THE ASYMPTOTIC BEHAVIOUR OF THE SAMPLE AUTOCOVARIANCE FUNCTION FOR AN AUTOREGRESSIVE INTEGRATED MOVING AVERAGE PROCESS

Junji Nakano, Shigemi Tagami
1987 Journal of the Japan Statistical Society, Japanese Issue  
We derive the first two asymptotic moments of the sample autocovariance func tion of a time series generated from an autoregressive d-th integrated moving average process for any positive integer d. The obtained results show that the sample auto covariance function is a random variable of order N2d-1, where N is the observed length of data.
doi:10.11329/jjss1970.17.31 fatcat:uden572a3vcejfuxsv2m5xrkfe