Robust estimation of the mAR index of high grossing films at the US box office, 1935 to 2005

Nick Redfern

doi:10.6339/jds.201404_12(2).0004

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 inuence 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 _lm 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.

Highlights

Cutting, De Long, and Nothelfer(2010) proposed the modified autoregressive index as a statistic of film style measuring the degree to which shots of similar duration cluster together in a motion picture
We note the dispersion of the rank index is greater for films in the sample indicating more variation in editing style than that suggested by the cmAR index: the range and standard deviation for the rmAR index are 7.37 and 1.40, respectively, and the corresponding statistics for the cmAR index are 4.01 and 0.79
The classical modified autoregressive (mAR) index shows a gradual trend to increased shot clustering, and is consistent with the monotonic trend reported by Cutting, De Long, and Nothelfer in Figure 2.a of their article

Summary

Introduction

Cutting, De Long, and Nothelfer(2010) proposed the modified autoregressive (mAR) index as a statistic of film style measuring the degree to which shots of similar duration cluster together in a motion picture They calculate the mAR index as the intercept of the negative exponential function 1/[1 + lag]β fitted to the partial autocorrelation function out to lag-20 with a critical value based on the average number of shots in a motion picture from a sample. Estimates of the mAR index determined in this way will not accurately describe the style of a film and lead to incorrect conclusions about the nature of film style Because these long takes are ‘true’ outliers representing the decisions of filmmakers about the arrangement of stylistic elements (staging, cinematography, editing, etc) we are interested in using robust statistical methods that perform reliably in the presence of outliers and departures from the assumptions that underpin statistical methods(Marrona, Martina and Yohai, 2006). This paper calculates robust estimates of the mAR index using a rank-based autocorrelation function (rmAR) and compares these values to the index based on classical autocorrelation function (cmAR)

Methods

Results

Conclusion