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Change Point Statistics of Rényi Type
Abstract
This is the presentation for my first oral examination. In this presentation I discuss change point test statistics of Rényi-type. Change point tests are statistical tests to determine whether the parameters of a model are constant over a window of (serial) data or whether, at some unknown point, the parameters of the model change. In this presentation I discuss a new change point test statistic that is well equipped to detect structural change when the change occurs very early or late in the window. Using simulation studies I demonstrate that the statistic does better than other well-known and popular statistics at detecting early/late changes. I also demonstrate how the statistic performs when computed on the residuals of the Fama-French five-factor model computed for a portfolio of banking sector stocks near the 2008 financial crisis.
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A five-factor model directed at capturing the size, value, profitability, and investment patterns in average stock returns performs better than the three-factor model of Fama and French (FF, 1993). The five-factor model's main problem is its failure to capture the low average returns on small stocks whose returns behave like those of firms that invest a lot despite low profitability. The model's performance is not sensitive to the way its factors are defined. With the addition of profitability and investment factors, the value factor of the FF three-factor model becomes redundant for describing average returns in the sample we examine.
This paper gives an account of some of the recent work on structural breaks in time series models. In particular, we show how procedures based on the popular cumulative sum, CUSUM, statistics can be modified to work also for data exhibiting serial dependence. Both structural breaks in the unconditional and conditional mean as well as in the variance and covariance/correlation structure are covered. CUSUM procedures are nonparametric by design. If the data allows for parametric modeling, we demonstrate how likelihood approaches may be utilized to recover structural breaks. The estimation of multiple structural breaks is discussed. Furthermore, we cover how one can disentangle structural breaks (in the mean and/or the variance) on one hand and long memory or unit roots on the other. Several new lines of research are briefly mentioned.
Testing for structural stability has attracted a lot of attention in theoretical and applied research. Oftentimes the test is based on the supremum of, for example, the Wald statistic when the break is assumed to be in the interval [ n] < s < n [ n] for some > 0 and where n denotes the sample size. More recently there has been some work to allow the possibility that the break lies at the end of the sample, i.e. when s 2 (n s; n) for some …nite number s. However, the previous setups do not include the important intermediate case when s 2 (s; [ n])[(n [ n] ; n s), or more generally when we do not wish to assume any prior knowledge on the location of the break. The aim of the paper is thus to extend existing results on stability tests in the later scenario for models useful in economics such as nonlinear simultaneous equations and transformation models. Letting the time of the break to be anywhere in the sample might not only be more realistic in applied research, but it avoids also the unpleasant need to choose either or s. In addition we show that, contrary to the conventional tests, the tests described and examined in the paper are consistent irrespective of the location of the break.
This paper considers tests for structural instability of short duration, such as at the end of the sample. The key feature of the testing problem is that the number, m, of observations in the period of potential change is relatively small-possibly as small as one. The well-known F test of Chow (1960) for this problem only applies in a linear regression model with normally distributed iid errors and strictly exogenous regressors, even when the total number of observations, n+m, is large. Copyright The Econometric Society 2003.