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Discrete-Time Fractional Difference Calculus
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Differences are introduced as outputs of linear systems called differencers, being considered two classes: shift and scale-invariant. Several types are presented, namely: nabla and delta, bilateral, tempered, bilinear, stretching, and shrinking. Both continuous and discrete-time differences are described. ARMA-type systems based on differencers are introduced and exemplified. In passing, the incorrectness of the usual delta difference is shown.
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ARFIMA ARMA bilateral difference bilinear delta difference nabla difference stretching difference tempered Analysis Statistical and Nonlinear Physics Statistics and Probability