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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. Similarly, it will test at other
lags. 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's and PACF's 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.
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