Testing for Smooth Structural Changes in Time Series Models via Nonparametric Regression

Checking parameter stability of econometric models is a long‐standing problem. Almost all existing structural change tests in econometrics are designed to detect abrupt breaks. Little attention has been paid to smooth structural changes, which may be more realistic in economics. We propose a consistent test for smooth structural changes as well as abrupt structural breaks with known or unknown change points. The idea is to estimate smooth time‐varying parameters by local smoothing and compare the fitted values of the restricted constant parameter model and the unrestricted time‐varying parameter model. The test is asymptotically pivotal and does not require prior information about the alternative. A simulation study highlights the merits of the proposed test relative to a variety of popular tests for structural changes. In an application, we strongly reject the stability of univariate and multivariate stock return prediction models in the postwar and post‐oil‐shocks periods.     

Tests for Parameter Instability in Regressions with 1(1) Processes

This article derives the large-sample distributions of Lagrange multiplier (LM) tests for parameter instability against several alternatives of interest in the context of cointegrated regression models. The fully modified estimator of Phillips and Hansen is extended to cover general models with stochastic and deterministic trends. The test statistics considered include the SupF test of Quandt, as well as the LM tests of Nyblom and of Nabeya and Tanaka. It is found that the asymptotic distributions depend on the nature of the regressor processes—that is, if the regressors are stochastic or deterministic trends. The distributions are noticeably different from the distributions when the data are weakly dependent. It is also found that the lack of cointegration is a special case of the alternative hypothesis considered (an unstable intercept), so the tests proposed here may also be viewed as a test of the null of cointegration against the alternative of no cointegration. The tests are applied to three data sets—an aggregate consumption function, a present value model of stock prices and dividends, and the term structure of interest rates.     

Testing Parameter Constancy in Unit Root Autoregressive Models Against Multiple Continuous Structural Changes

This article considers tests for logistic smooth transition autoregressive (LSTAR) models accommodating multiple time dependent transitions between regimes when the data generating process is a random walk. The asymptotic null distributions of the tests, in contrast to the standard results in Lin and Teräsvirta (1994 Lin , C. F. J. , Teräsvirta , T. ( 1994 ). Testing the constancy of regression parameters against continuous structural change . Journal of Econometrics 62 : 211 – 228 .[Crossref], [Web of Science ®] , [Google Scholar]), are nonstandard. Monte Carlo experiments reveal that the tests have modest size distortions and satisfactory power against LSTAR models with multiple smooth breaks. The tests are applied to Swedish unemployment rates and the hysteresis hypothesis is over-turned in favour of an LSTAR model with two transitions between extreme regimes.