A Note on spurious regression in the presence of ARCH effects: some Monte Carlo results

Spurious behaviours in regression analysis with independent random walks or even with stationary series are well known. However, how their spuriousity is affected by heteroscedastic errors or by nonlinearity in series has not been discussed in the literature. Using a Monte Carlo analysis, this study investigates the effect of autoregressive conditional heteroscedasticity (ARCH) on spurious regression, and it finds that only ARCH in variable models can neutralize most of spuriousity, an outcome that will have implications for unit root and cointegration analysis and it also finds evidence of autocorrelated errors, while the Cochrane-Orcutt procedure helps to resolve these issues.