An application of a time series inequality to the detection of non-invertible moving average processes

This paper deals with the detection of the non-invertibility in moving average (MA) models. We derive an inequality for MA processes. This inequality establishes bounds for the la-weighted sum of the autocorrelations of processes with positive real unit roots depending on the structure of the autocorrelation function and furthermore, can be used as a tool in model process identification. We discuss a new test for the autocorrelations of MA processes and obtain a simple MA(1) unit root test as a special case. Under the null hypothesis this test statistic is asymptotically standard normal. The test has the advantages of its easy computation and that doesn't need to estimate the parameters of the model. Finally, the empirical power of the test is investigated using Monte Carlo experiments.