Nearest‐neighbour Methods for Time Series Analysis

Abstract. The nearest‐neighbour method, because of its intuitively appealing nature and competitive theoretical properties, deserves consideration in time‐series applications akin to attention it has received lately in the i.i.d. case. Here it is shown that as a nonparametric regression device, like the kernel method, under the G 2 mixing assumption, it converges in quadratic mean at the Stone‐optimal rate. In the closing sections, our methodology is extended to a broader pattern‐recognition context, and applied to hydrologic data.