TS Module 13: Parameter estimation least squares HW


TS Module 13: Parameter estimation least squares HW

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NEAS
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TS Module 13: Parameter estimation least squares HW

 

(The attached PDF file has better formatting.)

 

Homework assignment: Estimating parameters by regression

 

An AR(1) process has the following values:

 

0.44    1.05    0.62    0.72    1.08    1.24    1.42    1.35    1.50

 


A.     Estimate the parameter ö by regression analysis.

B.     What are 95% confidence intervals for the value of ö?

C.    You initially believed that ö is 50%. Should you reject this assumption?

 

The time series course does not teach regression analysis. You are assumed to know how to run a regression analysis, and you must run regressions for the student project.

 

Use the Excel regression add-in. The 95% confidence interval is the estimated â ± the t-value × the standard error of â. The t-value depends on the number of observations. Excel has a built-in function giving the t-value for a sample of N observations.

 

 

 


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I have a question on how the standard deviation should be calculated. Using the formula on page 41, I calculate the standard deviation as s=((sum(Yt-phi)^2)/8)^.5. This however does not get me close to the standard deviation I get from my excel analysis (0.27476412), it got me to 0.653814. I don’t understand the assumption that the standard error is =((1-0.542508^2)/8)^0.5=0.297. Where does this formula come from?


 
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