Econometrics Assignment Example | Topics and Well Written Essays - 1250 words

Econometrics - Assignment Example Frequently Box and Jenkin’s is an iterative method and there may be competing candidates to describe a series. To achieve stationarity or remove trend two techniques are usually applied. The first one involves fitting either a parametric model or a spline function. In this case the ARMA model is applied to the residuals. Alternatively, Box and Jenkins recommended taking suitable differences of the process to achieve stationarity. Here the assumption is that the original series is ARIMA and the difference gives rise to the ARMA series. To determine whether the series has been reduced to a stationary series, one may look at the autocorrelations. For a stationary series, the autocorrelation sequence would converge to 0 quickly as lag increases. The time plot given in Figure 2 is already a stationary series as there is no evidence of any trend. Both autocorrelation plot and partial autocorrelation plot need to be looked at simultaneously. The partial autocorrelation become 0 at lag p+1 or greater when the process is AR(p). Strictly speaking the largest PAC is at lag 2 and the second largest at lag 24. These are the only two significant partial autocorrelations. When consider the ACF at lag 24, no significance is noted. However at lag 16 ACF is significant, but no corresponding significance is noted in PACF. The two components of the observation vector y, the predicted part X ÃŽ ²-hat, and the residual y - X ÃŽ ²-hat are orthogonal. They are uncorrelated and since they follow multivariate normal distribution, they are also independent. Any function of the predicted random vector and any function of the residual vector will also be independently distributed. Using (9) and (12) given in Lecture 5 and using the result that ratio of two independent chi-square variables divided by their respective degrees of freedom, follows an F distribution with proper d.f. the F-statistic for testing parameter of linear regression