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Mayer, Alexander

Estimation and inference in adaptive learning models with slowly decreasing gains. (English) Zbl 07730963

J. Time Ser. Anal. 43, No. 5, 720-749 (2022).
Summary: An asymptotic theory for estimation and inference in adaptive learning models with strong mixing regressors and martingale difference innovations is developed. The maintained polynomial gain specification provides a unified framework which permits slow convergence of agents’ beliefs and contains recursive least squares as a prominent special case. Reminiscent of the classical literature on co-integration, an asymptotic equivalence between two approaches to estimation of long-run equilibrium and short-run dynamics is established. Notwithstanding potential threats to inference arising from non-standard convergence rates and a singular variance-covariance matrix, hypotheses about single, as well as joint restrictions remain testable. Monte Carlo evidence confirms the accuracy of the asymptotic theory in finite samples.

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MSC:

62Mxx Inference from stochastic processes
62F10 Point estimation
62F12 Asymptotic properties of parametric estimators
62F03 Parametric hypothesis testing
62F05 Asymptotic properties of parametric tests
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
37A25 Ergodicity, mixing, rates of mixing

Keywords:

adaptive learning; rational expectations; asymptotic collinearity; non-stationary regression; degenerate variances; co-integration; strong mixing; (generalized) Wald-statistic
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