Questions from Econometrics

Q: Suppose that Yt follows a stationary AR (1) model,

Suppose that Yt follows a stationary AR (1) model, Yt = b0 + b1Yt - 1 + ut. a. Show that the h-period ahead forecast of Yt is given by b. Suppose that Xt is related to Yt by Show that

Q: Consider the cointegrated model YT = uXt + v1t and Xt =

Consider the cointegrated model YT = uXt + v1t and Xt = Xt - 1 + v2t, where v1t and v2t are mean 0 serially uncorrelated random variables with E (v1t v2j) = 0 for all t and j. Derive the vector error...

Q: One version of the expectations theory of the term structure of interest

One version of the expectations theory of the term structure of interest rates holds that a long-term rate equals the average of the expected values of shortterm interest rates into the future plus a...

Q: X is a random variable with moments E(X), E

X is a random variable with moments E(X), E(X2), E(X3), and so forth. a. Show E (X - (3 = E(X3) – 3[E(X2)] [E(X) + 2[E(X)]3 b. Show E (X - (4 = E(X4) – 4[E(X)] [E(X3) + 6[E(X)]2 [E(X2) – 3[E(X)] 4

Q: Suppose that E (ut |ut - 1, ut -

Suppose that E (ut |ut - 1, ut - 2 . . .) = 0 and ut follows the ARCH process, 2t = 1.0 + 0.5 u2t - 1. a. Let E (u2t) = var (ut) be the unconditional variance of ut. Show that var (ut) = 2. (Hint: Us...

Q: Suppose that Yt follows the AR (p) model Yt =

Suppose that Yt follows the AR (p) model Yt = 0 + 1Yt - 1 + g+ bpYt - p + ut, where E (ut  Yt - 1, Yt - 2 …) = 0. Let Yt + ht = E (Yt + h  Yt, Yt - 1,). Show that Yt + h|t = 0 + 1Yt - 1 + h|t...

Q: Verify Equation (17.20). Data from Equation

Verify Equation (17.20). Data from Equation 17.20:

Q: A regression of Yt onto current, past, and future values

A regression of Yt onto current, past, and future values of Xt yields a. Rearrange the regression so that it has the form shown in Equation (17.25). What are the values of u, -1, &...

Q: Suppose that ∆Yt = ut, where ut is i.

Suppose that ∆Yt = ut, where ut is i.i.d. N (0, 1), and consider the regression Yt = bXt + error, where Xt = ∆Yt + 1 and error is the regression error. Show that

Q: Consider the following two-variable VAR model with one lag and

Consider the following two-variable VAR model with one lag and no intercept: a. Show that the iterated two-period ahead forecast for Y can be written as And derive values for 1 and...