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In technical analysis, a moving average is one of a family of similar statistical techniques used to analyse financial time series data.
A moving average series can be calculated for any time series, but is most often applied to time series of stock prices, returns or trading volumes. Moving averages are used to eliminate short-term fluctations in time series and highlight long-term trends and cycles. The threshold between short-term and long-term depends on the application, and the parameters of the moving average will be set accordingly.
A simple moving average is the unwieghted mean of the previous n data points in the time series. For example, a 10-day simple moving average closing price is the mean of the previous 10 days' closing prices.
A weighted moving average is a weighted mean of the previous n data points in the time series. When a weighting is not specified, the weighting can usually be taken to be linear i.e. varying from a relative weight of 1 assigned to time period t to a relative weight of 1/n assigned to time period t-n, with all previous time periods having a weight of 0. A weighted moving average is more responsive to recent movments than a simple moving average.
An exponentially weighted moving average or EWMA is an exponentially weighted mean of previous data points. The parameter of an EWMA can be expressed as a proportional percentage - for example, in a 10% EWMA, each time period is assigned a weight that is 90% of the weight assigned to the next (more recent) time period. Alternatively, the EWMA percentage may be expressed as an equivalent number of time periods. Although an EWMA calculation should, in theory, assign non-zero weights to all previous time periods, practical calculations usually terminate once weights fall below a small threshold.
Mathematically, each of these moving averages is an example of a convolution. These averages are also similar to the low-pass filters used in signal processing.
Other weighting systems are used occassionally - for example, a volume weighting will weight each time period in proportion to its trading volume.
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