ABSTRACT
INTRODUCTION The goal of time series prediction or forecasting can be stated succinctly as follows: given a sequence t/(l), t/(2),. . . , y(N) up to time N, find the continuation y ( N -f 1), y ( N + 2 ) ,__ The series may arise from the sampling of a continuous time system, and be either stochastic or deterministic in origin. The standard prediction approach involves constructing an underlying model which gives rise to the observed sequence. In the oldest and most studied method, which dates back to Yule (1927), a linear autoregression (AR) is fit to the data:
y(k) = ^ a(n)y(k — n) 4-e(k) = y(k) -f e (k) . n-l
This AR model forms y(k) as a, weighted sum of past values of the sequence. The single-step prediction for y(k) is given by y(k). The error term e(k) = y(k) — y(k) is often assumed to be a white noise process for analysis in a stochastic framework.
