Typically consumer confidence typically consumer

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Typically, consumer confidence Typically, consumer confidence will continue to be high e t > 0 will continue to be low e t < 0 this month; consumers will this month; consumers will spend more freely, spend less freely, consume more, this month consume less, this month As a consequence of the business cycle we would expect the error term to exhibit some “inertia.” Positive error terms tend to follow positive error terms; negative error terms tend to follow negative error terms. Consequently, we suspect that the error terms are not independent; instead, we suspect that the error terms will be positively correlated, positive autocorrelation. How can we “test” our suspicions?
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22 Of course we can never observe the error terms themselves. We can, however, use the residuals to estimate the error terms: Error Term Residual y t = β Const + β x x t + e t Res t = y t Est t e t = y t ( β Const + β x x t ) Res t = y t ( b Const + b x x t ) We can think of the residuals as the estimated errors. Since the residuals are observable we use the residuals as proxies for the error terms. Figure 17.8 plots the residuals. Figure 17.8: Plot of the Residuals The residuals are plotted consecutively, one month after another. As we can easy see, a positive residual is typically followed by another positive residual; a negative residual is typically followed by a negative residual. “Switchovers” do occur, but they are not frequent. This suggests that positive autocorrelation is present. Most statistical software provides a very easy way to look at the residuals.
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23 Getting Started in EViews___________________________________________ First, run the regression. In the Equation window, click View Click Actual, Fitted, Residual Click Residual Graph __________________________________________________________________ It is also instructive to construct a scatter diagram of the residuals versus the residuals lagged one month: Figure 17.9: Scatter Diagram of the Residuals Most of the scatter diagram points lie in the first and third quadrants. The residuals are positively correlated.
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24 Since the residual plots suggest that our fears are warranted, we now test the autocorrelation model more formally. While there are many different approaches, we shall focus on the Lagrange Multiplier (LM) approach which uses an artificial regression to test for autocorrelation. 3 We shall proceed by reviewing a mathematical model of autocorrelation. Autocorrelation Model: e t = ρ e t 1 + v t v t ‘s are independent ρ = 0 ρ 0 e t = v t e t depends on e t 1 No autocorrelation Autocorrelation present In this case, we believe that ρ is positive. A positive rho provides the error term with inertia. A positive error term tends to follow a positive error term and a negative error term tends to follow a negative term. But also note that there is a second term, v t . The v t ‘s are independent; they represent random influences which affect the error term also. It is the v t ‘s that “switch” the sign of the error term.
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