Asymmetric recursive methods for time series

summary:The problem of asymmetry appears in various aspects of time series modelling. Typical examples are asymmetric time series, asymmetric error distributions and asymmetric loss functions in estimating and predicting. The paper deals with asymmetric modifications of some recursive time series methods including Kalman filtering, exponential smoothing and recursive treatment of Box-Jenkins models

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Periodic moving average process

summary:Periodic moving average processes are representatives of the class of periodic models suitable for the description of some seasonal time series and for the construction of multivariate moving average models. The attention having been lately concentrated mainly on periodic autoregressions, some methods of statistical analysis of the periodic moving average processes are suggested in the paper. These methods include the estimation procedure (based on Durbin's construction of the parameter estimators in the moving average processes and on Pagano's results for the periodic autoregressions) and the test of the periodic structure. The results are demonstrated by means of numerical simulations

Investigation of periodicity for dependent observations

summary:It is proved that Hannan's procedure for statistical test of periodicity in the case of time series with dependent observations can be combined with Siegel's improvement of the classical Fischer's test of periodicity. Simulations performed in the paper show that this combination can increase the power of Hannan's test when at least two periodicities are present in the time series with dependent observations