Robust time series analysis of ITV news bulletins

I have mentioned numerous times on this blog the importance of using robust statistics to describe film style. This week I continue in this vein, albeit in a different context – time series analysis. In a much publicised piece of work James Cutting, Jordan De Long, and Christine Nothelfer (2010) calculated partial autocorrelation functions and a modified autoregressive index for a sample of Hollywood films. While I have no problems with the basis of this research, I do think the results are dubious due to the use of non-robust methods to determine the autocovariance between shot lengths in these films. The paper attached below analyses the editing structure of the set of ITV news bulletins I discussed in a paper last year, comparing the results produced using classical and robust autocovariance functions.

Robust time series analysis of ITV news bulletins

In this paper we analyse the editing of ITV news bulletins using robust statistics to describe the distribution of shot lengths and its editing structure. Commonly cited statistics of film style such as the mean and variance do not accurately describe the style of a motion picture and reflect the influence of a small number of extreme values. Analysis based on such statistics will inevitably lead to flawed conclusions. The median and  are superior measures of location and dispersion for shot lengths since they are resistant to outliers and unaffected by the asymmetry of the data. The classical autocovariance and its related functions based on the mean and the variance is also non-robust in the presence of outliers, and leads to a substantially different interpretation of editing patterns when compared to robust time statistics that are outlier resistant. In general, the classical methods underestimate the persistence in the time series of these bulletins indicating a random editing process whereas the robust time series statistics suggest an AR(1) or AR(2) model may be appropriate.

The pdf file is here: Nick Redfern – Robust Time Series Analysis of ITV News Bulletins

My original post on the time series analysis of ITV news bulletins can be accessed here, along with the datasets for each of the fifteen bulletins.

My new results indicate the conclusions of Cutting, De Long, and Nothelfer are flawed, and that it is very likely they have underestimated the autocovariance present in the editing of Hollywood films. The discrete and modified autoregressive indexes they present are likely to be too low, though there may be some instances when they are actually too high. This is not enough to reject their conclusion that Hollywood films have become increasingly clustered in packets of shots of similar length, and I have not yet applied this method to their sample of films. It is, however, enough to recognise there are some problems with the methodology and the results of this research.

References

Cutting JE, Delong JE, and Nothelfer CE 2010 Attention and the evolution of Hollywood film, Psychological Science 21 (3): 432-439.

I am an independent academic with over 15 years experience teaching film in higher education in the UK. I have taught film analysis, film industries, film theories, film history, science fiction at Manchester Metropolitan University, the University of Central Lancashire, and Leeds Trinity University, where I was programme leader for film from 2016 to 2020. My research interests include computational film analysis, horror cinema, sound design, science fiction, film trailers, British cinema, and regional film cultures.

Posted on April 5, 2012, in Cinemetrics, Film Analysis, Film Studies, Film Style, News, Statistics, Television, Time Series Analysis and tagged , , , , , , , . Bookmark the permalink. 3 Comments.

1. Hi, Nick. Jordan DeLong here.

You’re certainly right to point out how the modified autoregressive index (and by extension the autocorrelation function) can be influenced quite a bit by outliers in their stock incarnations. This is especially threatening because of the shot lengths falling in a log-normal distribution and outliers should be expected. I should probably say roughly log-normal, given your ardent (but completely fair) criticism of the example film I used in a chapter! (https://nickredfern.wordpress.com/2012/02/02/statistical-illiteracy-in-film-studies/)

The reasoning behind the methodology we use in the PsychScience paper was partially motivated by history; our paper hoped to follow the techniques of David Gilden, who had made a mainstream introduction of his brand of timeseries analysis to Psychologists. In lieu of being accused of doing much data massaging, we kept our analysis as straightforward as we could for the publication and audience.

We’ve evaluated the data in a number of other ways simply so that we can sleep easier at night. Some of the more simple methods involve removing the outliers (typically establishing shots) and transforming the data so it’s gaussian. More sophisticated techniques we’ve used are like those brought up by Ferrel, Wagenmakers and Ratcliff. These essentially use different ARIMA(p,d,q) models to test whether modeling a series with a fractional component (which is very much related to the autoregressive index) actually benefits the fit significantly. I’ve even conducted a Wald-Wolfowitz runs analysis to check for “streakiness”.

Long story short – the main claim that films are becoming more 1/f (like an fBmW sequence) holds up with all the different versions I’ve ran. As a sanity check, if you scramble the order of the shots in the film it all goes away. Using a Whittle Estimator [another ARIMA(p,d,q) model that is pleasantly robust to outliers] we get regularly lower estimate of the fractal dimension. Whether this is due to AR-type estimates being somewhat more “constrained” than Gilden’s spectral classifier or is simply a better estimate of the data I’m not certain, but certainly up for debate. I’d love to have more people download and play with the data we uploaded about a year ago to Yuri Tsavian’s awesome database (www.cinemetrics.lv).

Regardless, thanks for looking at our research and taking an interest! Your bibliography was essential background reading for my qualifying exams. I probably owe you a beer for it.

Cheers,
Jordan