Journal of Data Science

Linear regression models are widely used in empirical studies. When serial correlation is present in the residuals, generalized least squares (GLS) estimation is commonly used to improve estimation efficiency. This paper proposes the use of an alternative estimator, the approximate generalized least squares estimators based on high-order AR(p) processes (GLS-AR). We show that GLS-AR estimators are asymptotically efficient as GLS estimators, as both the number of AR lag, p, and the number of observations, n, increase together so that $p=o({n^{1/4}})$ in the limit. The proposed GLS-AR estimators do not require the identification of the residual serial autocorrelation structure and perform more robust in finite samples than the conventional FGLS-based tests. Finally, we illustrate the usefulness of GLS-AR method by applying it to the global warming data from 1850–2012.

Abstract: The modified autoregressive (mAR) index has been proposed as a description of the clustering of shots of similar duration in a motion picture. In this paper we derive robust estimates of the mAR index for high grossing films at the US box office using a rank-based autocorrelation function resis tant to the influence of outliers and compare this to estimates obtained using the classical, moment-based autocorrelation function. The results show that (1) The classical mAR index underestimates both the level of shot clustering in a film and the variation in style among the films in the sample; (2) there is a decline in shot clustering from 1935 to the 1950s followed by an increase from the 1960s to the 1980s and a levelling off thereafter rather than the monotonic trend indicated by the classical index, and this is mirrored in the trend of the median shot lengths and interquartile range; and (3) the rank mAR index identifies differences between genres overlooked when using the classical index.