Forecasting for discrete time processes based on causal band-limited approximation
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We study causal dynamic smoothing of discrete time processes via approximation by band-limited discrete time processes. More precisely, a part of the historical path of the underlying process is approximated in Euclidean norm by the trace of a band-limited process. We analyze related optimization problem and obtain some conditions of solvability and uniqueness. An unique extrapolation to future times of the optimal approximating band-limited process can be interpreted as an optimal forecast.
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Dokuchaev, Nikolai (2017)The paper suggests a method of recovering of missing values based on optimal approximation by band-limited processes for sequences, i.e. discrete time processes, that are not necessarily band-limited. The problem is ...
Dokuchaev, Nikolai (2012)Pathwise predictability and predictors for discrete time processes are studied in deterministic setting. It is suggested to approximate convolution sums over future times by convolution sums over past time. It is shown ...
Dokuchaev, Nikolai (2014)The paper studies frequency characteristics and predictability of real sequences, i.e., discrete time processes in deterministic setting. We consider band-limitness and predictability of one-sided sequences. We establish ...