Spurious Regression and Econometric Trends

This paper analyses the asymptotic and finite sample implications of different types of nonstationary behavior among the dependent and explanatory variables in a linear spurious regression model. We study cases when the nonstationarity in the dependent and explanatory variables is deterministic as well as stochastic. In particular, we derive the order in probability of the t-statistic in a linear regression equation under a variety of empirically relevant data generation processes, and show that the spurious regression phenomenon is present in all cases considered, when at least one of the variables behaves in a nonstationary way. Simulation experiments confirm our asymptotic results.Spurious regression, trends, unit roots, trend stationarity, structural breaks

Spurious regression under broken trend stationarity

We study the phenomenon of spurious regression between two random variables when the generating mechanism for individual series follows a stationary process around a trend with (possibly) multiple breaks in its level and slope. We develop relevant asymptotic theory and show that spurious regression occurs independently of the structure assumed for the errors. In contrast to previous findings, the spurious relationship is less severe when breaks are present, whether or not the regression model includes a linear trend. Simulations confirm our asymptotic results and reveal that, in finite samples, the spurious regression is sensitive to the presence of a linear trend and to the relative locations of the breaks within the sampleSpurious regression, Structural breaks, Stationarity

Spurious regression under deterministic and stochastic trends

This paper analyses the asymptotic and finite sample implications of a mixed nonstationary behavior among the dependent and explanatory variables in a linear spurious regression model. We study the cases when the nonstationarity in the dependent variable is deterministic (stochastic), while the nonstationarity in the explanatory variable is stochastic (deterministic). In particular, we derive the asymptotic distribution of statistics in a spurious regression equation when one variable follows a difference stationary process (a random walk with and without drift), while the other is characterized by deterministic nonstationarity (a linear trend model with and without structural breaks in the trend function). We find that the divergence rate is sensitive to the assumed mixture of nonstationarity in the data generating process, and the phenomenon of spurious regression itself, contrary to previous findings, depends on the presence of a linear trend in the regression equation. Simulation experiments and real data confirm our asymptotic results.Unit roots, Trend stationarity, Structural breaks, Spurious regression

Spurious Regression and Trending Variables

This paper analyses the asymptotic and finite sample implications of different types of nonstationary behavior among the dependent and explanatory variables in a linear spurious regression model. We study cases when the nonstationarity in the dependent and explanatory variables is deterministic as well as stochastic. In particular, we derive the order in probability of the t-statistic in a linear regression equation under a variety of empirically relevant data generation processes, and show that he spurious regression phenomenon is present in all cases considered, when at least one of the variables behaves in a nonstationary way. Simulation experiments confirm our asymptotic results.Trend Stationarity, Structural Breaks, Spurious Regression, Unit Roots, Trends

Measuring Group Velocity in Seismic Noise Correlation Studies Based on Phase Coherence and Resampling Strategies

Seismic noise cross correlation studies are of increasing importance in the seismological research community due to the ubiquity of noise sources and advances on how to use the seismic noise wave field for structural imaging and monitoring purposes. Stacks of noise cross correlations are now routinely used to extract empirical Green's functions between station pairs. In regional and global scale studies, mostly surface waves are extracted due to their dominance in seismic noise wave fields. Group arrival times measured from the time-frequency representation of frequency dispersive surface waves are further used in tomographic inversions to image seismic structure. Often, the group arrivals are not clearly identified or ambiguous depending on the signal and noise characteristics. Here, we present a procedure to robustly measure group velocities using the time-frequency domain phase-weighted stack (PWS) combined with data resampling and decision strategies. The time-frequency PWS improves signal extraction through incoherent signal attenuation during the stack of the noise cross correlations. Resampling strategies help to identify signals robust against data variations and to assess their errors. We have gathered these ingredients in an algorithm where the decision strategies and tuning parameters are reduced for semiautomated processing schemes. Our numerical and field data examples show a robust assignment of surface-wave group arrivals. The method is computational efficient thanks to an implementation based on pseudoanalytic frames of wavelets and enables processing large amounts of data.This work was supported in part by the Project MISTERIOS under Grant CGL2013-48601-C2-1-R, in part by the MIMOSA under Grant ANR-14-CE01-0012, in part by the COST Action ES1401 TIDES, in part by AGAUR, and in part by the FP7 Marie Curie Project through SV's Beatriu de Pinos Fellowship under Contract 600385. This is IPGP contribution 3814.Peer reviewe

A Simple Test for Spurious Regressions

It has been found that the t-statistic for testing the null of no relationship between two independent variables diverges asymptotically under a wide variety of nonstationary data generating processes. This paper introduces a simple method which guarantees convergence of this t-statistic to a pivotal limit distribution, when there are drifts in the integrated processes generating the data, thus allowing asymptotic inference. This method can be used to distinguish a genuine relationship from a spurious one among integrated (I(1) and I(2)) processes. Simulation experiments show that the test has good properties in small samples. When applying the proposed procedure to real data (including the marriages and mortality data of Yule), we do not find (spurious) significant relationships between the variables.Spurious Regression, Integrated Process, Detrending, Asymptotic Theory, Cointegration, Monte Carlo Experiments.

Spurious Cointegration: The Engle-Granger Test in the Presence of Structural Breaks

This paper analyses the asymptotic behavior of the Engle-Granger t-test for cointegration when the data include structural breaks, instead of being pure I(1) processes. We find that the test does not possess a limiting distribution, but diverges as the sample size tends to infinity. Calculations involving the asymptotic expression of the t-test , as well as Monte Carlo simulations, reveal that the test can diverge in either direction, making it unreliable as a test for cointegration, when there are neglected breaks in the trend function of the data. Using real data on car sales and murders in the US, we present an empirical illustration of the theoretical results.Spurious cointegration, structural breaks, integrated processes

Numerical taxonomy of moderately halophilic Gram-negative bacteria from hypersaline soils

A total of 132 moderately halophilic bacteria were isolated from hypersaline soils with a C1- content between 2-36 and 12.72% (w/v) located near Alicante (S.E. Spain) and examined for 98 phenotypic characteristics including their response to cytological, physiological, biochemical and nutritional tests. They were submitted to a numerical analysis together with six reference strains using both simple matching (SsM)a nd Jaccard (S,) coefficients, and cluster analysis was carried out by the unweighted pair group method of association (UPGMA), single linkage and complete linkage. With the S, coefficient and UPGMA clustering, eight phenons were obtained at the 65% similarity level. From each phenon representative strains were chosen for the determination of DNA base composition and for electron microscopy. Bacteria belonging to phenons D, E, and F were assigned to the genus Alcaligenes. Phenon G included 27 strains assigned to Acinetobacter, but the high G + C composition (58.9 mol%) of a representative strain of this phenon suggests that it may represent a new taxon. Phenons A, B, and C were designated Flavobacterium and phenon H was Pseudomonas. The bacteria found in these environments are not related to those from hypersaline waters or normal soils

Spurious regression under broken trend stationarity

We study the phenomenon of spurious regression between two random variables,when the generating mechanism of individual series is assumed to follow a stationary process around a trend with (possibly) multiple breaks in the level and slope of trend. We develop the relevant asymptotic theory and show that the phenomenon of spurious regression occurs independently of the structure assumed for the errors. In contrast to previous findings, the presence of a spurious relationship will be less severe when breaks are present in the generating mechanism of individual series. This is true whether the regression model includes a linear trend or not. Simulations confirm our asymptotic results, and reveal that in finite samples, the phenomenon of spurious regression is sensitive to the presence of a linear trend in the regression model, and to the relative location of breaks within the sample

Spurious Regression and Trending Variables

This paper analyses the asymptotic and finite sample implications of different types of nonstationary behavior among the dependent and explanatory variables in a linear spurious regression model. We study cases when the nonstationarity in the dependent and explanatory variables is deterministic as well as stochastic. In particular, we derive the order in probability of the t−statistic in a linear regression equation under a variety of empirically relevant data generation processes, and show that the spurious regression phenomenon is present in all cases considered, when at least one of the variables behaves in a nonstationary way. Simulation experiments confirm our asymptotic results