We consider the Whittle likelihood estimation of Seasonal Autoregressive Fractionally Integrated Moving Average (SARFIMA) models in the presence of additional measurement errors. We show that the spectral maximum Whittle likelihood estimator is asymptotically normal. We illustrate by simulation that ignoring measurement errors may result in incorrect inference. Hence, it is pertinent to test for the presence of measurement error, which we do by developing a likelihood ratio (LR) test within the framework of Whittle likelihood. We derive the non-standard asymptotic null distribution of this LR test. Since in practice, we do not know the order of the SARFIMA model, we consider three modifications of the LR test that take the model uncertainty into account. We study the finite sample properties of the size and the power of the LR test and its modifications. The efficacy of the proposed approach is illustrated by an empirical example.
Joint work with Henghsiu Tsai and Edward Lin, Institute of Statistical Science, Academia Sinica