A GENERALIZED COVARIANCE ESTIMATOR FOR THE ANALYSIS OF ASYMMETRIC TIME SERIES

Asymmetric time series models, as introduced by William Wecker (1981), vary according to whether previous random shocks, or innovations, of the time series are positive or negative; and have been shown to be useful in modeling industrial price quotations. Identifying when a particular time series exhibits this asymmetric structure is the subject of this work. We have derived a new statistic, based on a standardized time series correlation,; (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI). where. (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI). which is demonstrated to be powerful in distinguishing between asymmetric and symmetric time series and is easier to compute them than the likelihood ratio test used by Wecker. A multivariate statistic based on several forms of this statistic, Z(,ij)(k), is shown to have greater power in distinguishing asymmetric and symmetric time series. Several forms of the statistic, Z(,ij)(k), are proven to be asymptotically normally distributed, and our data suggest that they are approximately distributed as N(0,1) in smaller samples, under the null hypothesis of symmetry. As well as identifying whether or not a time series is asymmetric, the new statistic can be use to estimate the parameters of the asymmetric model. Finally, it is shown that asymmetric times series can be used to model some well known sunspot data.