Spurious Regressions with Stationary Gegenbauer Processes and Harmonic Processes

This paper studies the spurious regressions among stationary Gegenbauer processes, stationary harmonic processes and deterministic trigonometric series. We find the spurious regression can occur between two stationary Gegenbauer processes, as long as their generalized fractional differencing parameters sum up to a value greater than 0.5 and their spectral densities have poles at the same location. The spurious regression may also be present between a stationary Gegenbauer process and a stationary harmonic process, or between a stationary Gegenbauer process and a deterministic trigonometric series, as long as the poles of the discreet Fourier transforms or the spectral densities of underlying processes are located at the same frequency. Our findings suggest that it is the strong persistence and cyclical comovement that cause the spurious effect. Our theoretical results are supported by simulations.