1. Consider the following difference equation: y = 0.8y + -0.5 t-1 (a) Derive the homogenous...

 

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1. Consider the following difference equation: y₁ = 0.8y₁₁ +₁ -0.5 t-1 (a) Derive the homogenous solution for this difference equation. Please show your work. (b) Derive the particular solution for this difference equation using the method of undetermined coefficients. Please show your work. (c) Suppose that &₁=+1. Assuming that there are no further shocks to y(t), use the derived coefficients of the particular solution to trace out the time path of the effects of ε1 on y₁, y2, y3,...... Discuss the shape of this impulse response function and what it implies for the stability of the difference equation stated at the beginning of this problem (a similar exercise was done in Part B, slide #12, of the lecture). (d) Suppose that the initial conditions are as follows: yo= 0 and &=0 for t≤0. Impose the initial conditions in order to find the general solution. 1. Consider the following difference equation: y₁ = 0.8y₁₁ +₁ -0.5 t-1 (a) Derive the homogenous solution for this difference equation. Please show your work. (b) Derive the particular solution for this difference equation using the method of undetermined coefficients. Please show your work. (c) Suppose that &₁=+1. Assuming that there are no further shocks to y(t), use the derived coefficients of the particular solution to trace out the time path of the effects of ε1 on y₁, y2, y3,...... Discuss the shape of this impulse response function and what it implies for the stability of the difference equation stated at the beginning of this problem (a similar exercise was done in Part B, slide #12, of the lecture). (d) Suppose that the initial conditions are as follows: yo= 0 and &=0 for t≤0. Impose the initial conditions in order to find the general solution.

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a To derive the homogeneous solution for the given difference equation we assume that y is a function of time t and substitute yt rt into the differen... View the full answer