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Real Estate Modelling and Forecasting by Chris Brooks and Sotiris Tsolacos_6

Tham khảo tài liệu 'real estate modelling and forecasting by chris brooks and sotiris tsolacos_6', tài chính - ngân hàng, đầu tư bất động sản phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Diagnostic testing 171 In this figure one point is a long way away from the rest. If this point is included in the estimation sample the fitted line will be the dotted one which has a slight positive slope. If this observation were removed the full line would be the one fitted. Clearly the slope is now large and negative. OLS will not select this line if the outlier is included since the observation is a long way from the others and hence when the residual the distance from the point to the fitted line is squared it will lead to a big increase in the RSS. Note that outliers could be detected by plotting y against x only in the context of a bivariate regression. In the case in which there are more explanatory variables outliers are identified most easily by plotting the residuals over time as in figure 6.10. It can be seen therefore that a trade-off potentially exists between the need to remove outlying observations that could have an undue impact on the OLS estimates and cause residual non-normality on the one hand and the notion that each data point represents a useful piece of information on the other. The latter is coupled with the fact that removing observations at will could artificially improve the fit of the model. A sensible way to proceed is by introducing dummy variables to the model only if there is both a statistical need to do so and a theoretical justification for their inclusion. This justification would normally come from the researcher s knowledge of the historical events that relate to the dependent variable and the model over the relevant sample period. Dummy variables may be justifiably used to remove observations corresponding to one-off or extreme events that are considered highly unlikely to be repeated and the information content of which is deemed of no relevance for the data as a whole. Examples may include real estate market crashes economic or financial crises and so on. Non-normality in the data could also arise from certain types of .