Question

1. Consider the following difference equation:

yt = 0.8yt-1 + εt -0.5εt-1

since the subscripts do not appear in here I will rewrite this equation in words where t = "today" and t-1 = "yesterday".

y"today" = 0.8y"yesterday" + epsilon"today" - 0.5epsilon"yesterday".

My assignment is to derive the homogenous and particular solutions while showing my work. Is anyone able to help with deriving the particular solution?

Answer 1

Hoot! You just asked your first question! Hang tight while I find people to answer it for you. You can thank people who give you good answers by clicking the 'Good Answer' button on the right!

Answer 2

Click 'insert equation' to insert equations. :) Makes things a bit easier to read. :)

Answer 3

y{t} = 0.8 y{t-1} + ε{t} -0.5ε{t-1}

is epsilon a function or a standin?

Answer 4

the epsilons seem to be part of another reurrsion

Answer 5

I have attached a document with the assignment. I need to use the method of undetermined coefficients to solve for my particular solution..

Answer 6

Video, notes, and more videos:

1) http://patrickjmt.com/method-of-undetermined-coefficients-2nd-order-linear-de/

2) http://tutorial.math.lamar.edu/Classes/DE/UndeterminedCoefficients.aspx

3) http://www.khanacademy.org/video/undetermined-coefficients-1?playlist=Differential%20Equations&sort=2

Hope this helps! :D

Answer 7

well, if i recall correctly, the homogenous part is:

y{t} -.8y{t-1} = 0 right?

Answer 8

y{t} = .8^n y{0}

Answer 9

does that seem right?

Answer 10

I believe that the homogenous piece is y{t} = A(.8^t) where A=some arbitrary constant.

Answer 11

I believe that the homogenous piece is y{t} = A(.8)^t where A=some arbitrary constant

Answer 12

yeah, im used to an 'n' :) forgot to adapt for a t

Answer 13

the rest if it im not to sure about tho..... its been awhile

Answer 14

Thanks for attempt. I'll keep studying..