Tools

Interpreting an Autocorrelation Chart

The ACF will first test whether adjacent observations are autocorrelated; that is, whether there is correlation between observations #1 and #2, #2 and #3, #3 and #4, etc. This is known as lag one autocorrelation, since one of the pair of tested observations lags the other by one period or sample. Using SPC software will allow you to conveniently test at other lags as well. For instance, the autocorrelation at lag four tests whether observations #1 and #5, #2 and #6, ...,#19 and #23, etc. are correlated. In general, we should test for autocorrelation at lags one to lag n/4, where n is the total number of observations in the analysis. Estimates at longer lags have been shown to be statistically unreliable (Box and Jenkins, 1970).

In some cases, the effect of Autocorrelation at smaller lags will influence the estimate of autocorrelation at longer lags. For instance, a strong lag one autocorrelation would cause observation #5 to influence observation #6, and observation # 6 to influences #7. This results in an apparent correlation between observations #5 and #7, even though no direct correlation exists. The Partial Autocorrelation Function (PACF) removes the effect of shorter lag autocorrelation from the correlation estimate at longer lags. This estimate is only valid to one decimal place.

ACF and PACF each vary between plus and minus one. Values closer to plus or minus one indicate strong correlation. The confidence limits are provided to show when ACF or PACF appears to be significantly different from zero. In other words, lags having values outside these limits (shown as red bars) should be considered to have significant correlation.