Rolling Averages

Rolling averages, also known as moving averages, are a type of chart analysis technique used to examine survey data collected over extended periods of time, for example, in political tracking polls. They are typically utilized to smooth out data series. The ultimate purpose of rolling averages is to identify long—term trends. They are calculated by averaging a group of observations of a variable of interest over a specific period of time. Such averaged number becomes representative of that period in a trend line. It is said that these period-based averages “roll,” or “move,” because when a new observation is gathered over time, the oldest observation of the pool being averaged is dropped out and the most recent observation is included into the average. The collection of rolling averages is plotted to represent a trend.

An example of how rolling averages are calculated is as follows. Imagine that a survey analyst is interested in computing 7-day rolling averages (i.e. a 1-week period) for a period of 52 weeks (364 days, approximately 1 year). Let us assume that the variable of interest was measured daily over a period of 52 weeks. The analyst would have to consider the simple average of Day 1 to Day 7 as the first rolling average, represented as . The second 7-day rolling average would be the average of Day 2 to Day 8, represented as . Subsequent rolling averages would be . The analyst then would have 358 points or rolling averages to plot a trend across the 364-day year.

In general, simple rolling averages are calculated as where RAt represents the set of rolling averages for specific time periods (t), di represents one unit in the rolling average, and (k − i) + l is the total number of time points in the rolling average (e.g. in the 7-day rolling averages example, k = 7). Overall, it is up to the analyst to decide the total number of time points, (k − i) + l, to be averaged. For example, when variations are expected to occur within a 1-week period, the analyst can select 3-, 5-, or 7-day rolling averages, whereas in studies whose variations occurs monthly, 15-, 28-, or 30-day rolling averages could be selected. In studies with a larger scope, 1-, 2-, 3-year, or longer rolling averages would be needed.

Rolling averages reduce short-term effects; as a consequence, variations across time are decreased and the direction of the trend is more readily clarified. In that sense, variables subject to seasonality or periodic fluctuations in long-term studies are conveniently represented as rolling averages. For example, results of daily pre-election surveys conducted under the same methodology and by the same polling agency tend to fluctuate frequently because of campaigns, media-related effects, or any other aspect around elections; thus, a way to reduce variability and emphasize a voting-intention trend would be by means of rolling averages. Other variables subject to seasonality are, for instance, measures of donation behavior in fund-raising studies or measures of exercise levels in health fitness surveys. These variables would be likely to display noticeable peaks or dips in winter and summer months.

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