13.35 Runs test and autocorrelation.
Suppose you have three different time series S1, S2, and S3. The observed number of runs for series S1 is significantly less than the expected number of runs. The observed number of runs for series S2 is significantly greater than the expected number of runs. The observed number of runs for series S3 is not significantly different from the expected number of runs. If you were to plot observations of a given series against its first lag, explain what you would likely see.
13.35
S1 would show a strong positive relationship with its first lag, S2 would show a strong negative relationship with its first lag, and S3 would show no particular relationship with its first lag.