An omnibus test for the time series model AR(1)

An omnibus test is given for the hypothesis that a given time series sample comes from an autoregressive model of order 1. The test is of Cramér–von Mises type, based on the discrepancy between the standardized spectral distribution and its sample estimate. Tables are given to make the test for the case when the correlation between successive observations is known, and also for the case when this parameter is unknown and is estimated from the sample values. Two examples are given.