Monitoring for outliers and level shifts in Kalman filter implementations of exponential smoothing

Article Abstract:

Kalman filter implementation of exponential smoothing is analyzed with monitoring for steady, outlier, and level shift models, using statespace, sequential data processing. This study's main advantage is the utilization of the maximum likelihood function to calculate the parameters. Three state model-selection criteria, including the mean absolute deviation, F and Bayesian classification types, are each assigned individual models yet have similar results. However, a fourth criterion, the Bayes mixture, was superior in two cases, particularly in one with abrupt level shifts and outliers.

Usage, Maximum likelihood estimates (Statistics), Outliers (Statistics), Kalman filtering, Maximum likelihood (Statistics)

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Prediction intervals for exponential smoothing using two new classes of state space models

Article Abstract:

An analysis of the three classes of state space models using the single source of error formulation is discussed. The first class is the standard linear with homoscedastic errors; the second retains the linear structure but incorporates a dynamic form of homoscedasticity, and the third allows for non-linear structure in the observation equation as well as homoscedasticity. These three classes provide stochastic models for a wide variety of exponential smoothing methods.

Analysis, Stochastic analysis

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Exponential smoothing of seasonal data: a comparison

Article Abstract:

A new seasonal model for forecasting time-series is described.

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