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

Econometrics - Assignment ExampleFrequently Box and Jenkins is an iterative method and there whitethorn be competing candidates to describe a series.To achieve stationarity or remove trend ii techniques are usually applied. The first one involves fitting either a parametric model or a spline portion. 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. present 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 overtone autocorrelation plot need to be looked at simultaneously. The pa rtial 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 -hat, and the residual y - X -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