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Spurious regression analysis in panel data when the time series are cross-section dependent is analyzed in the article. The set-up includes (possibly unknown) multiple structural breaks that can affect both the deterministic and the common factor components. We show that consistent estimation of the long-run average parameter is possible once cross-section dependence is controlled using cross-section averages in the spirit of Pesaran's common correlated effects approach. This result is used to design individual and panel cointegration test statistics that accommodate the presence of structural breaks that can induce parameter instabilities in the deterministic component, the cointegration vector and the common factor loadings. [ABSTRACT FROM AUTHOR]

Previous literature on European regions has shown that structural estimation of New Economic Geography (NEG) wage-type equations obtains results similar to those obtained using old regional economics techniques. I show that this similarity is due to the presence of global spatial trends in the variables (first-order non-stationarity), which produce spurious regressions. Formal tests and graphical models confirm that any variable displaying a core–periphery spatial pattern produces similar predictions for European regional per capita income. Empirical tests of spatial theories should thus pay attention to the geographical features of the administrative units and the global spatial trends of the variables analysed. [ABSTRACT FROM AUTHOR]

Abstract This paper contributes to the social science literature when analyzing survey or time series data social scientists use spurious regression without due consideration of its assumptions and the data structure. This results in misinterpretation and misleading conclusions about the population. The paper reviews basic statistical and econometrics literature which led to the development of modern time series analysis in the presence of spurious regression. It concludes that the term ‘Spurious’ was well known before the Granger and Yule’s work in time series context rather than cross-sectional data. The same reasons can produce spurious regression today and surely the solution doesn’t exist in the cointegration analysis. Social scientists and applied econometrician investigators need more serious thinking and care to avoid spurious regression, if it is necessary even if data is stationary or cross-sectional. In this study, we extended the Ghouse experiment which is based on simulated data by employing real-world data to assess the effectiveness of the newly proposed Ghouse Equation in comparison to conventional approaches. The findings demonstrate that the Ghouse Equation produces the lowest probability of spurious regression as compared to its counterparts. Moreover, in forecasting performance, Ghouse Equation outperformed its counterparts. These results highlight the Ghouse Equation as a valuable and better tool for econometric analysis for nonstationary time series.

The regression of mutually independent time series, whether stationary or non-stationary, will result in autocorrelation in the random error term. This leads to the over-rejection of the null hypothesis in the conventional t-test, causing spurious regression. We propose a new method to reduce spurious regression by applying the Cochrane-Orutt feasible generalized least squares method based on a bias-corrected method for a first-order autoregressive model in finite samples. This method eliminates the requirements for a kernel function and bandwidth selection, making it simpler to implement than the traditional heteroskedasticity and autocorrelation consistent method. A series of Monte Carlo simulations indicate that our method can decrease the probability of spurious regression among stationary, non-stationary, or trend-stationary series within a sample size of 10–50. We applied this proposed method to the actual data studied by Yule in 1926, and found that it can significantly minimize spurious regression. Thus, we deduce that there is no significant regressive relationship between the proportion of marriages in the Church of England and the mortality rate in England and Wales.

This paper contributes to the social science literature when analyzing survey or time series data social scientists use spurious regression without due consideration of its assumptions and the data structure. This results in misinterpretation and misleading conclusions about the population. The paper reviews basic statistical and econometrics literature which led to the development of modern time series analysis in the presence of spurious regression. It concludes that the term 'Spurious' was well known before the Granger and Yule's work in time series context rather than cross-sectional data. The same reasons can produce spurious regression today and surely the solution doesn't exist in the cointegration analysis. Social scientists and applied econometrician investigators need more serious thinking and care to avoid spurious regression, if it is necessary even if data is stationary or cross-sectional. In this study, we extended the Ghouse experiment which is based on simulated data by employing real-world data to assess the effectiveness of the newly proposed Ghouse Equation in comparison to conventional approaches. The findings demonstrate that the Ghouse Equation produces the lowest probability of spurious regression as compared to its counterparts. Moreover, in forecasting performance, Ghouse Equation outperformed its counterparts. These results highlight the Ghouse Equation as a valuable and better tool for econometric analysis for nonstationary time series. [ABSTRACT FROM AUTHOR]

In this paper we apply the unit root and cointegration methodology as well as other methods of modern econometric time series analysis to estimate popularity functions for the Austrian parties in power since the mid-1970s. We find only very rare evidence for economic variables influencing the popularity of the main political parties in the federal government, thereby challenging previous studies that claimed to have established such influences. When considering the determinants of the popularity of the incumbent party (the sum of the popularities of the parties in government), the unemployment rate turns out to have a negative short-run influence. The robustness of this result is checked by various methods, demonstrating the usefulness of the applied methodology to clarify such issues. [ABSTRACT FROM AUTHOR]

This article explores the issue of spurious regression in econometric models, focusing on the case of imports in the United States. It explains that a high coefficient of determination (R2) without significant parameters can indicate the presence of spurious regression. The article warns that spurious regression can lead to misleading conclusions and offers recommendations for avoiding it in econometric models. It also discusses the importance of studying time series stability, the limitations of ordinary least squares (OLS) method, and the Gauss-Markov theory. Additionally, the article examines factors affecting imports and suggests methods to avoid spurious regression, such as following econometric methodology, using appropriate sample sizes, and utilizing modern econometric tools. It emphasizes the need for careful model specification, estimation, testing, and forecasting to prevent spurious regression. [Extracted from the article]

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]

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. [ABSTRACT FROM AUTHOR]

We show that time-varying parameter state-space models estimated using the Kalman filter are particularly vulnerable to the problem of spurious regression, because the integrated error is transferred to the estimated state equation. We offer a simple yet effective methodology to reliably recover the instability in cointegrating vectors. In the process, the proposed methodology successfully distinguishes between the cases of no cointegration, fixed cointegration, and time-varying cointegration. We apply these proposed tests to elucidate the relationship between concentrations of greenhouse gases and global temperatures, an important relationship to both climate scientists and economists. [ABSTRACT FROM AUTHOR]

This paper draws parallels between the principal components analysis of factorless high‐dimensional nonstationary data and the classical spurious regression. We show that a few of the principal components of such data absorb nearly all the data variation. The corresponding scree plot suggests that the data contain a few factors, which is corroborated by the standard panel information criteria. Furthermore, the Dickey–Fuller tests of the unit root hypothesis applied to the estimated "idiosyncratic terms" often reject, creating an impression that a few factors are responsible for most of the nonstationarity in the data. We warn empirical researchers of these peculiar effects and suggest to always compare the analysis in levels with that in differences. [ABSTRACT FROM AUTHOR]

Nelson and Kang (1984) showed that regression of a unit root time-series on a linear time trend provides significant results even if there is no forecast able association amongst the path of the time-series and linear trend. Using Monte Carlo simulations, this paper shows that phenomenon also exists in stationary time series and regression of a stationary time series on linear trend also produces significant results without the existence of any predictable relationship between the time-series and linear trend. The spurious trend is observable in most of the moderate sample sizes and sometimes in sufficiently large samples of size over 500 observations. The implications of these findings for unit root test procedures are discussed briefly. [ABSTRACT FROM AUTHOR]

In conventional Econometrics, the unit root and cointegration analysis are the only ways to circumvent the spurious regression which may arise from missing variable (lag values) rather than the nonstationarity process in time series data. We propose the Ghouse equation solution of autoregressive distributed lag mechanism which does not require additional work in unit root testing and bound testing. This advantage makes the proposed methodology more efficient compared to the existing cointegration procedures. The earlier tests weaken their position in comparison to it, as they had numerous linked testing procedures which further increase the size of the test and/or reduce the test power. The simplification of the Ghouse equation does not attain any such type of error, which makes it a more powerful test as compared to widely cited exiting testing methods in econometrics and statistics literature.

This paper proposes a convergent t-statistic for spurious regressions. The new t-statistic is based on the heteroscedasiticity and autocorrelation consistent (HAC) standard error estimate with the bandwidth equal to the sample size. Using autocovariances of all lags, the so-defined HAC estimator is capable of capturing the high persistence of the regressor and regression residuals. It is shown that the new t-statistic converges to a non-degenerate limiting distribution for all cases of spurious regressions considered in the literature. This finding suggests that inferences based on the new t-statistic and asymptotic theory developed in this paper will not result in the finding of a significant relationship that does not actually exist.

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.

Power output from photovoltaic (PV) systems in outdoor conditions is substantially influenced by climatic parameters such as solar irradiance and temperature. PV manufacturers always provide technical specifications in laboratory conditions but reliable relationship for the power output must be determined for accurate prediction under real operating conditions. For the present study, solar irradiance G, temperature T and electrical power output P data under real conditions are methodically and regularly inscribed in dataloggers. Hence, in this paper, we investigate rigorous and robust statistical methods for small sample such as Augmented Dickey-Fuller and Engle Granger for stationary series to determine the estimate regression between variables P, G & T. A first regression of power output P time series variable on solar irradiance G time series has shown spurious results and thus spurious regression. The first differences of such time series are stationary and a regression is proposed whereas temperature variable is identified as not significant and where autocorrelation of residuals is suspected. Finally, the novelty of this paper is the Engle & Granger method that is used to provide a relationship between variables P and G in a difference level. A final relationship without suspicious heteroscedasticity has been determined. Our model is formulated on the basis of PV real conditions statistical approach and is more realistic than steady approach models.

This paper introduces a representation of an integrated vector time series in which the coefficient of multiple correlation computed from the long-run covariance matrix of the innovation sequences is a primitive parameter of the model. Based on this representation, we propose a notion of near cointegration, which helps bridging the gap between the polar cases of spurious regression and cointegration. Two applications of the model of near cointegration are provided. As a first application, the properties of conventional cointegration methods under near cointegration are characterized, hereby investigating the robustness of cointegration methods. Secondly, we illustrate how to obtain local power functions of cointegration tests that take cointegration as the null hypothesis.

The aim of this paper is to examine the performance of the geographically weighted regression (GWR) technique in terms of recognizing linear relationships at the local level. Using a Monte Carlo analysis with two independent spatially autocorrelated SAR(1) processes, this study finds that spurious behavior exists at the local level along with spatially autocorrelated errors. Therefore, GWR estimation results must be interpreted with caution. [ABSTRACT FROM AUTHOR]

We develop a simple method that completely eliminates the specification error and spurious relationships in regression. Furthermore, we introduce a stronger test of causality. We apply our method to oil prices. [ABSTRACT FROM AUTHOR]

We introduce a method that eliminates the specification error and spurious relationships in regression. In addition, we introduce a test of strong causality. Furthermore, hypothesis testing (inference) becomes almost unneeded. Moreover, this method virtually resolves error problems such as heteroscedasticity, autocorrelation, non-stationarity and endogeneity. [ABSTRACT FROM AUTHOR]

This paper develops a new estimator for cointegrating and spurious regressions by applying a two-stage generalized Cochrane-Orcutt transformation based on an autoregressive approximation framework, even though the exact form of the error term is unknown in practice. We prove that our estimator is consistent for a wide class of regressions. We further show that a convergent usual t-statistic based on our new estimator can be constructed for the spurious regression cases analyzed by (Granger, C. W. J., and P. Newbold. 1974. "Spurious Regressions in Econometrics." Journal of Econometrics 74: 111-120) and (Granger, C. W. J., N. Hyung, and H. Jeon. 2001. "Spurious Regressions with Stationary Series." Applied Economics 33: 899-904). The implementation of our estimator is easy since it does not necessitate estimation of the long-run variance. Simulation results indicate the good statistical properties of the new estimator in small and medium samples, and also consider a more general framework including multiple regressors and endogeneity. [ABSTRACT FROM AUTHOR]

It is known that the traditional prewhitening heteroscedasticity-autocorrelation consistent (HAC) methods have finite sample bias, leading to a spurious regression between stationary processes. This paper proposes a modified prewhitening HAC method by the first-order and higher-order medianunbiased estimation, and adjusts the standard error of t-statistics in OLS estimation through the modified prewhitening HAC methods, and reveals their applicability in spurious regression probability between stat ionary processes. The result shows that: first, the modified prewhitening HAC methods can reduce finite sample bias in long-run variance estimation; second, the modified HAC methods have a robustness property to persistence of data process, GARCH heteroscedasticity and non-noraial innovations. [ABSTRACT FROM AUTHOR]

This article examines the spurious regression phenomenon between long memory series if the generating mechanism of individual series is assumed to follow a stationary/nonstationary process with mis-specified breaks. By using least-squares regression, the t-ratio becomes divergent and spurious regression is present. The intuition behind this is that the long memory series with change points can increase persistency in the level of regression errors and cause such spurious relationship. Simulation results indicate that the extent of spurious regression heavily relies on memory index, sample size, and location of break. As a remedy, we employ a four-stage procedure motivated by Maynard, Smallwood and Wohar (2013, Econ. Rev., 32, 318-360) to alleviate the size distortions. Finally, an empirical illustration using some stock price data from Shanghai Stock Exchange is reported. [ABSTRACT FROM AUTHOR]

Power output from photovoltaic (PV) systems in outdoor conditions is substantially influenced by climatic parameters such as solar irradiance and temperature. PV manufacturers always provide technical specifications in laboratory conditions but reliable relationship for the power output must be determined for accurate prediction under real operating conditions. For the present study, solar irradiance G, temperature T and electrical power output P data under real conditions are methodically and regularly inscribed in dataloggers. Hence, in this paper, we investigate rigorous and robust statistical methods for small sample such as Augmented Dickey- Fuller and Engle Granger for stationary series to determine the estimate regression between variables P, G & T. A first regression of power output P time series variable on solar irradiance G time series has shown spurious results and thus spurious regression. The first differences of such time series are stationary and a regression is proposed whereas temperature variable is identified as not significant and where autocorrelation of residuals is suspected. Finally, the novelty of this paper is the Engle & Granger method that is used to provide a relationship between variables P and G in a difference level. A final relationship without suspicious heteroscedasticity has been determined. Our model is formulated on the basis of PV real conditions statistical approach and is more realistic than steady approach models. [ABSTRACT FROM AUTHOR]

This paper examines the effects of permanent changes in the variance of the errors on routine applications of standard t-ratio test in regression models. It is shown the asymptotic distribution of t-ratio test is not invariant to non-stationary in variance, and the phenomenon of spurious regression will occur independently of the structure assumed for these time series. The intuition behind this is that the non-stationary volatility can increase persistency in the level of regression errors, which then leads to spurious correlation. Monte Carlo experiment evidence indicates that, in contrast to the broken level/trend case, the presence of spurious relationship critically depends on the location and magnitude of changes, regardless of the sample size. Finally, some real data sets from the Shanghai stock database are reported for illustration. [ABSTRACT FROM AUTHOR]

Declining inflation persistence has been documented in numerous studies. We show that when time series with changes in persistence are analyzed in a regression framework with other persistent time series like interest rates, spurious regressions are likely to occur. We propose the coefficient of determination R2 as a simple test statistic to distinguish between spurious and genuine regressions in situations where time series possibly exhibit changes in persistence. We extend the analysis towards fractional (co-)integration as well. To this end, we establish the limit theory for the R2 statistic and conduct a Monte Carlo study where we investigate its finite-sample properties. The test performs remarkably well in terms of size and power and is robust to level shifts and multiple changes in persistence. Finally, we apply the test to the Fisher equation for the United States. The newly proposed R2-based test offers robust evidence favourable to the Fisher hypothesis. [ABSTRACT FROM AUTHOR]

The HadCRUT4 time series of 166 annual values of global average temperature was analysed both deterministically and stochastically and the results compared. The deterministic model comprised the sum of a linear trend and a multi-decadal oscillation fitted by ordinary least squares regression. The stochastic model was an ARMA(1,2) model with a drift term included. The deterministic model showed a linear trend of 0.5°C per century while the stochastic model showed no significant drift. In both cases, the residuals were tested for self-correlation using standard statistical tests. The residuals from the deterministic model were significantly selfcorrelated whereas those from the stochastic model were not. We conclude that the stochastic model was a much better fit to the data and that the apparent linear trend of the deterministic model was spurious and a consequence of performing a regression in which time was the explanatory variable. [ABSTRACT FROM AUTHOR]

Contrary to common belief, cointegration testing may not distinguish between spurious relations and genuine ones. It is demonstrated that highly correlated series appear as cointegrated, even though common sense tells us that the underlying relation does not make sense. Empirical testing using simulated data, data from daily life and historical data on interest rates shows that cointegration may fail not only to detect spurious correlation but also to capture cointegration in a genuine relation. Cointegration testing to reveal spurious correlation can only be used in conjunction with theory, common sense and intuition. [ABSTRACT FROM AUTHOR]

This article extends the theoretical analysis of spurious relationship and considers the situation where the deterministic components of the processes generating individual series are independent heavy-tailed with structural changes. It shows when those sequences are used in ordinary least-square regression, the convenientt-statistic procedures wrongly indicate that (i) the spurious significance is established when regressing mean-stationary and trend-stationary series with structural changes, (ii) the spurious relationship occurs under broken mean-stationary and difference-stationary sequences, and (iii) the extent of spurious regression becomes stronger between difference-stationary and trend-stationary series in the presence of breaks. The spurious phenomenon is present regardless of the sample size and structural breaks taking place at the same points or not. Simulation experiments confirm our asymptotic results and reveal that the spurious effects are not only sensitive to the relative location of structural changes with the sample, but seriously depend on the stable indexes. [ABSTRACT FROM PUBLISHER]

Granger and Newbold (1974) proposed the idea of spurious regression in econometrics. They showed that with I(1) dependent and independent variables, if a regression model is estimated by OLS method, the results may be spurious. This idea is extended to variables with different order of integration. In this paper , we review the literature of spurious regression and show that when the variables have different order of integration , for example I(1) & I(2) , and I(1) & I(0) , the spurious results may occur.

In order to diminish size distortions of the t test in a time series linear specification, Agiakloglou (Agiakloglou in Empir Econ, 45(3):1361-1366, 2013) proposed to (1) include the first lag of the dependent variable as a regressor or (2) estimate it using the first differences of the variables. He provided finite-sample evidence to support his proposal. In this paper, we extend the Monte Carlo experiment to different data-generating processes and calculate the asymptotic behavior of the modified specifications. We show that including the lag of the dependent variable as a regressor reduces size distortions when the variables are driftless unit roots, but this approach does not hold under the presence of long memory, nonlinearities, or structural breaks. [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]

The traditional prewhitening HAC methods have finite sample bias, leading to spurious regression probability is higher in regression models between independent stationary processes. This paper proposes to modify the traditional prewhitening HAC methods by using the bootstrap-correction method in the estimation of autoregressive coefficients, aims to reduce their finite sample bias, thus further reducing the possibility of spurious regression. At the same time, by comparing with the first-order bias-correction prewhitening HAC methods, we find the bootstrap-correction prewhitening HAC methods can not only reduce finite sample bias, but also obviously reduce spurious regression probability, and has better robustness than the first-order bias-correction methods under GARCH heteroscedasticity and higher-order autoregressive data generation processes. [ABSTRACT FROM AUTHOR]

This paper answers two questions: “What impact have natural resources had on the spread of the HIV epidemic so far?” and “What role can natural resource rents play in order to finance the long-run response to HIV/AIDS?” Using a panel dataset covering 137 countries from 1990 until 2008, de Soysa and Gizelis (2013) provided evidence in Social Science & Medicine that oil-rich countries are more deeply affected by the HIV and TB epidemics. They concluded that government of resource-rich countries failed to implement effective public policies for dealing with the epidemics. In this paper, I show that their results are (1) not robust, (2) based on an inappropriate choice of dependent variable and (3) spurious because series are non-stationary. After correcting for these issues, I find no robust relationship between resource rents and the spread of HIV and TB. The paper concludes by emphasizing the potential of natural resources rents for financing the long-term liability brought about by the HIV/AIDS epidemic in sub-Saharan Africa. [ABSTRACT FROM AUTHOR]

Spurious regression occurs when two independent stationary or nonstationary time series are found to be correlated. Spurious behaviour is also detected in spatial data. Using a Monte Carlo analysis, this study examines the spurious phenomenon for two independent stationary spatial autoregressive processes of order one, that is, SAR(1), and it finds that when spatial econometric models are estimated, as suggested by the LM specification tests, the spurious behaviour is not detected nor the presence of spatially autocorrelated errors. [ABSTRACT FROM PUBLISHER]

This paper examines whether stock market returns forecasts should take account of the political party in power by re-examining the prior literature to demonstrate that US stock market political regime differences are neither significant nor long-lasting. We demonstrate that the presidential regime dummy variable used in prior studies is highly auto-correlated, thus potentially violating the ordinary least squares assumption of independently distributed regression errors. Simulation and bootstrap analyses are used to demonstrate that prior findings of higher returns and lower risk under Democratic presidencies are less than would be expected by chance, once account is taken of the persistence properties of the presidential regime dummy variable used in prior studies. Theoretical considerations are also used to explain why presidential regime differences are unlikely to persist, thus further reconciling the paper’s findings with prior studies. [ABSTRACT FROM AUTHOR]