Question Details

(solution) Consider the Switching AR(1) model y t = ( μ 0 + φ 0 y t − 1 ) + ( μ 1 + φ


Consider the Switching AR(1) model y t = ( μ 0 + φ 0 y t − 1 ) + ( μ 1 + φ 1 y t − 1 ) s t + ε t for t = 1 ,..., T with ε t ∼ N (0 ,σ 2 ), where s t is a latent binary random variable with exp( δ + γ y t − 1 ) Pr[ s t = 1] = F ( δ + γ y t − 1 ) = 1 + exp( δ . + γ y t − 1 ) What is/are the key difference(s) between the Switching AR(1) model and the LSTAR(1) model given by y t = ( μ 0 + φ 0 y t − 1 ) + ( μ 1 + φ 1 y t − 1 ) F ( δ + γ y t − 1 ) + ε t for t = 1 ,..., T with ε t ∼ N (0 ,σ 2 ) or are both models the same? Derive the unbiased 1-step ahead forecasts of y T + 1 made at time T for the Switching AR(1) model and for the LSTAR(1) model. Consider the Switching AR(1) model with exp( δ + γ s t − 1 ) Pr[ s t = 1] = 1 + exp( δ . + γ s t − 1 ) Show that this model is the same as a Markov Switching AR(1) model where Pr[ s t = 1| s t − 1 = 1] = p and Pr[ s t = 0| s t − 1 = 0] = q . Express p and q in terms of δ and γ . Suppose that you have observed yt for t = 1,..., T . A recession is defined as a period where for at least 2 consecutive periods st = 1. Suppose that ST = 0. Derive the probability in terms of p and q that the period [T + 1, T + 3] contains a recession.

 


Solution details:

Pay using PayPal (No PayPal account Required) or your credit card . All your purchases are securely protected by .
SiteLock

About this Question

STATUS

Answered

QUALITY

Approved

DATE ANSWERED

Sep 13, 2020

EXPERT

Tutor

ANSWER RATING

GET INSTANT HELP/h4>

We have top-notch tutors who can do your essay/homework for you at a reasonable cost and then you can simply use that essay as a template to build your own arguments.

You can also use these solutions:

  • As a reference for in-depth understanding of the subject.
  • As a source of ideas / reasoning for your own research (if properly referenced)
  • For editing and paraphrasing (check your institution's definition of plagiarism and recommended paraphrase).
This we believe is a better way of understanding a problem and makes use of the efficiency of time of the student.

NEW ASSIGNMENT HELP?

Order New Solution. Quick Turnaround

Click on the button below in order to Order for a New, Original and High-Quality Essay Solutions. New orders are original solutions and precise to your writing instruction requirements. Place a New Order using the button below.

WE GUARANTEE, THAT YOUR PAPER WILL BE WRITTEN FROM SCRATCH AND WITHIN A DEADLINE.

Order Now