Testing for smooth structural changes in time series models via nonparametric regression (original) (raw)

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.

A sequential approach to testing for structural change in econometric models

Empirical Economics, 1989

The paper shows that the sequential approach to testing econometric models, particularly testing for structural change, is both feasible and potentially very useful. In fact, this paper makes clear the possibility of using the sequential approach as suggested by Dhrymes et al. (1972) and shows that the statistical dependence between successive tests can be overcome in some cases.

Detecting for Smooth Structural Changes in Garch Models

Econometric Theory, 2015

Detecting and modeling structural changes in GARCH processes have attracted increasing attention in time series econometrics. In this paper, we propose a new approach to testing structural changes in GARCH models. The idea is to compare the log likelihood of a time-varying parameter GARCH model with that of a constant parameter GARCH model, where the time-varying GARCH parameters are estimated by a local quasi-maximum likelihood estimator (QMLE) and the constant GARCH parameters are estimated by a standard QMLE. The test does not require any prior information about the alternatives of structural changes. It has an asymptotic N(0,1) distribution under the null hypothesis of parameter constancy and is consistent against a vast class of smooth structural changes as well as abrupt structural breaks with possibly unknown break points. A consistent parametric bootstrap is employed to provide a reliable inference in finite samples and a simulation study highlights the merits of our test.

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.

Characterizing Economic Growth Paths Based on New Structural Change Tests

Economic Inquiry, 2014

One of the prevalent topics in the economic growth literature is the debate between neoclassical, semi-endogenous, and endogenous growth theories regarding the model that best describes the data. An important part of this discussion can be summarized in three mutually exclusive hypotheses: the "constant trend", the "level shift", and the "slope shift" hypotheses. In this paper we propose the characterization of a country's economic growth path according to these break hypotheses. We address the problem in two steps. First, the number and timing of trend breaks is determined using new structural change tests that are robust to the presence, or not, of unit roots, surpassing technical and methodological concerns of previous empirical studies. Second, conditional on the estimated number of breaks, break dates, and coefficients, a statistical framework is introduced to test for general linear restrictions on the coefficients of the suggested linear disjoint broken trend model. We further show how the aforementioned hypotheses, regarding the economic growth path, can be analysed by a test of linear restrictions on the parameters of the breaking trend model. We apply the methodology to historical per capita GDP for an extensive list of countries. The results support the three alternative hypotheses for different sets of countries. (JEL C22, F43, O40)

Testing the constancy of regression parameters against continuous structural change

Journal of Econometrics, 1994

A standard explicit or implicit assumption underlying many parameter constancy tests in linear models is that there is a single structural break in the sample. In this paper that assumption is replaced by a more general one stating that the parameters of the model may change continuously over time. The pattern of change is parameterized giving rise to a set of parameter constancy tests against a parameterized alternative. The power properties of the LM type tests in small samples are compared to those of other tests like the CUSUM and Fluctuation

The properties of cointegration tests in models with structural change

In this paper we examine, by means of Monte Carlo simulation, the properties of several cointegration tests when long run parameters are subject to structural changes. We allow for di¤erent types of stochastic and deterministic regime shifts, more speci…cally, changes governed by Markov chains, martingale parameter variation, sudden multiple breaks and gradual changes. Our Monte Carlo analysis reveals that tests with cointegration as the null hypothesis perform badly, while tests with the null of no cointegration retain much of their usefulness in this context.

On the Usefulness or Lack Thereof of Optimality Criteria for Structural Change Tests

Econometric Reviews, 2014

considered the problem of testing for general types of parameter variations, including infrequent breaks. They developed a framework that yields optimal tests, in the sense that they nearly attain some local Gaussian power envelop. The main ingredient in their setup is that the variance of the process generating the changes in the parameters must go to zero at a fast rate. They recommended the so-calledqLL test, a partial sums type test based on the residuals obtained from the restricted model. We show that for breaks that are very small, its power is indeed higher than other tests, including the popular sup-Wald test. However, the differences are very minor. When the magnitude of change is moderate to large, the power of the test is very low in the context of a regression with lagged dependent variables or when a correction is applied to account for serial correlation in the errors. In many cases, the power goes to zero as the magnitude of change increases. The power of the sup-Wald test does not show this non-monotonicity and its power is far superior to thê qLL test when the break is not very small. We claim that the optimality of theqLL test does not come from the properties of the test statistics but the criterion adopted, which is not useful to analyze structural change tests. Instead, we use the concept of the relative approximate Bahadur slopes to assess the relative efficiency of two tests. When doing so, it is shown that the sup-Wald test indeed dominates theqLL test and, in many cases, the latter has zero relative asymptotic efficiency. JEL Classification Number: C22.

Parametric Inference using Structural Break Tests

The Stata Journal: Promoting communications on statistics and Stata, 2013

We present methods for testing hypotheses and estimating confidence sets for structural parameters of economic models in the presence of instabilities and breaks of unknown form. These methods constructively explore information generated by changes in the data-generating process to improve the inference of parameters that remain stable over time. The proposed methods are suitable for models cast in the generalized method of moments framework, which makes their application wide. Moreover, they are robust to the presence of weak instruments. The genstest command in Stata implements these methods to conduct hypothesis tests and to estimate confidence sets.

Testing for Structural Breaks and other forms of Non-stationarity: a Misspecification Perspective

2006

In the 1980s and 1990s the issue of non-stationarity in economic time series has been in the context of unit roots vs. mean trends in AR(p) models. More recently this perspective has been extended to include structural breaks. In this paper we take a much broader perspective by viewing the problem as one of misspecification testing: assessing the stationarity of the underlying process. The proposed misspecification testing procedure relies on resampling techniques to enhance the informational content of the observed data in an attempt to capture heterogeneity 'locally' using rolling window estimators of the primary moments of the stochastic process. The effectiveness of the testing procedure is assessed using extensive Monte Carlo simulations.