Spurious Regression Phenomenon Research Articles

Spurious regression between long memory series due to mis-specified structural breaks

ABSTRACTThis 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.

Spurious regression due to neglected of non-stationary volatility

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.

Prediction of primary energy demand in China based on AGAEDE optimal model

In this article, we present an application of Adaptive Genetic Algorithm Energy Demand Estimation (AGAEDE) optimal model to improve the efficiency of energy demand prediction. The coefficients of the two forms of the model (both linear and quadratic) are optimized by AGA using factors, such as GDP, population, urbanization rate, and R&D inputs together with energy consumption structure, that affect demand. Since the spurious regression phenomenon occurs for a wide range of time series analysis in econometrics, we also discuss this problem for the current artificial intelligence model. The simulation results show that the proposed model is more accurate and reliable compared with other existing methods and the China’s energy demand will be 5.23 billion TCE in 2020 according to the average results of the AGAEDE optimal model. Further discussion illustrates that there will be great pressure for China to fulfill the planned goal of controlling energy demand set in the National Energy Demand Project (2014–2020).

Spurious Relationship of AR(P) Stable Sequences in Presence of Trends Breaks

This paper analyzes spurious regression phenomenon involving AR(p) stable processes with trend breaks. It shows that when those time series are used in ordinary least squares regression, the convenient t-ratios procedures wrongly indicate that the spurious relationship is present as the pair of independent stable series contains trend changes. The spurious relationship becomes stronger as the sample size approaches to infinite. As a result, spurious effects might occur more often than we previously believed as they can arise even between AR(p) stable series in present of trend breaks.

Polynomial cointegration tests of anthropogenic impact on global warming

Abstract. We use statistical methods for nonstationary time series to test the anthropogenic interpretation of global warming (AGW), according to which an increase in atmospheric greenhouse gas concentrations raised global temperature in the 20th century. Specifically, the methodology of polynomial cointegration is used to test AGW since during the observation period (1880–2007) global temperature and solar irradiance are stationary in 1st differences, whereas greenhouse gas and aerosol forcings are stationary in 2nd differences. We show that although these anthropogenic forcings share a common stochastic trend, this trend is empirically independent of the stochastic trend in temperature and solar irradiance. Therefore, greenhouse gas forcing, aerosols, solar irradiance and global temperature are not polynomially cointegrated, and the perceived relationship between these variables is a spurious regression phenomenon. On the other hand, we find that greenhouse gas forcings might have had a temporary effect on global temperature.

Resolving spurious regressions and serially correlated errors

This study investigates the spurious regression phenomenon for two independent stationary and non-stationary processes and illustrates, using a Monte Carlo analysis, that estimation of the spurious regression in first differences or with a lagged dependent variable eliminates the spurious regression problem. Moreover, the results also apply in eliminating the problem of serially correlated errors as well as the problem of ARCH(1) errors.

Spurious Instrumental Variables

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.

Spurious Regressions of Stationary AR(p) Processes with Structural Breaks

When a pair of independent series is highly persistent, there is a spurious regression bias in a regression between these series, closely related to the classic studies of Granger and Newbold (1974). Although this is well known to occur with independent I(1) processes, this paper provides theoretical and numerical evidence that the phenomenon of spurious regression also arises in regressions between stationary AR(p) processes with structural breaks, which occur at different points in time, in the means and the trends. The intuition behind this is that structural breaks can increase the persistence levels in the processes (e.g., Granger and Hyung (2004)), which then leads to spurious regressions. These phenomena occur for general distributions and serial dependence of the innovation terms.

Spurious Regressions of Stationary AR(p) Processes with Structural Breaks

When a pair of independent series are highly persistent, there is a spurious regression bias in a regression between these series, closely related to the classic studies of Granger and Newbold [1974]. Although this is well known to occur with independent I(1) processes, this paper provides theoretical and numerical evidences that the phenomenon of spurious regression also arises in regressions between stationary AR(p) processes with structural breaks in the means and the trends. An intuition behind this is that structural breaks can increase the persistence levels in the processes (see, e.g., Granger and Hyung [2004]), which then leads to spurious regressions. These phenomena occur for general distributions and serial dependence of the innovation terms.

Evidence of ARCH(1) Errors in the Context of Spurious Regressions

The spurious regression phenomenon is related to first-order serially correlated errors. This study, using a Monte Carlo analysis, finds that this phenomenon is also related to ARCH(1) type errors.

Spurious Regression

The spurious regression phenomenon in least squares occurs for a wide range of data generating processes, such as driftless unit roots, unit roots with drift, long memory, trend and broken‐trend stationarity. Indeed, spurious regressions have played a fundamental role in the building of modern time series econometrics and have revolutionized many of the procedures used in applied macroeconomics. Spin‐offs from this research range from unit‐root tests to cointegration and error‐correction models. This paper provides an overview of results about spurious regression, pulled from disperse sources, and explains their implications.

A note on spurious regression in seasonal time series

This paper considers spurious regression between two different types of seasonal time series: one with a deterministic seasonal component and the other with a stochastic seasonal component. When one type of seasonal time series is regressed on the other type and they are independent of each other, the phenomenon of spurious regression occurs. Asymptotic properties of the regression coefficient estimator and the associated regression ‘t-ratio’ are studied. A Monte Carlo simulation study is conducted to confirm the phenomenon of spurious regression and spurious rejection of seasonal cointegration for finite samples.

Spurious Regression and Trending Variables*

AbstractThis paper analyses the asymptotic and finite‐sample implications of different types of non‐stationary behaviour among the dependent and explanatory variables in a linear spurious regression model. We study cases when the non‐stationarity 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 spurious regression equation under a variety of empirically relevant data generation processes, and show that the spurious regression phenomenon is present in all cases when both dependent and explanatory variables behave in a non‐stationary way. Simulation experiments confirm our asymptotic results.

Spurious Regression Under Broken‐Trend Stationarity

Abstract. 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 independent 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 regressions with stationary processes around linear trends

In this paper we consider the situation where the deterministic components of the processes generating individual series are linear trends and the individual series are independent I(0) processes. We show that when those time series are used in ordinary least squares regression, the phenomenon of spurious regression occurs.

Spurious Regressions with Processes Around Linear Trends or Drifts

In this paper we consider the situation where the deterministic components of the processes generating individual series are linear trends and the individual series are independent I(0) or I(1) processes. We show that when those time series are used in ordinary least square regression, the phenomenon of spurious regression occurs regardless of whether a time trend is included in the regression.

Deterministic seasonal models and spurious regressions

This paper examines the consequences of using seasonal dummies in regressions when seasonality is generated by seasonal unit roots. A unit root process can produce a deterministic seasonal pattern if the starting values contain a strong seasonal. It is shown, however, that subtraction of fixed seasonal means from a seasonally integrated series changes the covariance structure of the series, and often the means-subtracted series may take the appearance of a stationary series in small samples. Monte Carlo results based on series with at least one seasonal unit root show that spurious regressions are very likely if seasonal dummies are used to remove seasonality. Applications to ten real GDP series provide supporting evidence for the spurious regression phenomenon. However, seasonal dummies may provide a reasonable approximation in certain cases. An alternative approach is to use the seasonal filter S(L).