TS Module 3: Trends HW

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TS Module 3: Trends HW

TS Module 3: Trends HW

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NEAS	NEAS posted 17 Years Ago #8685 #
Supreme Being Group: Administrators Posts: 4.5K, Visits: 1.6K	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 å_t 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. Y_t = ì + e_t + e_t-1 2. Y_t = ì + e_t + ½ e_t-1 3. Y_t = ì + e_t 4. Y_t = ì + e_t – ½ e_t-1 5. Y_t = ì + e_t – e_t-1 (See page 50 of the Cryer and Chan text, Exercise 3.2) Attachments TS Module 3 variance of mean HW.pdf (2.4K views, 32.00 KB) 0
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NEAS	NEAS posted 12 Years Ago #13039 #
Supreme Being Group: Administrators Posts: 4.5K, Visits: 1.6K	Jacob: Formula 3.2.3 applied to the first time series gives y-bar = 0.0792. But mu + e_t + e_t-1 from 1 to 50 is (1/2500) × Var(50 mu + å ₍₅₀₎ + 2 × e₍₁₎ + …+ 2 × e₍₄₉₎ ) = (1/2500) × (0 + Var(e ₍₅₀₎ + 4 × (e₍₁₎ + …+ e₍₄₉₎ ) ) ) = (1 + 4 × 49) / 2500 = 0.0788 Rachel:The difference is subtle. The formula in the textbook assumes 50 observations are taken from this time series. Your second method assumes the time series starts at observation #1. The difference is one error term. Your second method doesn’t have an error term for period zero. Including this error term raises the variance of y-bar by 0.004. Intuition: The formula in the textbook assumes the time series process is infinite. We observe fifty values, such as 1.014 through 1.063, and compute the variance of y-bar. Your computation assumes the series starts at observation #1, so the error term e₀ is zero. Use the formula in the textbook, since its assumptions are closer to real life. We may observe only certain observations, but the time series may have existed for much longer. 0
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TS Module 3: Trends HW

NEAS - 17 Years Ago

Shouldn't this homework be moved to a place where the moving average...

LBJ82 - 16 Years Ago

Well, the HW can be done from a direct application of equation 3.2.3...

sbenidt - 16 Years Ago

1st of all p1 for an MA(1) process is not 1. It can never be one. p1...

Tom McNamara III - 16 Years Ago

For part B, what does "pattern" mean? Are we supposed to graph a few...

Luke Grady - 16 Years Ago

Mr. McNamara III, The answer for A1, using the 3.2.3, should be...

djfobster - 16 Years Ago

I don't have my hw in front of me but I got .0792 too. Where is the 2...

Luke Grady - 16 Years Ago

The equation is from the book (3.2.3). Am I using the wrong equation?...

djfobster - 16 Years Ago

Dude! I was just using the upper version and ignoring that k can be -1...

Luke Grady - 16 Years Ago

If I am not mistaken, you are using the correct equation, just not...

RayDHIII - 16 Years Ago

I understood all of raydhiii's post until: = 0+2Var(e t )due to...

peat0801 - 16 Years Ago

We are given in the assignment that Var(e t ) = 1. (I assume this...

RayDHIII - 16 Years Ago

Okay, I get it now. That's what I thought maybe it was but I wasn't...

peat0801 - 16 Years Ago

For process 5, Yt = mu + et - et-1 I use equation 3.2.3, I got result...

Delta - 16 Years Ago

Y-bar = (1/n)*sum (from t=1 to t=n) (Y t ). For our fifth process,...

RayDHIII - 16 Years Ago

Where is the square coming from for the gamma over n term? I just...

Luke Grady - 16 Years Ago

Look to appendix A for the rules on variance: Var(a+bX) = b 2 Var(X),...

RayDHIII - 16 Years Ago

I'm still struggling with how to get rho 1 ; could some one walk me...

Mark L - 16 Years Ago

Mark, rho k is the autocorrelation functionat lag k, which is given...

RayDHIII - 16 Years Ago

Thanks raydhiii, I think I have everything pretty much figured out,...

Mark L - 16 Years Ago

Hey Mark, pages 14-15 on "A Moving Average" might answer that...

RayDHIII - 16 Years Ago

raydhiii, maybe this is a typo, but referring to your recent post,...

hs1234 - 16 Years Ago

What is part B asking for? What is the first and last time series?

hs1234 - 16 Years Ago

Happy Monday, everyone! hs, I believe there is already a post about...

RayDHIII - 16 Years Ago

Sorry for being slow, but I still don't get part B, so are we talking...

jzz - 16 Years Ago

Right, so isn't the following true? Var(Y t ) = Var(mu + e t + .5e...

hs1234 - 16 Years Ago

Yes RDH

RayDHIII - 16 Years Ago

just want to check, did anyone get .0495 for the second series?

Luke Grady - 16 Years Ago

If Var(Y-bar) = (gamma 0 /n)[1+2(1-1/n)(rho 1 )], and you got 0.0495...

RayDHIII - 16 Years Ago

In problem A, we can consider for all 5 series a general form: Y(t) =...

Romas - 16 Years Ago

Not sure if this is frowned upon, but I found this section really...

dom2114 - 16 Years Ago

I got: A1) 0.0792 A2) 0.0446 A3) 0.02 A4) 0.0054 A5) 0.0008 I have...

melinda829 - 16 Years Ago

I also got the same answers. A1) 0.0792 A2) 0.0446 A3) 0.02 A4)...

dditch - 16 Years Ago

Sure. I wouldn't mind at all. It'll help me refresh.

melinda829 - 16 Years Ago

Number 4 is giving me all kinds of trouble. I'm getting -.0046 too. I...

Bryan03Cobra - 15 Years Ago

Nevermind, I'm an idiot and forgot how to take a simple variance....

Bryan03Cobra - 15 Years Ago

How does the homework relate to the textbook. The first few lines has...

AlexanderMelvinKao - 15 Years Ago

Alex, if you still need help, post and I can try to help you, ill...

Jeffryfl - 15 Years Ago

To help with parts B and C, think of real world applications of The...

dwscott07 - 15 Years Ago

I have seriously read over every single comment on this thread, and...

LIAPP - 15 Years Ago

LIAPP, I used the following 'givens' and I made a table like the one...

nacho - 15 Years Ago

Jacob: Formula 3.2.3 applied to the first time series gives...

NEAS - 12 Years Ago

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