Moving Average: Library of Methods and Models

The moving average method is based on representing a series as a sum of sufficiently smooth trend and a random component. Moving averages need to be estimated when it is not clear, which function must be selected for a trend.

The method is used by default.

The value of the moving average at t time is the arithmetic mean of the sequence of time series values in the time interval [t - w, t + w], the center of which is t point. To calculate the w time:

Where p - moving average depth.

Define via Mtp the value of the moving average at t time determined by p points. For example:

And so on.

This makes obvious that the number of points p must be odd, otherwise the arithmetic mean must be attributed to a fractional point in time. However, in actual practice the number p is more conveniently selected as even. Then the arithmetic mean is calculated using some weights. For example, if we assume that p = 4, Mt4 can be calculated as follows:

The calculation of the moving average by four points amounted to the calculation by five points with the set of weights (1, 2, 2, 2, 1). The method of calculating moving average by the even number of points is named mean correction.

The value of the moving average at the t time is the arithmetic mean of the sequence of time series values in the time interval [t + 1, t + p], where p - moving average depth:

Define via Mtp the value of the moving average at t time determined by p points. For example:

And so on.

The value of the moving average at t time is the arithmetic mean of the sequence of time series values in the time interval [t - p, t - 1], where p - moving average depth:

Define via Mtp the value of the moving average at t time determined by p points. For example:

And so on.