Question Details

(solution) Suppose the time series y t is generated according to the following threshold process y t = r


Suppose the time series y t is generated according to the following threshold process y t = r − δ + ε t if q t ≤ c δ + ε t if q t > c with δ > 0, ε t is a white noise series with E[ ε t ] = 0 and E[ ε 2 = σ 2 ] for all t , and t ε the threshold variable q t is i.i.d. standard normally distributed. Furthermore, ε t and q t are independent. Derive an expression (in terms of the parameters δ , σ 2 and c ) for the following ε characteristics of the time series y t : the unconditional mean μ y = E[ y t ], the unconditional variance γ0(y) = E[(yt − E[yt ])2], and the first-order autocorrelation ρ 1 ( y ) = γ 1 ( y ) /γ 0 ( y ), where γ 1 ( y ) is the first- order autocovariance of y t , that is, γ 1 ( y ) = E[( y t − E[ y t ])( y t − 1 − E [ y t − 1 ])]. Hint: Use the fact that the covariance between two random variables X and Z can be written as E[( X − E[ X ])( Z − E[ Z ])] = E[ XZ ] − E[ X ]E[ Z ]. Interpret these expressions, and discuss how they behave as a function of the parameters.

 


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