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Tham khảo tài liệu 'real estate modelling and forecasting by chris brooks and sotiris tsolacos_5', tài chính - ngân hàng, đầu tư bất động sản phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Diagnostic testing 139 Figure 6.2 Graphical illustration of heteroscedasticity ũt Ạ of the explanatory variables this phenomenon is known as autoregressive conditional heteroscedasticity ARCH . Fortunately there are a number of formal statistical tests for heteroscedas-ticity and one of the simplest such methods is the Goldfeld-Quandt 1965 test. Their approach is based on splitting the total sample of length T into two subsamples of length T1 and T2. The regression model is estimated on each subsample and the two residual variances are calculated as 1 u 1Ũ1 T1 k and 2 u 2u2 T2 k respectively. The null hypothesis is that the variances of the disturbances are equal which can be written H0 ơỊ ơị against a two-sided alternative. The test statistic denoted GQ is simply the ratio of the two residual variances for which the larger of the two variances must be placed in the numerator i.e. 1 is the higher sample variance for the sample with length T1 even if it comes from the second subsample GQ ị 6.1 2 The test statistic is distributed as an F T1 k T2 k under the null hypothesis and the null of a constant variance is rejected if the test statistic exceeds the critical value. The GQ test is simple to construct but its conclusions may be contingent upon a particular and probably arbitrary choice of where to split the sample. Clearly the test is likely to be more powerful when this choice 140 Real Estate Modelling and Forecasting is made on theoretical grounds - for example before and after a major structural event. Suppose that it is thought that the variance of the disturbances is related to some observable variable Zt which may or may not be one of the regressors a better way to perform the test would be to order the sample according to values of zt rather than through time and then to split the reordered sample into T1 and T2. An alternative method that is sometimes used to sharpen the inferences from the test and to increase its power is to omit some of the observations
