Neas-Seminars

TS Module 13: Parameter estimation least squares HW


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By NEAS - 12/4/2009 7:55:21 AM

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.

 

 

 
By palantathraiel - 1/28/2012 6:45:08 AM

This would be a lot easier to understand if you have already taken the Regression Analysis Course.

Basically, SE(phi) = sqrt( (RSS / n-2) / sum(X* ^2) )
where n = the no. of observations (so yes, you are correct in supposing that degrees of freedom = 6 = 8-2)

RSS = the sum of the squares of the differences between Y and the fitted Y from the regression
--> Using the first observation (X = 0.44, Y = 1.05), the fitted Y is computed as follows:
fitted Y = the intercept from the regression (0.585417) + the estimated phi (0.542508) * X (0.44) = 0.82412

--> Then (Y - fitted Y)^2 = (1.05 - 0.82412)^2 = 0.051022

Do this for all observations and get the sum, which would be the RSS.

X* ^2 = (X - average of all the X's)^2
e.g. for the first observation, this would be (0.44 - 0.99)^2 = 0.3025
Then do this for all observations yet again and get the sum.



I hope this makes sense to you.