Correlation In Two Series

Answer:

The permutation test for parallelism assumes exchangeability in the pair of residuals at each time period. When errors of the two series are correlated, this assumption is violated, so the permutation p-value will not be accurate. Errors in series are correlated, for example, when the two series come from the same population or sub-population measured from the same survey (e.g. obesity and diabetes for white males from the same survey) or the same cancer registry (e.g. white male colorectal and prostate cancer rates from the same registry). Errors in series may be considered uncorrelated when the observations in the two series come from different samples of the same population (e.g. obesity for white males measured from one national survey and diabetes for white males measured from a different national survey).

One way to test for parallelism in two series with correlated errors is to compute a new time series, the difference between the original two series. The series are parallel if the difference time series has a constant mean. One way this can be checked is by fitting a simple linear regression and testing whether the slope coefficient is zero.