Unit Root Hypothesis , 1989 .

[15]  Christopher G. Lamoureux,et al.  Persistence in Variance, Structural Change, and the GARCH Model , 1990 .

[16]  P. Perron,et al.  Testing For A Unit Root In A Time Series With A Changing Mean , 1990 .

[17]  Adrian F. M. Smith,et al.  Sampling-Based Approaches to Calculating Marginal Densities , 1990 .

[18]  J. Stock,et al.  Recursive and Sequential Tests of the Unit Root and Trend Break Hypothesis: Theory and International Evidence , 1990 .

[19]  Robert F. Engle,et al.  Stock Volatility and the Crash of '87: Discussion , 1990 .

[20]  N. Kashiwagi.  Bayesian detection of structural changes , 1991 .

[21]  Charles J. Geyer,et al.  Practical Markov Chain Monte Carlo , 1992 .

[22]  D. Andrews,et al.  Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis , 1992 .

[23]  G. Casella,et al.  Explaining the Gibbs Sampler , 1992 .

[24]  B. Raj.  International Evidence on Persistence in Output in the Presence of an Episodic Change , 1992 .

[25]  P. Perron,et al.  Nonstationarity and Level Shifts With an Application to Purchasing Power Parity , 1992 .

[26]  Adrian F. M. Smith,et al.  Hierarchical Bayesian Analysis of Changepoint Problems , 1992 .

[27]  D. Zelhorst,et al.  Does output have a unit root? New international evidence , 1993 .

[28]  M. Tanner.  Tools for statistical inference: methods for the exploration of posterior distributions and likeliho , 1994 .

[29]  D. Andrews.  Tests for Parameter Instability and Structural Change with Unknown Change Point , 1993 .

[30]  C. Inclan,et al.  Detection of Multiple Changes of Variance Using Posterior Odds , 1993 .

[31]  M. Newton.  Approximate Bayesian-inference With the Weighted Likelihood Bootstrap , 1994 .

[32]  Pierre Perron,et al.  Additional Tests for a Unit Root Allowing for a Break in the Trend Function at an Unknown Time , 1998 .

[33]  The Distribution of Exchange Rates in the EMS , 1994 .

[34]  René Garcia,et al.  Série Scientifique Scientific Series an Analysis of the Real Interest Rate under Regime Shifts , 2022 .

[35]  David H. Papell,et al.  The Great Wars, the Great Crash, and the Unit Root Hypothesis: Some New Evidence About an Old Stylized Fact , 1994 .

[36]  Pierre Perron,et al.  Trend, Unit Root and Structural Change in Macroeconomic Time Series , 1994 .

[37]  P. Perron,et al.  Further Evidence on Breaking Trend Functions in Macroeconomic Variables. , 1997 .

[38]  Jun S. Liu,et al.  Covariance structure of the Gibbs sampler with applications to the comparisons of estimators and augmentation schemes , 1994 .

[39]  Adrian F. M. Smith,et al.  Simple conditions for the convergence of the Gibbs sampler and Metropolis-Hastings algorithms , 1994 .

[40]  D. Stephens.  Bayesian Retrospective Multiple‐Changepoint Identification , 1994 .

[41]  G. C. Tiao,et al.  Use of Cumulative Sums of Squares for Retrospective Detection of Changes of Variance , 1994 .

[42]  A. Gelfand,et al.  Bayesian Model Choice: Asymptotics and Exact Calculations , 1994 .

[43]  L. Tierney.  Markov Chains for Exploring Posterior Distributions , 1994 .

[44]  Eric Zivot,et al.  A Bayesian Analysis of Trend Determination in Economic Time Series , 1994 .

[45]  Martin D. D. Evans,et al.  Do expected shifts in inflation affect estimates of the long-run Fisher relation? , 1995 .

[46]  David H. Papell,et al.  The great wars, the great crash, and steady state growth: Some new evidence about an old stylized fact , 1995 .

[47]  Testing for a Break in Output: New International Evidence , 1995 .

[48]  David B. Dunson,et al.  Bayesian Data Analysis , 2010 .

[49]  Real exchange rates under the gold standard: can they be explained by the trend break model? , 1995 .

[50]  M. Chinn,et al.  DETERMINISTIC, STOCHASTIC, AND SEGMENTED TRENDS IN AGGREGATE OUTPUT: A CROSS-COUNTRY ANALYSIS , 1995 .

[51]  Bayesian Tests for Co-Integration in the Case of Structural Breaks: An Application to the Analysis of Wage Moderation in France , 1995 .

[52]  S. Chib.  Marginal Likelihood from the Gibbs Output , 1995 .

[53]  A. Maddison,et al.  Monitoring the world economy, 1820-1992 , 1995 .

[54]  C. Inclan,et al.  Detecting volatility changes across the oil sector , 1996 .

[55]  G. S. Maddala,et al.  Structural change and unit roots , 1996 .

[56]  G. Maddala,et al.  Bayesian Detection of Structural Changes , 1996 .

[57]  Chang‐Jin Kim,et al.  The Long-Run U.S./U.K. Real Exchange Rate , 1996 .

[58]  The Distribution of Exchange Rates in the EMS , 1996 .

[59]  Siddhartha Chib,et al.  Markov Chain Monte Carlo Simulation Methods in Econometrics , 1996, Econometric Theory.

[60]  L. Wasserman,et al.  Computing Bayes Factors by Combining Simulation and Asymptotic Approximations , 1997 .

[61]  W. Fong.  Volatility Persistence and Switching ARCH in Japanese Stock Returns , 1997 .

[62]  J. Bai,et al.  Estimating Multiple Breaks One at a Time , 1997, Econometric Theory.

[63]  J. Bai,et al.  Estimation of a Change Point in Multiple Regression Models , 1997, Review of Economics and Statistics.

[64]  Arjun K. Gupta,et al.  Testing and Locating Variance Changepoints with Application to Stock Prices , 1997 .

[65]  J. Zidek,et al.  ON SEGMENTED MULTIVARIATE REGRESSION , 1997 .

[66]  David H. Papell,et al.  IS THERE A UNIT ROOT IN THE INFLATION RATE? EVIDENCE FROM SEQUENTIAL BREAK AND PANEL DATA MODELS , 1997 .

[67]  Robin L. Lumsdaine,et al.  Multiple Trend Breaks and the Unit-Root Hypothesis , 1997, Review of Economics and Statistics.

[68]  Timothy J. Vogelsang,et al.  Wald-Type Tests for Detecting Breaks in the Trend Function of a Dynamic Time Series , 1997, Econometric Theory.

[69]  Robin L. Lumsdaine,et al.  Unit roots, postwar slowdowns and long-run growth: Evidence from two structural breaks , 1998 .

[70]  Testing for a unit root in ERM exchange rates in the presence of structural breaks: evidence from the bootstrap , 1998 .

[71]  S. Chib.  Estimation and comparison of multiple change-point models , 1998 .

[72]  J. Stock,et al.  Testing for and Dating Common Breaks in Multivariate Time Series , 1998 .

[73]  Chang‐Jin Kim,et al.  Has the U.S. Economy Become More Stable? A Bayesian Approach Based on a Markov-Switching Model of the Business Cycle , 1999, Review of Economics and Statistics.

[74]  David H. Papell.  The Great Appreciation, the Great Depreciation, and the Purchasing Power Parity Hypothesis , 2002 .