LOCAL LIMIT THEORY AND SPURIOUS NONPARAMETRIC REGRESSION

Local Limit Theory and Spurious Nonparametric Regression

A local limit theorem is proved for sample covariances of nonstationary time series and integrable functions of such time series that involve a bandwidth sequence. The resulting theory enables an asymptotic development of nonparametric regression with integrated or fractionally integrated processes that includes the important practical case of spurious regressions. Some local regression diagnos...

Nonparametric Regression

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Spurious Regression

The spurious regression phenomenon in least squares occurs for a wide range of data generating processes, such as driftless unit roots, unit roots with drift, long memory, trend and brokentrend stationarity. Indeed, spurious regressions have played a fundamental role in the building of modern time series econometrics and have revolutionized many of the procedures used in applied macroeconomics....

Bayesian Nonparametric Regression with Local Models

We propose a Bayesian nonparametric regression algorithm with locally linear models for high-dimensional, data-rich scenarios where real-time, incremental learning is necessary. Nonlinear function approximation with high-dimensional input data is a nontrivial problem. For example, real-time learning of internal models for compliant control may be needed in a highdimensional movement system like...

A Distribution-Free Theory of Nonparametric Regression