The statistical analysis of the US domestic box office (Jan 2000- Dec 2013)

IntroductionBox office refers to the money spent on tickets at movie theatres. The analysis of these earnings is very important for the US film industry, and it helps the US industry to find out what type of movie will most of the people be interested in. It is also very influential for the production and funding of future works.

Purpose

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Residuals

Decomposition of data:Total.Gross

Total gross variability expressed as a range is $1.4 - $0.4 = $1 billion.

The trend position change is from about $600 to $900 million, i.e. $300 million in 14 years, so this trend explains up to 30% of the total variation. (3 / 10 = 0.3)

The average seasonal effect varies from about $-300 to $400 million ($700 million change) representing up to 70% of the total gross variation. (7 / 10 = 0.7)

This shows us that most of the long term change is caused by the seasonal component. The seasonal effects can have a greater effect on total gross and will be important for forecasting.

This will be particularly true for school days and holiday analysis containing July and September months when the seasonal effect is large.

Residual sizes in this model are $200 million providing up to 20% of total variation ($200 / $10 = 0.2)

This will add significant uncertainty to forecasting as the amount of residuals is big. For a well-fitted model, it is important that…*****

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Time series plot for Total.Gross

The LOWESS smoother shows that on average, the total gross is increasing over time. The trend line is fairly stationary. Between 2000 and 2008, the trend is increasing at the beginning, until 2005 and 2007 where a little trough is shown on the time series plot; during 2008 to 2014, the trend is increasing over time, except a downfall around 2011, the trend line then started to increase again.

The overall change in the trend position is from $600 to $900 million in 14 years. This suggests an average long term total gross growth rate is about $21 million per year. ($900 - $600 = $300, $300 / 14 = $21)

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Seasonal plot for Total.Gross

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Additive seasonal effects

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The seasonal plot for total gross shows an unsteady pattern. The total gross in July are on average about $400 million above trend. The regular July maximums can be explained by the US school holiday period which encourages the increased spending.

The total gross in September on average are about $290 million below trend.

Looking along the LOWESS smoother,

Holt-Winters prediction for Total.Gross

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Time

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