Dealing with serially correlated errors in the context of spurious regression for two independent stationary AR(1) processes

ABSTRACT

Serially correlated errors are most likely to appear in regression analysis when time-series data are used either as a true symptom of autocorrelation or as an indication of a false specification among variables. This study examines the problem of serially correlated errors in the context of spurious regression for two independent stationary AR(1) processes, showing evidence of removing the presence of both symptoms using a Monte Carlo analysis.

KEYWORDS:

• Serially correlated errors
• spurious regression
• independent stationary AR(1) processes
• simple regression model

JEL CLASSIFICATION:

• C22
• C32

Acknowledgments

We are indebted to the editor and to the two anonymous referees for the useful comments and suggestions that improved the overall research and the presentation of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ Note that stronger evidence of false specifications will appear in regression analysis for two independent random walk processes with drift. The null hypothesis will be rejected 100%, regardless of sample size, if both drifts are not equal to zero.

² The values of A₁ and A₂ are calculated individually in every trial using the sample correlation coefficient r of X_t and the estimated value of ρ obtained by estimating model (5) using the residuals obtained from the OLS estimation of model (1). The whole simulation process is conducted in R.:

³ For small sample size and for large value of the autoregressive parameter, i.e. for φ = 0.9 and n = 50, the test over performs, i.e. 3.3% rejection of the null hypothesis at the 5% nominal level, a result that is probably related to the mixed use of estimated and true values.