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Where is the EViews function for computing the correlation between two series XI and X2. The text value was obtained using the EViews command This value differs slightly from that reported in the text which is r 1 – 0.404. The values obtained for their sums are, leading to a value for r 1 of
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The first observation in each of the series EE1 and E1E1 will be NA. We have created two new series, e te t-1 and e² t-1, and then found their sum. The numerator and denominator of this quantity can be computed using the following commands Now consider the first-order correlation r, given in equation (9.18) on page 234 of the text When asked to perform calculations that include this first observation, EViews will omit it. Because there is no observation e 0, the first observation on EHAT_1 is “not available” and is recorded as NA. The 2nd observation for EHAT_1 is e, the 3rd observation is e 2, and so on. They are illustrated on the following page. To appreciate how lagged observations are stored, we create a group containing EHAT and EHAT_1 and examine the first few observations in the spreadsheet. Writing ehat(-1) has the effect of lagging the observations in EHAT by one period. To compute this quantity we begin by creating the variable e. The sample correlation between the least squares residuals e t and their lagged values e,_, is an important quantity for assessing whether or not the equation errors are autocorrelated. If you then follow up by clicking, you will be able to edit and save the graph. For example, you could open the series EHAT and then select View/Graph/Basic graph/Line & Symbol. There are other ways to create this graph. To save this graph in your workfile, click on [Freeze 1 and then [Name! and enter a suitable name. To obtain the plot in Figure 9.3 open the least-squares estimated equation and go to View/Actual, Fitted, Residual/Residual Graph. The first and last 8 values are as follows.Ī plot of the residuals against time can indicate whether positive residuals tend to follow positive residuals and negative residuals tend to follow negative residuals – a sign of positive autocorrelation.
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The command series ehat = resid saves the residuals as To view them double click on EHAT and select View/SpreadSheet. As a first step for this example, we save them and then check them against the values that appear in Table 9.1. Various ways of examining the residuals were described at the beginning of Chapter 8. We are interested in examining the residuals from this estimated equation, as displayed in Table 9.1 on page 233 of the text. The Equation specification and resulting least-squares output are We have 34 annual observations stored in the fde bangla.wfl. In contrast to earlier chapters where the index used for the observations was mainly i, here we use the index t to denote time-series observations. The first example considered in Chapter 9 is an area response model for sugarcane in Bangladesh where area sown to sugarcane A is related to price P by the equation LEAST-SQUARES RESIDUALS: SUGARCANE EXAMPLE The point that I want to make is the following: Testing for non-stationarity and co-integration of your variables is still useful as it guides you towards the optimal model choice (VECM, ARDL in levels, ARDL in first differences).1. If all of your variables are I(0) then you obviously do not have any problem with the ARDL model. However, in this case it would be more efficient to estimate an ARDL model directly in first differences. If your variables are I(1) but you do not have any co-integrating relationship among them, estimation is still fine because there exist values for the population parameters such that the error term can be I(0) due to the inclusion of lags of the dependent variable (the sum of the coefficients for the lags of depvar would equal unity in the underlying data generating process such that the level term drops out in the error-correction representation of the model similarly for indepvars that are I(1)). All those components are then I(0) which shows that you can safely estimate this ARDL model in levels. If your variables are I(1) and you have exactly one co-integrating relationship, you can rewrite the ARDL model analytically in error-correction representation with first-differences of depvar on the left-hand side, the co-integrating relationship of the level variables as well as additional lags of first-differenced depvar and indepvars on the right-hand side.
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In that case you would prefer to estimate a vector error-correction model (VECM). If your variables are I(1) and you have more than one co-integrating relationship among them, the single-equation ARDL model would be misspecified as it can accommodate only one co-integrating relationship.