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Limit theory for overfit models


This dissertation consists of three independent papers. Collectively they attempt to formalize a notion of model "overfit"--the idea that a large econometric model can appear to fit a particular dataset well simply because it is large. This behavior is modeled by using asymptotic approximations that allow the number of regressors in a linear regression model to increase with the number of total observations. The first chapter looks at the behavior of the F-test under this asymptotic theory, shows that the F-test is generally invalid for these overfit models, and derives a correction that gives a valid test statistic. The second chapter looks at the behavior of pseudo out-of-sample comparisons of forecasting models under this asymptotic theory, shows that this asymptotic theory resolves some technical issues that lead to nonstandard test statistics, and gives conditions under which standard procedures remain valid for overfit models. The third chapter conducts an empirical comparison of several methods for comparing forecasting models out-of- sample.

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