Integer-valued autoregressive (INAR) processes have been introduced to model non-negative integer-valued phenomena that evolve in time. The distribution of an INAR(p) process is determined by two parameters: a vector of survival probabilities and a probability distribution on the non-negative...

Haugh [Journal of the American Statistical Association (1976) Vol. 71, pp. 378-85] developed an approach to the problem of testing non-correlation (at all leads and lags) between two univariate time series. Haugh's tests however have low power against two series which are related over a long...