Lower Bounds for Nonlinear Prediction Error in Moving Average Processes

Prediction in moving average processes

For the stationary invertible moving average process of order one with unknown innovation distribution F , we construct root-n consistent plug-in estimators of conditional expectations E(h(Xn+1)|X1, . . . , Xn). More specifically, we give weak conditions under which such estimators admit Bahadur type representations, assuming some smoothness of h or of F . For fixed h it suffices that h is loca...

Moving Average Processes with Infinite Variance

The sample autocorrelation function (acf) of a stationary process has played a central statistical role in traditional time series analysis, where the assumption is made that the marginal distribution has a second moment. Now, the classical methods based on acf are not applicable in heavy tailed modeling. Using the codifference function as dependence measure for such processes be shown it be as...

Moving Average Processes

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Some Lower Bounds for Estrada Index

On error bounds for lower semicontinuous functions

We give some sufficient conditions for proper lower semicontinuous functions on metric spaces to have error bounds (with exponents). For a proper convex function f on a normed space X the existence of a local error bound implies that of a global error bound. If in addition X is a Banach space, then error bounds can be characterized by the subdifferential of f . In a reflexive Banach space X, we...