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We consider N panels and each panel is based on T observations. We are interested to test if the means of the panels remain the same during the observation period against the alternative that the means change at an unknown time. We provide tests which are derived from a likelihood argument and they are based on the adaptation of the CUSUM method to panel data. Asymptotic distributions are derived under the no change null hypothesis and the consistency of the tests are proven under the alternative. The asymptotic results are shown to work in case of small and moderate sample sizes via Monte Carlo simulations.

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Summary  We consider a linear regression model with errors modelled by martingale difference sequences, which include heteroskedastic augmented GARCH processes. We develop asymptotic theory for two monitoring schemes aimed at detecting a change in the regression parameters. The first method is based on the CUSUM of the residuals and was studied earlier in the context of independent identically distributed errors. The second method is new and is based on the squares of prediction errors. Both methods use a training sample of size m. We show that, as m→∞, both methods have correct asymptotic size and detect a change with probability approaching unity. The methods are illustrated and compared in a small simulation study.

Despite substantial criticism, variants of the capital asset pricing model (CAPM) remain to this day the primary statistical tools for portfolio managers to assess the performance of financial assets. In the CAPM, the risk of an asset is expressed through its correlation with the market, widely known as the beta. There is now a general consensus among economists that these portfolio betas are time-varying and that, consequently, any appropriate analysis has to take this variability into account. Recent advances in data acquisition and processing techniques have led to an increased research output concerning high-frequency models. Within this framework, we introduce here a modified functional CAPM and sequential monitoring procedures to test for the constancy of the portfolio betas. As our main results we derive the large-sample properties of these monitoring procedures. In a simulation study and an application to S&P 100 data we show that our method performs well in finite samples.

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Bootstrap methods for sequential change-point detection procedures in linear regression models are proposed. The corresponding monitoring procedures are designed to control the overall significance level. The bootstrap critical values are updated constantly by including new observations obtained from the monitoring. The theoretical properties of these sequential bootstrap procedures are investigated, showing their asymptotic validity. Bootstrap and asymptotic methods are compared in a simulation study, showing that the studentized bootstrap tests hold the overall level better especially for small historic sample sizes while having a comparable power and run length.