Testing for Parameter Instability in Competing Modeling Frameworks

We develop a new parameter stability test against the alternative of observation driven generalized autoregressive score dynamics. The new test generalizes the ARCH-LM test of Engle (1982) to settings beyond time-varying volatility and exploits any autocorrelation in the likelihood scores under the alternative. We compare the test's performance with that of alternative tests developed for competing time-varying parameter frameworks, such as structural breaks and observation driven parameter dynamics. The new test has higher and more stable power against alternatives with frequent regime switches or with non-local parameter driven time-variation. For parameter driven time variation close to the null or for infrequent structural changes, the test of Muller and Petalas (2010) performs best overall. We apply all tests empirically to a panel of losses given default over the period 1982--2010 and find significant evidence of parameter variation in the underlying beta distribution.

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

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

[3]  H. Manner,et al.  Dynamic stochastic copula models: Estimation, inference and applications , 2012 .

[4]  R. Engle,et al.  A Multiple Indicators Model for Volatility Using Intra-Daily Data , 2003 .

[5]  Ruey S. Tsay,et al.  High Dimensional Dynamic Stochastic Copula Models , 2014 .

[6]  T. Ouarda,et al.  Generalized autoregressive conditional heteroscedasticity modelling of hydrologic time series , 2012 .

[7]  A. Harvey.  Dynamic Models for Volatility and Heavy Tails: With Applications to Financial and Economic Time Series , 2013 .

[8]  Andre Lucas,et al.  TI 11-042 / DSF 16 Observation Driven Mixed-Measurement Dynamic Factor Models with an Application to Credit Risk , 2011 .

[9]  Luc Bauwens,et al.  The Stochastic Conditional Duration Model: A Latent Factor Model for the Analysis of Financial Durations , 2004 .

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

[11]  Anke Schmid.  Advances In Econometrics Fifth World Congress , 2016 .

[12]  Jeffrey R. Russell.  Econometric Modeling of Multivariate Irregularly-Spaced High-Frequency Data , 2000 .

[13]  John H. H. Lee.  A Lagrange Multiplier Test for Garch Models , 1991 .

[14]  M. Pitt,et al.  Likelihood analysis of non-Gaussian measurement time series , 1997 .

[15]  Efficient Estimation of the Parameter Path in Unstable Time Series Models , 2010 .

[16]  B. Hansen.  The New Econometrics of Structural Change: Dating Breaks in U.S. Labour Productivity , 2001 .

[17]  J. Richard,et al.  Efficient high-dimensional importance sampling , 2007 .

[18]  Andrew J. Patton,et al.  Dynamic Copula Models and High Frequency Data , 2013 .

[19]  Drew D. Creal,et al.  Generalized autoregressive score models with applications ∗ , 2010 .

[20]  Siem Jan Koopman,et al.  A Dynamic Multivariate Heavy-Tailed Model for Time-Varying Volatilities and Correlations , 2010 .

[21]  J. Durbin,et al.  Monte Carlo maximum likelihood estimation for non-Gaussian state space models , 1997 .

[22]  Andrew J. Patton.  Modelling Asymmetric Exchange Rate Dependence , 2006 .

[23]  Pierre Perron,et al.  Dealing with Structural Breaks , 2005 .

[24]  Graham Elliott,et al.  Efficient Tests for General Persistent Time Variation in Regression Coefficients , 2006 .

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

[26]  D. Andrews.  Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation , 1991 .

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

[28]  Andrew Harvey,et al.  Testing for deterministic trend and seasonal components in time series models , 1983 .

[29]  Maxwell L. King,et al.  Locally Best Invariant Tests of the Error Covariance Matrix of the Linear Regression Model , 1985 .

[30]  J. Nyblom,et al.  Comparisons of Tests for the Presence of Random Walk Coefficients in a Simple Linear Model , 1983 .

[31]  Andrew Harvey,et al.  Forecasting, Structural Time Series Models and the Kalman Filter. , 1991 .

[32]  F. Fisher.  Tests of Equality Between Sets of Coefficients in Two Linear Regressions: An Expository Note , 1970 .

[33]  D. Andrews,et al.  Optimal Tests When a Nuisance Parameter Is Present Only Under the Alternative , 1992 .

[34]  Siem Jan Koopman,et al.  Time Series Analysis by State Space Methods , 2001 .

[35]  P. Perron,et al.  Estimating and Testing Structural Changes in Multivariate Regressions , 2007 .

[36]  W. Krämer,et al.  A new test for structural stability in the linear regression model , 1989 .

[37]  Andrew J. Patton,et al.  Time-Varying Systemic Risk: Evidence From a Dynamic Copula Model of CDS Spreads , 2013 .

[38]  P. Perron,et al.  Computation and Analysis of Multiple Structural-Change Models , 1998 .

[39]  J. MacKinnon,et al.  Specification Tests Based on Artificial Regressions , 1990 .

[40]  Hedley Rees,et al.  Advances in Econometrics: Fifth World Congress, Volume II. , 1988 .

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

[42]  W. Dunsmuir,et al.  Observation-driven models for Poisson counts , 2003 .

[43]  N. Shephard.  Stochastic Volatility: Selected Readings , 2005 .

[44]  J. Nyblom.  Testing for the Constancy of Parameters over Time , 1989 .

[45]  S. Koopman,et al.  Predicting Time-Varying Parameters with Parameter-Driven and Observation-Driven Models , 2012 .

[46]  Fabrizio Cipollini,et al.  Semiparametric Vector MEM , 2008 .

[47]  Drew D. Creal.  A Survey of Sequential Monte Carlo Methods for Economics and Finance , 2012 .

[48]  Siem Jan Koopman,et al.  Time Series Analysis of Non-Gaussian Observations Based on State Space Models from Both Classical and Bayesian Perspectives , 1999 .