A Mixed Spectrum Analysis of the Lynx Data

SUMMARY The P(A) test suggested by Priestley (1962a, b) is applied to the Lynx data to test for the presence of unknown harmonic terms. This test detects one significant harmonic term of frequency 2XT/9.5. A second-order autoregressive model is fitted to the residuals obtained after removing the contribution of this harmonic term. The decision on the order of the autoregression to be fitted to the residuals was made using the FPEacriterion studied by Bhansali and Downham (1977). Although obtained by a slightly different method, our fitted model, including the estimates of the autoregressive coefficients, the amplitude, phase and the frequency of the harmonic term, agrees with the corresponding model fitted by Campbell and Walker (1977) to the same series.