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2. Auto-regressive time series prediction. Suppose that a: is an N-vector representing time series data. The (one step ahead) prediction problem is to guess n+1, based on 1:1, . ..,s;,3. We will base our prediction EH1 of $t+1 on the previous M values, $g,$g_1,...,$g_M+1. (The number M is called the memory length of our predictor.) When the prediction is a linear function, t+1 = 5113: + 523331 + ' ' ' + M-TtM+1: it is called an auto-regressive predictor. (It is possible to add an oset to it\