Spatial autocorrelation approaches to testing residuals from least squares regression

In statistics, the Durbin-Watson test is always employed to detect the presence of serial correlation of residuals from a least squares regression analysis. However, the Durbin-Watson statistic is only suitable for ordered time or spatial series. If the variables comprise cross-sectional data coming from spatial random sampling, the Durbin-Watson will be ineffectual because the value of Durbin-Watson's statistic depends on the sequences of data point arrangement. Based on the ideas from spatial autocorrelation, this paper presents two new statistics for testing serial correlation of residuals from least squares regression based on spatial samples. By analogy with the new form of Moran's index, an autocorrelation coefficient is defined with a standardized residual vector and a normalized spatial weight matrix. Then on the analogy of the Durbin-Watson statistic, a serial correlation index is constructed. As a case, the two statistics are applied to the spatial sample of 29 China's regions. These results show that the new spatial autocorrelation model can be used to test the serial correlation of residuals from regression analysis. In practice, the new statistics can make up for the deficiency of the Durbin-Watson test.Comment: 27 pages, 4 figures, 5 tables, 2 appendice

Testing for Serial Correlation, Spatial Autocorrelation and Random Effects

This paper considers a spatial panel data regression model with serial correlation on each spatial unit over time as well as spatial dependence between the spatial units at each point in time. In addition, the model allows for heterogeneity across the spatial units using random effects. The paper then derives several Lagrange Multiplier tests for this panel data regression model including a joint test for serial correlation, spatial autocorrelation and random effects. These tests draw upon two strands of earlier work. The first is the LM tests for the spatial error correlation model discussed in Anselin and Bera (1998) and in the panel data context by Baltagi, Song and Koh (2003). The second is the LM tests for the error component panel data model with serial correlation derived by Baltagi and Li (1995). Hence the joint LM test derived in this paper encompasses those derived in both strands of earlier works. In fact, in the context of our general model, the earlier LM tests become marginal LM tests that ignore either serial correlation over time or spatial error correlation. The paper then derives conditional LM and LR tests that do not ignore these correlations and contrast them with their marginal LM and LR counterparts. The small sample performance of these tests is investigated using Monte Carlo experiments. As expected, ignoring any correlation when it is significant can lead to misleading inferencepanel data, spatial correlation

Statistical properties and economic implications of Jump-Diffusion Processes with Shot-Noise effects

This paper analyzes the Shot-Noise Jump-Diffusion model of Altmann, Schmidt and Stute (2008), which introduces a new situation where the effects of the arrival of rare, shocking information to the financial markets may fade away in the long run. We analyze several economic implications of the model, providing an analytical expression for the process distribution. We also prove that certain specifications of this model can provide negative serial persistence. Additionally, we find that the degree of serial autocorrelation is related to the arrival and magnitude of abnormal information. Finally, a GMM framework is proposed to estimate the model parameters

The Slowdown in Soviet Defense Expenditures: Comment

The reason for the apparently opposing results in Brada and Graves\u27 (1988) attempt to explain the reasons for the slowdown in USSR defense expenditures in the mid-1970s is that their analysis suffers from a serious serial correlation problem. The majority of the regressions display Durbin-Watson statistics that reject the null hypothesis of no autocorrelation. A reestimation of their results, after correcting for serial correlation, changes some of their major conclusions regarding the factors influencing Soviet defense spending. The corrected results indicate that no structural break occurred in the mid-1970s. These results suggest that there has been no change in Soviet military doctrine or in the Soviet leadership\u27s preferences in the 1970s. In reply, Brada and Graves argue that the evidence for the existence of serially correlated disturbances is much more tenuous than Chowdhury suggests and that the evidence is more consistent with the existence of a structural break and no serial correlation of disturbances

A Durbin-Watson serial correlation test for ARX processes via excited adaptive tracking

We propose a new statistical test for the residual autocorrelation in ARX adaptive tracking. The introduction of a persistent excitation in the adaptive tracking control allows us to build a bilateral statistical test based on the well-known Durbin-Watson statistic. We establish the almost sure convergence and the asymptotic normality for the Durbin-Watson statistic leading to a powerful serial correlation test. Numerical experiments illustrate the good performances of our statistical test procedure

Statistical Properties and Economic Implications of Jump-Diffusion Processes with Shot-Noise Effects

This paper analyzes the Shot-Noise Jump-Diffusion model of Altmann, Schmidt and Stute (2008), which introduces a new situation where the effects of the arrival of rare, shocking information to the financial markets may fade away in the long run. We analyze several economic implications of the model, providing an analytical expression for the process distribution. We also prove that certain specifications of this model can provide negative serial persistence. Additionally, we find that the degree of serial autocorrelation is related to the arrival and magnitude of abnormal information. Finally, a GMM framework is proposed to estimate the model parameters.Filtered Poisson Process, Characteristic Function, Generalized Method of Moments

The Slowdown in Soviet Defense Expenditures: Comment

The reason for the apparently opposing results in Brada and Graves\u27 (1988) attempt to explain the reasons for the slowdown in USSR defense expenditures in the mid-1970s is that their analysis suffers from a serious serial correlation problem. The majority of the regressions display Durbin-Watson statistics that reject the null hypothesis of no autocorrelation. A reestimation of their results, after correcting for serial correlation, changes some of their major conclusions regarding the factors influencing Soviet defense spending. The corrected results indicate that no structural break occurred in the mid-1970s. These results suggest that there has been no change in Soviet military doctrine or in the Soviet leadership\u27s preferences in the 1970s. In reply, Brada and Graves argue that the evidence for the existence of serially correlated disturbances is much more tenuous than Chowdhury suggests and that the evidence is more consistent with the existence of a structural break and no serial correlation of disturbances

Asymptotic Variance of Brier (Skill) Score in the Presence of Serial Correlation

We propose autocorrelation-robust asymptotic variances of the Brier score and Brier skill score, which are generally applicable in circumstances with weak serial correlation. An empirical application in macroeconomics underscores the importance of taking care of serial correlation. We find that the conventional variances are too conservative to account for the sampling variability in estimating the Brier (skill) score

Alternative approaches to implementing Lagrange multiplier tests for serial correlation in dynamic regression models

An approximate F-form of the Lagrange multiplier test for serial correlation in dynamic regression models is compared with three bootstrap tests. In one bootstrap procedure, residuals from restricted estimation under the null hypothesis are resampled. The other two bootstrap tests use residuals from unrestricted estimation under an alternative hypothesis. A fixed autocorrelation alternative is assumed in one of the two unrestricted bootstrap tests and the other is based upon a Pitman-type sequence of local alternatives. Monte Carlo experiments are used to estimate rejection probabilities under the null hypothesis and in the presence of serial correlation

Volatility persistence and time-varying betas in the UK real estate market

This paper investigates the degree of return volatility persistence and the time-varying behaviour of systematic risk (beta) for 31 market segments in the UK real estate market. The findings suggest that different property types exhibit differences in volatility persistence and time variability. There is also evidence that the volatility persistence of each market segment and its systematic risk are significantly positively related. Thus, the systematic risks of different property types tend to move in different directions during periods of increased market volatility. Finally, the market segments with systematic risks less than one tend to show negative time variability, while market segments with systematic risk greater than one generally show positive time variability, indicating a positive relationship between the volatility of the market and the systematic risk of individual market segments. Consequently safer and riskier market segments are affected differently by increases in market volatility