Granger and Newbold (1973) examine the phenomenon of spurious regressions in econometrics, where time series regression equations show high $ R^2 $ values but low Durbin-Watson statistics, indicating potential issues with autocorrelated errors. Despite warnings in econometric textbooks, such cases are common in applied work. They argue that these regressions may be spurious, meaning they do not reflect true relationships. Autocorrelated errors in regression analysis lead to three main issues: inefficient coefficient estimates, sub-optimal forecasts, and invalid significance tests. The paper focuses on the third issue, highlighting the need for careful error specification in time series analysis.
The authors discuss the implications of non-stationary economic time series, which often exhibit high serial correlation. They argue that naive models may provide adequate forecasts but are not optimal. They also note that economic time series often follow random walk or integrated moving average processes, which can lead to spurious relationships when regressed on levels.
Through simulation studies, they demonstrate that when variables are random walks or integrated processes, regression models may produce high $ R^2 $ values and low Durbin-Watson statistics, suggesting spurious relationships. They emphasize the importance of considering time series properties in econometric modeling and recommend using first differences for highly autocorrelated variables to improve model accuracy.
The paper concludes that mis-specified regression equations with strongly autocorrelated residuals are likely to be incorrect, regardless of high $ R^2 $ values. They suggest that econometricians should consider time series properties when building models and recommend using first differences for highly autocorrelated variables. They also note that while first differencing is not a universal solution, it can improve model interpretability. The authors stress the importance of careful model specification and the potential for spurious regressions in econometric literature.Granger and Newbold (1973) examine the phenomenon of spurious regressions in econometrics, where time series regression equations show high $ R^2 $ values but low Durbin-Watson statistics, indicating potential issues with autocorrelated errors. Despite warnings in econometric textbooks, such cases are common in applied work. They argue that these regressions may be spurious, meaning they do not reflect true relationships. Autocorrelated errors in regression analysis lead to three main issues: inefficient coefficient estimates, sub-optimal forecasts, and invalid significance tests. The paper focuses on the third issue, highlighting the need for careful error specification in time series analysis.
The authors discuss the implications of non-stationary economic time series, which often exhibit high serial correlation. They argue that naive models may provide adequate forecasts but are not optimal. They also note that economic time series often follow random walk or integrated moving average processes, which can lead to spurious relationships when regressed on levels.
Through simulation studies, they demonstrate that when variables are random walks or integrated processes, regression models may produce high $ R^2 $ values and low Durbin-Watson statistics, suggesting spurious relationships. They emphasize the importance of considering time series properties in econometric modeling and recommend using first differences for highly autocorrelated variables to improve model accuracy.
The paper concludes that mis-specified regression equations with strongly autocorrelated residuals are likely to be incorrect, regardless of high $ R^2 $ values. They suggest that econometricians should consider time series properties when building models and recommend using first differences for highly autocorrelated variables. They also note that while first differencing is not a universal solution, it can improve model interpretability. The authors stress the importance of careful model specification and the potential for spurious regressions in econometric literature.