Time series

Discussion in 'CS2' started by Anu Joshi, Mar 3, 2019.

  1. Anu Joshi

    Anu Joshi Active Member

    Hello .
    In time series chapter , I'm able to do questions which are about calculating ACF and PACF or of identifying the model using graph or check whether it's a white noise or turning points or ljung box test . But when they give questions like that of April 2015 (CT6) I'm not able to do it. I understood the part i) but doing the part iii) of the question seems tricky. I didn't understand why the choosed y11,y12,y13 ..
     
  2. Sid Kumar

    Sid Kumar Member

    Mate, in these type of questions (where you are looking at an MA(q) process), the approach is to open both terms in the calculation of covariance ie. y0=(Xt, Xt)=(e0+b1et-1+...., e0+b1et-1+....). Then you can see that the error terms have zero covariance at all lags EXCEPT with same lags (ie (cov(e0,e0)=sigma square)). Therefore at lag 11 (for y11) the first term in Xt-11 is et-11, second term is b1et-12 and so on, therefore y11=cov(Xt, Xt-11)=cov(e0+b1et-1+b12et-12+b1b12et-13, et-11+b1et-12+b12et-23+b1b12et-24)= b1b12sigma square. this process stops at y13 as the first term in Xt-13 is et-13 which has a covariance with b1b12et-13 in Xt. You can see that y14 has all terms for lagged Xt-14 will have zero covariance with terms in Xt. As the lag increases, the same applies therefore it stops after lag 13
     

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