The present paper is focused on a fully nonparametric regression model for autocorrelation structure of errors in time series over total ozone data. We propose kernel methods which represent one of the most effective nonparametric methods.
But there is a serious difficulty connected with them – the choice of a smoothing parameter called a bandwidth. In the case of independent observations the literature on bandwidth selection methods is quite extensive. Nevertheless, if the observations are dependent, then classical bandwidth selectors have not always provided applicable results.
There exist several possibilities for overcoming the effect of dependence on the bandwidth selection. In the present paper we use the results of Chu and Marron (1991) and Kolåcek (2008) and develop two methods for the bandwidth choice. We apply the above mentioned methods to the time series of ozone data obtained from the Vernadsky station in Antarctica. All discussed methods are implemented in Matlab.