Improved Support of Random Processes in Expectation 

Mathematica 10's improved integration of random process and probability and statistics frameworks enables symbolic computation with many slices of a process. In particular, this example investigates two estimators of the absolute autocorrelation function and explores the trade between the estimator's bias and its population variance.

Let denote values of a random process arma at time .

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Consider two-sample estimator of the absolute correlation function sequence and .

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Compute population expectation of these estimators for ARMA(1,1) process.

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The first estimator, , is biased, while the second, , is unbiased.

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Compute population variances of these estimators.

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The variance of the unbiased estimator grows for large lags.

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Therefore, AbsoluteCorrelationFunction uses the biased estimator.

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