Question

2. FoRECASTING wITH MA PROCESSES. (i) How to check the invertibility of an MA(1) model? (ii) Suppose we use an MA model to model the process represented in Figure 2. Write down the model and find the estimates of the coefficients. (15 marks) 200 225 250 275 300 325 350 375 400 Sample: 1 2000 Included observations: 1999 Autocorrelation Partial Correlation AC PAC 10.498 0.498 2-0.042-0.386 -0.081 0.220 40.042 -0.183 5 0.003 0.157 6 0.013-0.127 7 0.019 0.131 8 0.013-0.112 9-0.004 0.092 10 -0.010 -0.088 Figure 2: Time Series Plot and Autocorrelation Functions 1

Answer 1

Time series is the method of analyzing data for future prediction, estimation, and forecasting. The types of such analyzing are trend, cycle, and seasonal.

Features are as below:

Trend: This is the long-term analyzing of data, which gives estimation for future. If the trend is increasing, such estimation should also be increased; or vice versa.

Cycle: This is the short-period rotation of ups and downs of data analyzing. It gives idea when will be the cycle starts and ends in future. Usually it takes to complete a rotation around 2.5 year time.

Seasonal: This is all those fixed periods when data used to increase. Example is increasing revenue on Christmas time. Such data are highly predictable in f