TY  - BOOK
AU  - Phillips,Peter C.B.
TI  - Local limit theory and spurious nonparametric regression
SN  - 02664666
AV  - HB139.T52 ECO 
PY  - 2009///
CY  - Cambridge
PB  - Cambridge University Press
KW  - Time series analysis
KW  - Stochastic process
KW  - Nonparametric statistics
N2  - 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 R2 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 R2 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
UR  - https://doi.org/10.1017/S0266466609990223
ER  -