Chih‐Ling Tsai

A bias correction to the Akaike information criterion, AIC, is derived for regression and autoregressive time series models. The correction is of particular use when the sample size is small, or when the number of fitted parameters is a moderate to large fraction of the sample size. The corrected method, called AICC, is asymptotically efficient if the true model is infinite dimensional. Furthermore, when the true model is of finite dimension, AICC is found to provide better model order choices than any other asymptotically efficient method. Applications to nonstationary autoregressive and mixed autoregressive moving average time series models are also discussed.

We analyze tests for long‐run abnormal returns and document that two approaches yield well‐specified test statistics in random samples. The first uses a traditional event study framework and buy‐and‐hold abnormal returns calculated using carefully constructed reference portfolios. Inference is based on either a skewness‐adjusted t ‐statistic or the empirically generated distribution of long‐run abnormal returns. The second approach is based on calculation of mean monthly abnormal returns using calendar‐time portfolios and a time‐series t ‐statistic. Though both approaches perform well in random samples, misspecification in nonrandom samples is pervasive. Thus, analysis of long‐run abnormal returns is treacherous.

Summary Many different methods have been proposed to construct nonparametric estimates of a smooth regression function, including local polynomial, (convolution) kernel and smoothing spline estimators. Each of these estimators uses a smoothing parameter to control the amount of smoothing performed on a given data set. In this paper an improved version of a criterion based on the Akaike information criterion (AIC), termed AICC, is derived and examined as a way to choose the smoothing parameter. Unlike plug-in methods, AICC can be used to choose smoothing parameters for any linear smoother, including local quadratic and smoothing spline estimators. The use of AICC avoids the large variability and tendency to undersmooth (compared with the actual minimizer of average squared error) seen when other ‘classical’ approaches (such as generalized cross-validation (GCV) or the AIC) are used to choose the smoothing parameter. Monte Carlo simulations demonstrate that the AICC-based smoothing parameter is competitive with a plug-in method (assuming that one exists) when the plug-in method works well but also performs well when the plug-in approach fails or is unavailable.

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Introduction to model selection the univariate regression model the univariate autoregressive model the multivariate regression model the vector autoregressive model the cross-validation and bootstrap robust and quasi-likelihood model selections non-parametric regressions and wavelets simulations and case studies.