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2.2.4.1.2 Algorithm for Moving Average

Contents

1 Moving Average

Moving Average

Moving average calcualtes the mean of the $m$ consecutive data as the smoothed value.

$\hat{y_t} = \frac{1}{m} \sum_{i=t-m+1}^{t}y_i$

Centered moving average, if $m$ is an odd number

$\hat{y_t} = \frac{1}{m} \sum_{i=t-\frac{m-1}{2}}^{t+\frac{m-1}{2}}y_i$

Centered moving average, if $m$ is an even number

$\hat{y_t} = \frac{1}{2}[ \frac{1}{m} \sum_{i=t-\frac{m}{2}}^{t+\frac{m}{2}-1}y_i + \frac{1}{m} \sum_{i=t-\frac{m}{2}+1}^{t+\frac{m}{2}}y_i]$