Eac/256 Week 1 Research Paper

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Exercise 1 for ECP 256 1. Identification Figure 1 Figure 2 (1) According to the graph and the correlogram of the original data, it Is obviously that there is a downward trend without any obvious outlying observations (Figure 1). Also, a unit root exists because the autocorrelations decline linearly rather than exponentially towards to zero (Figure 2) so that the data should be differenced before estimation to make it stationary, as well as take the logarithm of the series. Figure 3 Figure 4 (2) By taking the first difference, the trend has been removed and the series seems to be random (Figure 3). As can be seen from the correlogram of dlog(oil), the autocorrelations behave differently (Figure 4). Most of them die down to zero very quickly but every fourth seems to be really significant, picking up the seasonal pattern which also has been shown in the graph. So, taking the fourth difference of the logarithm of the series might be a better choice. Figure 5 Figure 6 (3) After that, the series appears to behave without any trend or strong seasonal pattern (Figure 5), which is effectively and expected. The next step is to re-examine the correlogram and decide how many AR and MA lags to …show more content…

So the goodness of fit is nice until now, but the behaviour of the residuals appears to be not flat (Figure 8). The fourth order autocorrelation is still significant (maybe it is because the frequency of data is quarter) so a MA(4) term should be add to capture that and re-examine whether the model improves or

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