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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 diagnostics are suggested for forensic analysis of such regresssions, including a local R 2 and a localdoi:10.1017/s0266466609990223 fatcat:vigamfehozhyvht6hsnmqlgtd4