The University of Western Australia School of Mathematics & Statistics STAT7450: Time Series Methods and Applications Assignment 2 (2012) Submit solutions by end of Friday 4th May. In these questions, (At) is a white noise process. 1 (a) Is the MA(2) process et = At – 0.1At-1 + 0.21At-2 stationary, or invertible? Give reasons, and find the correlation structure. (b) Let q be a positive integer and t = (1 + q)-1Pqj=0 At-j . Using a scale change, express this process as an ARMA, identifying its orders. Is it stationary or invertible? Determine its correlation structure.
Document Preview:
Need a Professional Writer to Work on this Paper and Give you an A+ 100 % Original Paper? CLICK HERE TO GET THIS PAPER WRITTEN
The University of Western Australia School of Mathematics & Statistics STAT7450: Time Series Methods and Applications Assignment 2 (2012) Submit solutions by end of Friday 4th May. In these questions, (At) is a white noise process. 1 (a) Is the MA(2) process et = At – 0.1At-1 + 0.21At-2 stationary, or invertible? Give reasons, and find the correlation structure. (b) Let q be a positive integer and t = (1 + q)-1Pqj=0 At-j . Using a scale change, express this process as an ARMA, identifying its orders. Is it stationary or invertible? Determine its correlation structure. (c) Show that the ARMA(2,2) process t = 0.4t-1 + 0.45t-2 + At + At-1 + 0.25At-2 can be reduced to an ARMA(1,1), and determine the difference equation form of the reduced process. 2. An MA(6) process has weights 1 = 0.5, 2 = -0.25, 3 = 0.125, 4 = -0.0625, 5 = 0.03125 & 6 = -0.015625. By considering MA(1) representations, find a (very) low order autoregressive process whose GLP weights are essentially the same as for the ’s. Compare the variances and correlations of the two processes, i.e., tabulate them for lags ` = 1, . . . , 6. [Hint: Look at how the weights relate to each other.] You lose no generality by assuming vA = 1, so do this. 3. Let || `). Is the process stationary? Determine circumstances for which Corr(t, t-`) `. (b) Show that redefining 1 = A1/p1 – 2 gives a stationary process. 4. There is quite a lot of fairly recent work in the journal literature about models for stationary processes which have discrete marginal laws. Here is one such. For t = 0,±1,±2, . . ., 1let t = At – 12At-1 where the At’s are independent and standard normal. (a) Show that {t} is strictly stationary and find its correlation structure. Now define the ‘clipped’ process…
Need a Professional Writer to Work on this Paper and Give you an A+ 100 % Original Paper? CLICK HERE TO GET THIS PAPER WRITTEN
The University of Western Australia School of Mathematics & Statistics STAT7450: Time Series Methods and Applications Assignment 2 (2012) Submit solutions by end of Friday 4th May. In these questions, (At) is a white noise process. 1 (a) Is the MA(2) process et = At – 0.1At-1 + 0.21At-2 stationary, or invertible? Give reasons, and find the correlation structure. (b) Let q be a positive integer and t = (1 + q)-1Pqj=0 At-j . Using a scale change, express this process as an ARMA, identifying its orders. Is it stationary or invertible? Determine its correlation structure. (c) Show that the ARMA(2,2) process t = 0.4t-1 + 0.45t-2 + At + At-1 + 0.25At-2 can be reduced to an ARMA(1,1), and determine the difference equation form of the reduced process. 2. An MA(6) process has weights 1 = 0.5, 2 = -0.25, 3 = 0.125, 4 = -0.0625, 5 = 0.03125 & 6 = -0.015625. By considering MA(1) representations, find a (very) low order autoregressive process whose GLP weights are essentially the same as for the ’s. Compare the variances and correlations of the two processes, i.e., tabulate them for lags ` = 1, . . . , 6. [Hint: Look at how the weights relate to each other.] You lose no generality by assuming vA = 1, so do this. 3. Let || `). Is the process stationary? Determine circumstances for which Corr(t, t-`) `. (b) Show that redefining 1 = A1/p1 – 2 gives a stationary process. 4. There is quite a lot of fairly recent work in the journal literature about models for stationary processes which have discrete marginal laws. Here is one such. For t = 0,±1,±2, . . ., 1let t = At – 12At-1 where the At’s are independent and standard normal. (a) Show that {t} is strictly stationary and find its correlation structure. Now define the ‘clipped’ process…
No comments:
Post a Comment