<Article>The Exact Expectations and Distributions of the Sample Autocorrelation Coefficients for an Integrated Moving Average Process <Article>The Exact Expectations and Distributions of the Sample Autocorrelation Coefficients for an Integrated Moving Average Process

The behaviour of the sample autocorrelation coefficients is important for the identification of the time series process. In this note the exact expectations and distributions of the sample autocorrelation coefficients for a particular unstationary time series process IMA (1, 1) are evaluated numerically. It turns out that the exact expectation of the sample autocorrelation coefficients are smaller than the Wichern's estimates (1973), to which Box and Jenkins (1976, 200-1) referred. And also, from the exact distribution of the sample autocorrelation coefficients, we notice that using the autocorrelation coefficients in the identification of time series process is not necessarily exact.

The behaviour of the sample autocorrelation coefficients is important for the identification of the time series process. In this note the exact expectations and distributions of the sample autocorrelation coefficients for a particular unstationary time series process IMA (1, 1) are evaluated numerically. It turns out that the exact expectation of the sample autocorrelation coefficients are smaller than the Wichern's estimates (1973), to which Box and Jenkins (1976, 200-1) referred. And also, from the exact distribution of the sample autocorrelation coefficients, we notice that using the autocorrelation coefficients in the identification of time series process is not necessarily exact.