Homework 1 PROBLEM 1: You are going to do a time series decomposition step by step. I have given you 15 data points as followed. The data is seasonal with period 3. Part A: Do an initial estimate of the trend using the appropriate moving average model. Part B: Report your detrended data. Part C: Estimate your seasonal components from the detrended data. Part D: Report your deseasonalized data. Part E: Use linear regression to fit a better trend function to the deseasonalized data. Part F: Produce the following table with the decomposition of your data Part B Part C Part F Part A Centered MA Part D Part E Deseason Trend Data Detrended Seasonal Noise t 1 N 3 4 5 6 7 8 9 10 11 12 13 14 15 5.1 6.3 1.3 5.1 7.8 1.8 9.1 4 6.5 2.9 8.3 1.8 6 8.3 4.8 . PROBLEM 2: Suppose {Xi, t=1, ..., 15 is the data given in Problem 1 Part A: If Z, =V x,, what is the value of Z,? Part B: If Z, =V,X,, what is the value of Zz? Part C: If Z, =V x,, what is the value of Z14? Part D: If Z, = V X,, write out the general formula for Z in terms of the X's