Nonstationary nonlinear heteroskedasticity in regression

This paper considers the regression with errors having nonstationary nonlinear heteroskedasticity. For both the usual stationary regression and the nonstationary cointegrating regression, we develop the asymptotic theories for the least squares methods in the presence of conditional heterogeneity given as a nonlinear function of an integrated process. In particular, we show that the nonstationarity of volatility in the regression errors may induce spuriousness of the underlying regression, if excessive nonstationary volatility is present in the errors. Mild nonstationary volatilities do not render the underlying regression spurious, but their presence makes the least squares estimator asymptotically biased and inefficient and the usual chi-square test invalid.