Autocorrelation
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Calculate
Example: an ice-cream shop's quarterly sales over three years, always higher in summer. Does the autocorrelation show this 4-quarter cycle? Change the series and the maximum lag to work out your own case.
Step by step
What each term means
- Autocorrelation at Lag k (rₖ)
- The correlation of the series with itself k periods later, from −1 to 1. Positive at k = 1 means inertia; a spike at k = 4 or 12, seasonality.
- Lagged Products
- Multiplies each period's deviation by the deviation k periods ahead. If high values tend to be followed, k periods later, by high values, the sum comes out positive.
- Total Variation
- The sum of the squared deviations of the whole series. It is the same denominator for every lag, which keeps rₖ between −1 and 1.
When to use it, assumptions and alternatives: the Ljung–Box test in the statistical tests catalog.