Testing the constancy of regression parameters against continuous structural change (original) (raw)

Testing for Structural Change: A Misspecification Testing Perspective

2005

Testing for structural change (t-heterogeneity of parameters) is of great interest to researchers both in econometrics and statistics. In this paper we develop an approach to testing the t-invariance of the model parameters, by using the information in the marginal and joint distributions of the stochastic processes involved. The proposed procedure differs from the testing procedures suggested in the literature in two important ways: First, it is designed to detect t-heterogeneity that is a smooth function of time (t) rather than a discrete shift. Second it is based on rolling window estimates of the moments of the variables, rather than the residuals or the coefficients from the regression. Focusing on marginal and joint moments provides a more general perspective because it encompasses changes in the regression coefficients and/or the residual variance. The Maximum Entropy (ME) density Bootstrap of Vinod is an essential component of our procedure because it provides a reliable resampling algorithm for short nonstationary time series. We carry out a number of Monte Carlo simulations to evaluate the performance of the proposed testing procedure when the t-heterogeneity comes in the form of smooth functions of t, such as the Linear, Quadratic, Exponential and the Logistic. Results show that the testing procedure is effective even for small samples. Furthermore, it clearly distinguishes whether the model t-heterogeneity arises from changes in the mean or variance of the process. While this procedure is designed to capture smooth trends, the experimental results indicate that it can also be successfully applied to testing discrete single breaks.

Testing for Stability in Regression Models

Analysing Economic Data, 2014

An implicit assumption in all regression models is that their coeffi cients remain constant across all observations. When they do not-and this occurs regularly with time series data in particular-the problem of structural change is encountered. Aft er presenting a simulation example of a typical structural break in a regression, methods are introduced to test for such breaks, whether at a known point in time or when the breakpoint is unknown. An approach to modelling changing parameters using dummy variables is introduced and a detailed example of a shift ing regression relationship between infl ation and interest rates brought about by policy regime changes is presented.

On the reliability of Chow-type tests for parameter constancy in multivariate dynamic models

Economics Letters, 2001

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Exact Tests Structural Change in First-Order Dynamic Models

RePEc: Research Papers in Economics, 1995

Several finite-sample tests of parameter constancy against the presence of structural change are proposed for a linear regression model with one lagged dependent variable and independent normal disturbances. The procedures derived include analysis-ofcovariance, CUSUM, CUSUM-of-squares, and predictive tests. The approach used to obtain the tests involves the application of three techniques: derivation of an exact confidence set for the autoregressive parameter (based on using an appropriately extended regression), a union-intersection technique, and (when required) randomization. The tests proposed are illustrated with some artificial data and applied to a dynamic trend model of gross private domestic investment in the U.S.

Testing for smooth structural changes in time series models via nonparametric regression

Checking parameter stability of economic models is a long-standing problem in time series econometrics. A classical econometric procedure is test, which checks for the existence of a structural change on a known date. Various extensions have been made to test multiple changes with known or unknown change points. However, almost all existing structural change tests in econometrics are deigned to detect abrupt breaks. Little attention has been paid to smooth structural changes, which may be more realistic in economics. This paper proposes two consistent tests for smooth structural changes as well as abrupt structural breaks with known or unknown change points. The idea is to estimate the smooth time-varying parameters by local smoothing and compare them with the OLS parameter estimator. The …rst test compares the sums of squared residuals of the restricted constant parameter model and the unrestricted nonparametric time-varying parameter model, in a spirit similar to Chow's (1960) F test. The second test compares the …tted values of the restricted and unrestricted models, which can be viewed as a generalization of Hausman's (1978) test. Both tests have a convenient asymptotic N(0,1) distribution and do not require any prior information about the alternatives. Interestingly, unlike Chow's (1960) test, the generalized Chow test is no longer optimal; it is asymptotically less powerful than the generalized Hausman test. A simulation study highlights the merits of the proposed tests in comparison with a variety of popular tests for structural changes.

The Cusum Test for Parameter Change in Regression Models with ARCH Errors

JOURNAL OF THE JAPAN STATISTICAL SOCIETY, 2004

In this paper we consider the problem of testing for a parameter change in regression models with ARCH errors based on the residual cusum test. It is shown that the limiting distribution of the residual cusum test statistic is the sup of a Brownian bridge. Through a simulation study, it is demonstrated that the proposed test circumvents the drawbacks of Kim et al.'s (2000) cusum test. For illustration, we apply the residual cusum test to the return of yen/dollar exchange rate data.

Statistical analysis of “structural change”: An annotated bibliography

Empirical Economics, 1989

The typical "structural change" situation is -from the point of view of a statistician -as follows: To cope with a particular economic phenomenon a model is specified, and it is suspected that for different periods of time, or for different spatial regions, different sets of parameter values are needed in order to describe the reality adequately; the "change point" which separates these periods, or regions, is Unknown. Questions that arise in this context include: Is it necessary to assume that the parameters are changing? When, or where, does a change occur or -if it takes place over a certain period of time -what is its onset and duration? How much do parameters before and after the change differ? What type of model is appropriate in a particular situation (e.g., two-phase regression, stochastic parameter models)?