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This article studies spurious regression in the multivariate case for any finite number of fractionally integrated variables, stationary or not. We prove that the asymptotic behavior of the estimated coefficients and their t-statistics depend on the degrees of persistence of the regressors and the regressand. Nonsense inference could therefore be drawn when the sum of the degrees of persistence of the regressor and regressand is greater or equal than 1/2. Moreover, the asymptotic behavior from the most persistent regressor spreads to correlated regressors. Thus, the risk of uncovering spurious results increases as more regressors are included. Inference drawn from other test statistics such as the joint F test, the R-squared, and the Durbin-Watson is also misleading. Finite sample evidence supports our findings. [ABSTRACT FROM AUTHOR]

The literature on spurious regressions has found that the t-statistic for testing the null of no relationship between two independent variables diverges asymptotically under a wide variety of non stationary data-generating processes for the dependent and explanatory variables. This paper introduces a simple method which guarantees convergence of this t-statistic to a pivotal limit distribution, thus allowing asymptotic inference. This method can be used to distinguish a genuine relationship froma spurious one among integrated processes. We apply the proposed procedure to several pairs of apparently independent integrated variables, and find that our procedure does not find (spurious) significant relationships. [ABSTRACT FROM AUTHOR]

This article studies the asymptotic properties of least squares estimators and related test statistics in some spurious regression models that are generated by stationary or nonstationary fractionally integrated processes. We show that even when the fractionally integrated processes are long-range dependent, the asymptotic distributions of the least squares statistics, after appropriately rescaling and normalizing, are functionals of standard Brownian motions rather than of fractional Brownian motions. Some Monte Carlo simulations are provided to indirectly illustrate the performance of the asymptotic results for finite samples. [ABSTRACT FROM PUBLISHER]

Spurious regression phenomenon has been recognized for a wide range of Data Generating Processes: driftless unit roots, unit roots with drift, long memory, trend and broken-trend stationarity, etc. The usual framework is Ordinary Least Squares. We show that the spurious phenomenon also occurs in Instrumental Variables estimation when using non stationary variables, whether the non stationarity component is stochastic or deterministic. Finite sample evidence supports the asymptotic results. [ABSTRACT FROM AUTHOR]

A "spurious regression" is one in which the time-series variables are non stationary and independent. It is well known that in this context the OLS parameter estimates and the R2 converge to functionals of Brownian motions, the "t-ratios" diverge in distribution, and the Durbin-Watson statistic converges in probability to zero. We derive corresponding results for some common tests for the normality and homoskedasticity of the errors in a spurious regression. [ABSTRACT FROM AUTHOR]