Moving Average

A method of smoothing a time series to reduce the effects of random variation and reveal any underlying trend or seasonality. For the time series x₁, x₂,..., x_t the simple three-point moving average would replace the value of x_k, k=2, 3,..., t−1, with

. Often, different weights are used, as in this five-point moving average which could be used for k=3, 4,..., t−2:


. Another possibility is provided by Daniell weights: in the case of an average over m time points, the two end points are given weight


, with the others each being given weight


.

The four-point moving averages (appropriate for quarterly data) are


Twelve-point moving averages are similarly defined and are appropriate for monthly data.

For a cycle with an even period, e.g. quarterly or monthly data, the centred moving averages are the arithmetic means of the successive moving averages as defined above. For example, in the case of quarterly data the first centred moving average is


. The advantage of these centred moving averages is that the resulting values are associated with a time point rather than the midpoint of the interval between two successive time points.

A graph of moving averages against time may show changes against time which are obscured by cyclical effects. A line of best fit to the moving averages is a trend line, and its slope is the trend. The trend line may be used to forecast future values (in the short term). For example, for monthly data the average deviation of the January data from the trend line can be used as an estimate of the future deviation of the January deviation from the trend line. The deviation can be measured as either a difference or a ratio.

Note that the use of moving averages can introduce spurious cycles (see Slutzky–Yule effect).


Moving average. The graph shows annual sunspot activity (in standardized units) from 1750 to 2000. There is a strong cycle with a period of around eleven years. Also shown is the eleven-year moving average. This removes the obvious cycle but reveals longer-scale fluctuations.

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An indicator frequently used in technical analysis showing the average value of a security's price over a set period. Moving averages are generally used to measure momentum and define areas of possible support and resistance.

Investopedia Says:
Moving averages are used to emphasize the direction of a trend and to smooth out price and volume fluctuations, or "noise", that can confuse interpretation. Typically, upward momentum is confirmed when a short-term average (e.g.15-day) crosses above a longer-term average (e.g. 50-day). Downward momentum is confirmed when a short-term average crosses below a long-term average.

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Average of security or commodity prices constructed on a period as short as a few days or as long as several years and showing trends for the latest interval. For example, a thirty-day moving average includes yesterday's figures; tomorrow the same average will include today's figures and will no longer show those for the earliest date included in yesterday's average. Thus every day it picks up figures for the latest day and drops those for the earliest day. See also Momentum Indicators; 200-Day Moving Average.

Average that is updated as new information is received. With the moving average, an accountant employs the most recent observations to calculate an average, using the result as the forecast for the next period. For example, assume that the accountant has the following cash inflow data:

Using a four-period moving average, the accountant computes the predicted cash collection for October as follows: