Least Squares Estimation and Tests of Breaks in Mean and Variance Under Misspecification

In this paper we investigate the consequences of misspecification on the large sample properties of change-point estimators and the validity of tests of the null hypothesis of linearity versus the alternative of a structural break. Specifically this paper concentrates on the interaction of structural breaks in the mean and variance of a time series when either of the two is omitted from the estimation and inference procedures. Our analysis considers the case of a break in mean under omitted-regime-dependent heteroscedasticity and that of a break in variance under an omitted mean shift. The large and finite sample properties of the resulting least-squares-based estimators are investigated and the impact of the two types of misspecification on inferences about the presence or absence of a structural break subsequently analysed. Copyright Royal Economic Socciety 2004(This abstract was borrowed from another version of this item.)

[1]  J. Stock,et al.  A Comparison of Linear and Nonlinear Univariate Models for Forecasting Macroeconomic Time Series , 1998 .

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

[3]  D. Dijk,et al.  Short-term Volatility Versus Long-term Growth: Evidence in US Macroeconomic Time Series , 2001 .

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

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

[6]  Terence Tai Leung Chong,et al.  STRUCTURAL CHANGE IN AR(1) MODELS , 2001, Econometric Theory.

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

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

[9]  W. Newey,et al.  Large sample estimation and hypothesis testing , 1986 .

[10]  Filippo Altissimo,et al.  Strong Rules for Detecting the Number of Breaks in a Time Series , 2003 .

[11]  P. Perron,et al.  Estimating and testing linear models with multiple structural changes , 1995 .

[12]  J. Stock,et al.  Evidence on Structural Instability in Macroeconomic Time Series Relations , 1994 .

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

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

[15]  B. Hansen.  Approximate Asymptotic P Values for Structural-Change Tests , 1997 .

[16]  David V. Hinkley,et al.  Inference about the change-point in a sequence of binomial variables , 1970 .

[17]  Francis X. Diebold,et al.  Testing structural stability with endogenous breakpoint A size comparison of analytic and bootstrap procedures , 1996 .

[18]  Bruce E. Hansen,et al.  Testing for structural change in conditional models , 2000 .

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

[20]  Victor Solo,et al.  Asymptotics for Linear Processes , 1992 .

[21]  L. Horváth,et al.  Limit Theorems in Change-Point Analysis , 1997 .

[22]  Margaret Mary McConnell,et al.  Output Fluctuations in the United States: What Has Changed Since the Early 1980s? , 1998 .

[23]  S. Panchapakesan,et al.  Inference about the Change-Point in a Sequence of Random Variables: A Selection Approach , 1988 .

[24]  Jiahui Wang,et al.  A Bayesian Time Series Model of Multiple Structural Changes in Level, Trend, and Variance , 2000 .