Local Limit Theory and Spurious Nonparametric Regression
Publication Type
Journal Article
Publication Date
12-2009
Abstract
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.
Keywords
Integrated Time - series, Econometrics, Asymptotics, Convergence, Sums
Discipline
Econometrics
Research Areas
Econometrics
Publication
Econometric Theory
Volume
25
Issue
6
First Page
1466
Last Page
1497
ISSN
0266-4666
Identifier
10.1017/S0266466609990223
Publisher
Cambridge University Press
Citation
Peter C. B. PHILLIPS.
Local Limit Theory and Spurious Nonparametric Regression. (2009). Econometric Theory. 25, (6), 1466-1497.
Available at: https://ink.library.smu.edu.sg/soe_research/1815