Minimum Distance Estimation on Time Series Analysis with Little Data

Minimum distance estimate is a statistical parameter estimate technique that selects model parameters that minimize a good-of-fit statistic. Minimum distance estimation has been demonstrated better standard approaches, including maximum likelihood estimators and least squares, in estimating statistical distribution parameters with very small data sets. This research applies minimum distance estimation to the task of making time series predictions with very few historical observations. In a Monte Carlo analysis, we test a variety of distance measures and report the results based on many different criteria. Our analysis tests the robustness of the approach by testing its ability to make predictions when the fitted time-series model does not match the data generation model. Our analysis indicates benefits in applying minimum distance estimation when making time series prediction based on less than 30 observations.

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