This article investigates the power of cusum and cusumsq tests for parameter stability and demonstrates that this depends on the nature of the structural change taking place. It turns out that neither version is uniformly superior to the other. A simple test on structural change in longmemory time series. H is a 2by97 logical matrix containing the sequence of decisions for each iteration of each cusum of squares test. The condition for the consistency of the test is also the same as the standard cusum.
Testing, monitoring, and dating structural changes. Formal tests for structural stability of the regression coefficients may be. I was given a task to find a structural break in labor productivity using the following regression model. We show that the local power of the cusum of squares test equals its size for a wide class of structural changes, as compared to a nontrivial local power for the cusum test.
A simulation study shows that a parameter change in garch models can mislead analysts to choose an igarch model. This paper follows up the seminal work of brown, durbin. Because the cusum chart is cumulative, even minor drifting in the process mean will cause steadily increasing or decreasing cumulative deviation values. From the graph above, we see that the plot of the recursive.
The celebrated chow 1960 test was based on the f statistic for detection of structural change with known change points. We conduct cusum tests of structural change in a rational addiction model of cigarette demand estimated using a panel of annual time series of statelevel data. We next derive the limiting distribution of the stopping time. In terms of estimation techniques, we mainly focus. Monitoring parameter constancy with endogenous regressors. This paper follows up the seminal work of brown, durbin, and.
The cusum test for detecting structural changes in strong mixing processes article pdf available in communication in statistics theory and methods 4317 march 2012 with 140 reads. The backward cusum detector sequentially cumulates the recursive residuals in reverse chronological order, whereas the stacked backward cusum detector considers a triangular array of backward. Ploberger and kr amer 1992 suggested to base a structural change test on cumulative sums of the common ols residuals. A cusum test in the linear regression model with serially. Introduction most classical tests against changes in the coe. A topic that gained more interest rather recently is to monitor structural change, i. It is well known that the conventional cusum test suffers from low power and large detection delay. The chow test and the nyblomhansen test can be performed by setting type to chow or nyblomhansen, respectively. A modified cusum test for orthogonal structural changes. Testing for structural stability in linear time series regression is a widely studied. Alternative boundaries for the common recursive or standard cusum test and the olsbased cusum test for structural change are suggested and their properties are examined by simulation of expected p values. Introduction and summary this paper follows up the seminal work of brown, durbin, and evans 1975. Therefore, the wellknown cusum test can be used on the di. Under the null hypothesis, there is no structural change, such that t 0 for all 1 t t, while, under the alternative hypothesis, the coe cient vector changes at unknown time t, where 1 cusum test, consist of a detector statistic and a critical boundary function.
Power properties of the cusum and cusumsq tests for. Under the null hypothesis, there is no structural change, such that t 0 for all 1 t t, while, under the alternative hypothesis, the coe cient vector changes at unknown time t, where 1 pdf. The test statistics change direction around iteration 50, which is consistent with the simulated break in volatility in the data. There is a large literature on tests of structural change.
April 20, 2005 abstract this chapter is concerned with methodological issues related to estimation, testing and computation in the context of structural changes in the linear models. According to hansen 2000, the tests su er from size distortions when a change in the parameters of the marginal process occurs. Introduction in the modeling of time series, structural stability is of prime importance. Testing structural change in timeseries nonparametric. Testing structural change in timeseries nonparametric regression models liangjun su and zhijie xiao we propose a cusum type of test for structural change in dynamic nonparametric regression models.
A simple test on structural change in longmemory time. This issue was popularised by david hendry, who argued that lack of stability of coefficients frequently caused forecast failure, and therefore we must routinely test. In particular, when the structural change is orthogonal to the mean regressor, the cusum test has virtually no power to detect it. Pdf the cusum test for detecting structural changes in. He also proposed a variation of the cusum test for parameter stability in. The poor power of the tests for early and late structural changes can be improved for the olsbased version, whereas this weakness of the. The limiting distributions of the maximum statistics under suitable sequences of alternatives are derived for retrospective testing and fixed endpoint monitoring. We therefore propose two alternative detector statistics. Robustness of the cusum and cusum ofsquares tests to. Typically, while we cannot necessarily reject the null hypothesis as soon as a structural change occurs, we can detect it with lags after the break date. Cusum test is essentially a test to detect instability in intercept alone. It introduces a unified approach for implementing these tests and presents how these ideas have been realized in an r package called strucchange. The power of the cusum test of parameter constancy over time in linear regression models crucially depends on the angle between the mean regressor and the structural change.
Lectures on structural change uw faculty web server. Description testing, monitoring and dating structural changes in linear regression models. When i use growth rates, which i was advised to do, and run. We consider the local power of the cusum and cusum of squares tests for structural change in the linear regression model. It is based upon the cumulative sums of weighted residuals from a single nonparametric regression and complements the conven. While both the backward cusum detector and the stacked backward cusum detector are suitable for retrospective testing, only the stacked backward cusum detector can be monitored online. Our findings suggest that these tests perform better in the context of a dynamic model of the adl type, which is not affected by serial correlation or nonpredetermined regressors even if overspecified. Mcconnell and gabriel perez quiros1 february 10, 2000. This issue was popularised by david hendry, who argued that lack of stability of coefficients frequently caused forecast failure, and. Structural change, garch1,1 model, cusum of squares test, model misspeci. Backward cusum for testing and monitoring structural change. The cusum test for detecting structural changes in.
The well known cusum test for structural change is investigated when there are lagged dependent variables among the regressors in a linear model. The test statistic 1, often called the olscusum test, measures the. Testing for structural change in conditional models. The first row corresponds to the forward cusum of squares test, and the second row corresponds to.
This method is applied to simulated data of some linear and nonlinear models and power of the test is evaluated. In a simulation study, we compare our test with a cusum test on. Cusum test for structural change matlab cusumtest mathworks. An r package for testing for structural change in linear regression models. A simple test on structural change in longmemory time series kai wenger achristian leschinski philipp sibbertsen aleibnizuniversityhannover april, 2017 abstract we propose a simple test on structural change in longrange dependent time series. Robustness of the cusum and cusumofsquares tests to serial. Due to the law of the iterated logarithm, oneshot tests cannot. Asymptotic consistency of this test statistics is shown. This paper introduces ideas and methods for testing for structural change in linear regression models and presents how these have been realized in an r package called strucchange1. The rst class includes in particular the cusum and mosum tests and the uctuation test, while the chow and the supf test belong to the latter. The cusum chart plots the cumulative sums cusums of the deviations of each sample value from the target value. This paper considers a modified cusum test, suggested by dufour 1982 for parameter instability and structural change with an unknown change point in a linear model with serially correlated distur. Testing, monitoring and dating structural changes in linear regression models.
This paper attempts to remedy this deciency by deriving the large sample distributions of the test statistics allowing for structural change in the marginal distribution of the regressors. The local power of the cusum and cusum of squares tests. No matter how large a structural shift has occurred, the cumulated ols. Besides the test types described in efp and sctest. Test is for constancy of all parameters test is not informative about the date or type of structural change test is applicable for models estimated by methods other than ols distribution of lis di. Testing for structural change in dynamic models jstor. Monitoring structural change contemporary tests for structural change deal with detections of the oneshot type. Extending standard significance tests it contains methods to fit, plot and test empirical fluctuation processes like cusum, mosum and. This paper introduces ideas and methods for testing for structural change in linear regression models and presents how these have been realized in an r package called strucchange.
Learning about the cusum procedure f 541 display a trend chart below the cusum chart that plots a systematic or. Such a property is known as structural invariance see engle et al. Hello, first let me tell you that im not so experienced in sas. You can create either a tabular cusum or a vmask cusum. Pdf the issue related to a structural break or change point in the econometric and.
Testing and dating of structural changes in practice. Pdf tests for structural breaks in time series analysis. A note on volatility persistence and structural changes in. The test can be performed using the cusum from recursive residuals the default or using the cusum from ols residuals.
683 732 1191 853 753 1229 426 1496 513 911 834 1413 805 1413 1009 145 1098 1087 1088 1422 718 176 1332 441 109 239 156 1378 1281 80 729 624 310 662 224 792 1279