Prediction Of Shot Noise

Prediction of future values of a shot noise process observed on a discrete lattice of points is considered. The shot magnitudes are assumed to be independent and identically distributed and arrive via a Poisson process; the effect of each shot dissipates and/or accumulates according to a known shot function. Conditional mean and linear point predictors of future process values are developed. Distributional prediction, obtained through saddlepoint approximation of the conditional distributions of the process, is also explored. KEY WORDS: PREDICTION; SHOT NOISE; MEAN SQUARED ERROR; SADDLEPOINT APPROXIMATION. 1 Introduction. Consider a shot noise process A = fA t ; t 0g defined for t 0 by A t = N t X i=1 Y i h(t \Gamma ø i ); (1.1) where N = fN t ; t 0g is a Poisson process with arrival times fø i ; i 1g and rate generation parameter ? 0, and fY i ; i 1g is an independent and identically distributed (iid) sequence of "shot marks" that is independent of N . The shot function h..