Kernel Regression Smoothing of Time Series

Abstract. A class of non‐parametric regression smoothers for times series is defined by the kernel method. The kernel approach allows flexible modelling of a time series without reference to a specific parametric class. The technique is applicable to detection of non‐linear dependences in time series and to prediction in smooth regression models with serially correlated observations. In practice these estimators are to be tuned by a smoothing parameter. A data‐driven selector for this smoothing parameter is presented that asymptotically minimizes a squared error measure. We prove asymptotic optimality of this selector. We illustrate the technique with a simulated example and by constructing a smooth prediction curve for the variation of gold prices. In both cases the non‐parametric method proves to be useful in uncovering non‐linear structure.