We propose an online algorithm for tracking a multivariate time-varying parameter of a time series. The algorithm is driven by a gain function. Under assumptions on the gain function, we derive uniform error bounds on the tracking algorithm in terms of chosen step size for the algorithm and on the variation of the parameter of interest. We give examples of a number of different variational setups for the parameter where our result can be applied, and we also outline how appropriate gain functions can be constructed. We treat in some detail the tracking of time varying parameters of an AR($d$) model as a particular application of our method.
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|Published - 2013