Consider a standard multiple linear regression model with time series data: yt= βo+ β1xt+ βkxtk + µ1

Assume that Assumptions TS.1, TS.2, TS.3, and TS.4 all hold.

a. Suppose we think that the errors (ut) follow an AR(I) model with parameter rho and so we apply the Prais-Winsten method. If the errors do not follow an AR(I) model— for example, suppose they follow an AR(2) model, or an MA(I) model— why will the usual Prais-Winsten standard errors be incorrect?

b. Can you think of a way to use the Newey-West procedure, in conjunction with Prais- Winsten estimation, to obtain valid standard errors?
c. Explain why your answer to part (ii) should not change if we drop Assumption TS.4.

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

mxb67

step-by-step explanation: