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By Maurice G. Kendall, William R. Buckland

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10) j=0 ∞ where ψ0 = 1 and j=0 ψj2 < ∞, and {Zt } denotes a purely random process (or uncorrelated white noise) with zero mean and constant variance, σ 2 , which is uncorrelated with the deterministic part of the process (if any). The {Zt } are sometimes called innovations, as they are the one-step-ahead forecast errors when the best linear predictor is used to make one-step- c 2000 by Chapman & Hall/CRC ahead forecasts. 10) is an MA(∞) process, which is often called the Wold representation of the process.

1) for all t. The set of autocovariance coefficients {γk }, for k = 0, 1, 2, . . ) of the process. Note that γ0 equals the variance, σ 2 . Second-order stationarity is sometimes called covariance or weak stationarity. f. 2) for k = 0, 1, 2, . .. ) For stationary processes, ρk measures the correlation at lag k between Xt and Xt+k . f. is an even function of lag, since ρk = ρ−k , and has the usual property of correlation that |ρk | ≤ 1. ) which essentially measures the excess correlation at lag k which has not already been accounted for by autocorrelations at lower lags.

It is easy to say that this is just a silly misapplication of time-series methodology, which should not happen in a good statistical department. In fact, many companies have several hundred or even thousands of series to analyse, and this sort of thing can happen all too easily, even in a wellrun department. It reminds us that it is very easy to get bogged down in trying to make small improvements to statistical procedures, and lose sight of more important basic questions. 4 Stationary stochastic processes This section reviews some basic theory for time series.

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