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

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

A sharp analysis on the asymptotic behavior of the Durbin-Watson statistic for the first-order autoregressive process

The purpose of this paper is to provide a sharp analysis on the asymptotic behavior of the Durbin-Watson statistic. We focus our attention on the first-order autoregressive process where the driven noise is also given by a first-order autoregressive process. We establish the almost sure convergence and the asymptotic normality for both the least squares estimator of the unknown parameter of the autoregressive process as well as for the serial correlation estimator associated to the driven noise. In addition, the almost sure rates of convergence of our estimates are also provided. It allows us to establish the almost sure convergence and the asymptotic normality for the Durbin-Watson statistic. Finally, we propose a new bilateral statistical test for residual autocorrelation

On the Power of Invariant Tests for Hypotheses on a Covariance Matrix

The behavior of the power function of autocorrelation tests such as the Durbin-Watson test in time series regressions or the Cliff-Ord test in spatial regression models has been intensively studied in the literature. When the correlation becomes strong, Kr\"amer (1985) (for the Durbin-Watson test) and Kr\"amer (2005) (for the Cliff-Ord test) have shown that the power can be very low, in fact can converge to zero, under certain circumstances. Motivated by these results, Martellosio (2010) set out to build a general theory that would explain these findings. Unfortunately, Martellosio (2010) does not achieve this goal, as a substantial portion of his results and proofs suffer from serious flaws. The present paper now builds a theory as envisioned in Martellosio (2010) in a fairly general framework, covering general invariant tests of a hypothesis on the disturbance covariance matrix in a linear regression model. The general results are then specialized to testing for spatial correlation and to autocorrelation testing in time series regression models. We also characterize the situation where the null and the alternative hypothesis are indistinguishable by invariant tests

Pengaruh Jumlah Industri dan Tenaga Kerja Terhadap Nilai Produksi Industri Formal Kecil

The purpose of this study to analyze the effect of the number of industries and labor on the value of production in small industries in Lamongan Regency using the Durbin-Watson test. The Durbin-Watson test is an autocorrelation test that assesses the presence of autocorrelation in residuals. Data taken from the Central Bureau of Statistics of Lamongan Regency. Furthermore, it was analyzed using SPSS assistance. Based on the results of the analysis, it is known that there is no autocorrelation between the number of industries and workers on the value of production in small industries in Lamongan Regency

A New Approach to Detect Spurious Regressions using Wavelets

In this paper, we propose the use of wavelet covariance and correlation to detect spurious regression. Based on Monte Carlo simulation results and experiments with real exchange rate data, it is shown that the wavelet approach is able to detect spurious relationship in a bivariate time series more directly. Using the wavelet approach, it is sufficient to detect a spurious regression between bivariate time series if the wavelet covariance and correlation for the two series are significantly equal to zero. The wavelet approach does not rely on restrictive assumptions which are critical to the Durbin Watson test. Another distinct advantage of the graphical wavelet analysis of wavelet covariance and correlation to detect spurious regression is the simplicity and efficiency of the decision rule compared to the complicated Durbin-Watson decision rules.Wavelet analysis, spurious regression

Monte Carlo evidence on the power of the Durbin-Watson test against nonsense relationships

It is a well-known fact that, in linear regressions involving the levels of integeated processes spuriously related, the Durbin-Watson statistic converges in probability to zero. This, in turn, implies that this statistic can provide an useful testing procedure against the presence of nonsense relationships. Marmol (1997) extends this result to the case of spurious regressions among nonstationary fractionally integrated processes. The aim of this paper is to provide a theoretical overview of these asymptotic results as well as Monte Carlo evidence on the behavior of the Durbin-Watson test in small samples

A model of fractional cointegration, and tests for cointegration using the bootstrap

The paper proposes a framework for modelling cointegration in fractionally integrated processes, and considers methods for testing the existence of cointegrating relationships using the parametric bootstrap. In these procedures, ARFIMA models are fitted to the data, and the estimates used to simulate the null hypothesis of non-cointegration in a vector autoregressive modelling framework. The simulations are used to estimate p-values for alternative regression-based test statistics, including the F goodness-of-fit statistic, the Durbin–Watson statistic and estimates of the residual d. The bootstrap distributions are economical to compute, being conditioned on the actual sample values of all but the dependent variable in the regression. The procedures are easily adapted to test stronger null hypotheses, such as statistical independence. The tests are not in general asymptotically pivotal, but implemented by the bootstrap, are shown to be consistent against alternatives with both stationary and nonstationary cointegrating residuals. As an example, the tests are applied to the series for UK consumption and disposable income. The power properties of the tests are studied by simulations of artificial cointegrating relationships based on the sample data. The F test performs better in these experiments than the residual-based tests, although the Durbin–Watson in turn dominates the test based on the residual d

The impact of financial incentives on organizational commitment: a case study among staffs in Pejabat Pelajaran Daerah Bachok / Nurul Nabilah Mat Husin

This study employs to investigate the impact of financial incentives on organizational commitment among staffs. Research objectives are the main target what a research done in the study. In this study, there are two objectives that to achieve in this research which are to investigate the impact of financial incentives on organizational commitment. Then, the second objective is to examine the relationship between financial incentives and organizational commitment. For this study, the primary data are used. The method used in this research is descriptive method. Data obtained by distributing questionnaires to 120 staffs in Pejabat Pelajaran Daerah (PPD) Bachok. The participation in survey was voluntary and confidentiality of responses was ensured. The data has been analyzed by using SPSS program and tested by correlation coefficient (R), coefficient of determination (R²), F-test, T-test and Durbin Watson test. The researcher rejects Ho in all hypotheses and all variables of each questions considered being reliable and acceptable. For hypothesis 1, it indicating that promotional opportunities have a significant relationship with the organization commitment which results of R, R², F-test, T-test and Durbin Watson are positively significant and relatively internal consistency. For hypothesis 2, it indicating that reward and recognition have a significant relationship with the organization commitment which results of R, R², F-test, T-test and Durbin Watson showed that the model used in this study are strong and correct. It indicating that fringe benefits have a significant relationship with the organization commitment which results of R, R², F-test, T-test and Durbin Watson are significant and reject Ho in the hypothesis 3. From this study, it was found that all variables are significant with the organizational commitment. The statistical analysis showed that different dimensions of work motivation and job satisfaction are significantly correlated and promotional opportunities, reward and recognition and fringe benefits have great impact on organizational commitment