anonymous
  • anonymous
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?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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Owlfred
  • Owlfred
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mathteacher1729
  • mathteacher1729
Click 'insert equation' to insert equations. :) Makes things a bit easier to read. :)
amistre64
  • amistre64
y{t} = 0.8 y{t-1} + ε{t} -0.5ε{t-1} is epsilon a function or a standin?

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amistre64
  • amistre64
the epsilons seem to be part of another reurrsion
anonymous
  • anonymous
I have attached a document with the assignment. I need to use the method of undetermined coefficients to solve for my particular solution..
mathteacher1729
  • mathteacher1729
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
amistre64
  • amistre64
well, if i recall correctly, the homogenous part is: y{t} -.8y{t-1} = 0 right?
amistre64
  • amistre64
y{t} = .8^n y{0}
amistre64
  • amistre64
does that seem right?
anonymous
  • anonymous
I believe that the homogenous piece is y{t} = A(.8^t) where A=some arbitrary constant.
anonymous
  • anonymous
I believe that the homogenous piece is y{t} = A(.8)^t where A=some arbitrary constant
amistre64
  • amistre64
yeah, im used to an 'n' :) forgot to adapt for a t
amistre64
  • amistre64
the rest if it im not to sure about tho..... its been awhile
anonymous
  • anonymous
Thanks for attempt. I'll keep studying..

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