The lag is the number of time periods that separate the two time series. The default number of lags ranges from ( + 10) to ( + 10).
The cross correlation function is the correlation between the observations of two time series xt and yt, separated by k time units (the correlation between yt+k and xt).
Use the cross correlation function to determine whether there is a relationship between two time series. To determine whether a relationship exists between the two series, look for a large correlation, with the correlations on both sides that quickly become non-significant. Usually, a correlation is significant when the absolute value is greater than , where n is the number of observations and k is the lag. This calculation is a rule of thumb procedure based on large-sample normal approximation. If the population cross correlation of lag k is zero for k=1,2 ... then, for fairly large n, rxy(k) will be approximately normally distributed, with mean (μ) zero and standard deviation (σ) 1/. Since approximately 95% of a normal population is within 2 standard deviations of the mean, a test that rejects the hypothesis that the population cross correlation of lag k equals zero when |rxy(k) | is greater than 2/ has a significance level (α) of approximately 5%.
The interpretation for the cross correlation function depend on the assumption that there is no autocorrelation. For more information, go to Look for evidence of autocorrelation.