An annual time-series regression model was fit to data collected for 30 years. After studying and analyzing the results, the error terms were found to be first-order autocorrelated, and the independent variable is lagged, i.e., the value of x in year 1-1 also affects the value of y in year t. So, the following pair of models was studied: y₁= Bo + B₁ x₁ +B₂x₁-1 + ß² t + & and & = £ 1-1 + a, where the a, are i.i.d. N(0,0¹) for each t, t= 1,...,30. By using the 30 data points and applying the approximate method, the following estimates of the coefficients are obtained:ßo= 10, ß₁= 3.2, ß₂= 1.1, ß3= 1.5, = 0.74. Use the fitted model to forecast the value of y in year t= 31, given that y30=85, X29= 8.5, X30 = 4.75, and 231 = 6.9.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question
Problem 6
An annual time-series regression model was fit to data collected for 30 years. After studying
and analyzing the results, the error terms were found to be first-order autocorrelated, and the
independent variable is lagged, i.e., the value of x in year t-1 also affects the value of y in year t.
So, the following pair of models was studied:
y₁= Bo + B₁ x² + B₂ x₁-1 + ß3 t + & and & = $ £ 1-1 + a, where the a, are i.i.d. N(0,0²) for each t, t =
1,...,30. By using the 30 data points and applying the approximate method, the following
estimates of the coefficients are obtained:ßo= 10, B₁= 3.2, ₂= 1.1, ß3= 1.5, ô= 0.74. Use the
fitted model to forecast the value of y in year t = 31, given that y30= 85, x29= 8.5, X30 = 4.75, and
*31 = 6.9.
Transcribed Image Text:Problem 6 An annual time-series regression model was fit to data collected for 30 years. After studying and analyzing the results, the error terms were found to be first-order autocorrelated, and the independent variable is lagged, i.e., the value of x in year t-1 also affects the value of y in year t. So, the following pair of models was studied: y₁= Bo + B₁ x² + B₂ x₁-1 + ß3 t + & and & = $ £ 1-1 + a, where the a, are i.i.d. N(0,0²) for each t, t = 1,...,30. By using the 30 data points and applying the approximate method, the following estimates of the coefficients are obtained:ßo= 10, B₁= 3.2, ₂= 1.1, ß3= 1.5, ô= 0.74. Use the fitted model to forecast the value of y in year t = 31, given that y30= 85, x29= 8.5, X30 = 4.75, and *31 = 6.9.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman