How to check for Heteroscedasticity in XLSTAT The estimation of their variance is not reliable. Why is heteroscedasticity a problem? In linear regression analysis, the fact that the errors of the model (also named residuals) are not homoskedastic has the consequence that the model coefficients estimated using ordinary least squares (OLS) are neither unbiased nor those with minimum variance. Department of Economics, University of Canterbury.The concept of heteroscedasticity - the opposite being homoscedasticity - is used in statistics, especially in the context of linear regression or for time series analysis, to describe the case where the variance of errors of the model is not the same for all observations, while often one of the basic assumption in modeling is that the variances are homogeneous and that the errors of the model are identically distributed. Numerical distribution functions of likelihood ratio tests for cointegration (No. (1995). Likelihood based inference in cointegrated vector autoregressive models. Econometrica: Journal of the Econometric Society, pp.1551-1580. (1991). Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models. (1988). Statistical analysis of cointegration vectors. Journal of economic dynamics and control, 12(2), pp.231-254. (1974). Spurious regressions in econometrics. Journal of econometrics, 2(2), pp.111-120. 1998).Īdjustment coefficients (alpha): This table displays the resulting loading matrix α (see XLSTAT's help document for more details).Ĭointegration coefficients (beta): This table displays the cointegrating matrix β (see XLSTAT's help document for more details). Trace test: This table displays for each rank of cointegration tested the corresponding eigenvalue, the trace test statistic and the associated critical value and p-values (MacKinnon et al. Lambda max test: This table displays for each rank of cointegration tested the corresponding eigenvalue, the lambda max test statistic and the associated critical value and p-values (MacKinnon et al. Each line corresponds to the evaluation of one number of lags from 1 up to the maximum number of lag. VAR order estimation: If the automatic option is selected for the VAR order, this table displays the four criteria values for the VAR order estimation. It is not limited to two time series and allows you to test the existence of multiple cointegrating relationships. This approach, implemented in XLSTAT, is based on Vector Autoregressive (VAR) models. One of the most interesting approaches for testing for cointegration within a group of time series is the maximum likelihood methodology proposed by Johansen (1988, 1991). Those stationary combinations are called cointegrating equations. In other words, there exists one or more linear combination of those I(1) time series (or integrated of order 1, see unit root test) that is stationary (or I(0)). It identifies a situation where two or more non stationary time series are bound together in such a way that they cannot deviate from some equilibrium in the long term. The term of cointegration was first introduced by Engle and Granger (1987) after the work of Granger and Newbold (1974) on spurious regression. In finance, such relationships are expected for instance between the prices of the same asset on different market places. Examples of such relationships in economics include money with income, prices and interest rates or exchange rate with foreign and domestic prices. We say that those variables are cointegrated. Although those variables can derive from each other on a short term basis, the economic forces at work should restore the original equilibrium between them on the long run. What are cointegration tests?Įconomic theory often suggests long-term relationship between two or more economic variables. Use this module to perform VAR-based cointegration tests on a group of two or more I(1) time series using the approach proposed by Johansen (1991, 1995).
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