TS Module 3: Trends HW


TS Module 3: Trends HW

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NEAS
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TS Module 3: Trends HW

 

(The attached PDF file has better formatting.)

 

Homework assignment: MA(1) Process: Variance of mean

 

Five MA(1) processes with 50 observations are listed below. The variance of åt is 1.

 


A.     For each process, what is the variance of , the average of the Y observations?

B.     How does the pattern of the first time series differ from that of the last time series?

C.    Explain intuitively why oscillating patterns have lower variances of their means.

 

 


 

1.      Yt = ì + et + et-1

2.      Yt = ì + et + ½ et-1

3.      Yt = ì + et

4.      Yt = ì + et – ½ et-1

5.      Yt = ì + et – et-1


 

 

(See page 50 of the Cryer and Chan text, Exercise 3.2)

 

 


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TS Module 3 variance of mean HW.pdf (2.3K views, 32.00 KB)
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nacho
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LIAPP,

I used the following 'givens' and I made a table like the one below to help me through the calculations.  Hope it helps.

Givens: N=50; Var(e)=1; Var(Y_t) = Var(mu)+Var(A)+Var(B); rho_1=Cov(Y_t,Y_t-1)/Var(Y_t);  that last 'given' is explained in this forum and in the book (I think)

Table:

#     Var            Cov(Y_t,Y_t-1)            rho_1            Formula from bottom of page 28

1    0+1+1=2;      Var(e)=1;                   1 / 2 = .5;      2/50 * [1 + 2*(50-1)/50*(.5)]=0.0792

2    0+1+1/4=1.25; .5*Var(e)=.5 ;            .5/1.25=.4 ;   1.25/50[1+1.96*(.4)=0.0446

and so on and so forth.  I'd write it al lout, but I don't have the time.    


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