LOCAL LIMIT THEORY AND SPURIOUS NONPARAMETRIC REGRESSION
证明了非平稳时间序列样本协方差的局部极限定理，并用于分析非参数虚假回归，发现其统计显著性、低DW比和高R²等特征与线性虚假回归类似。
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 local Durbin–Watson ( DW ) ratio, and their asymptotic behavior is investigated. The most immediate findings extend the earlier work on linear spurious regression (Phillips, 1986, Journal of Econometrics 33, 311–340) showing that the key behavioral characteristics of statistical significance, low DW ratios and moderate to high R 2 continue to apply locally in nonparametric spurious regression. Some further applications of the limit theory to models of nonlinear functional relations and cointegrating regressions are given. The methods are also shown to be applicable in partial linear semiparametric nonstationary regression.