Questions from Econometrics

Q: Let X and Y be two random variables. Denote the mean

Let X and Y be two random variables. Denote the mean of Y given X = x by (x) and the variance of Y by 2(x). a. Show that the best (minimum MSPE) prediction of Y given X = x is (x) and the resulting...

Q: You have a sample of size n = 1 with data y1

You have a sample of size n = 1 with data y1 = 2 and x1 = 1. You are interested in the value of  in the regression Y = X + u. a. Plot the sum of squared residuals (y1 - bx1)2 as function of b. b. Sh...

Q: Consider the AR (1) model Yt = 0 +

Consider the AR (1) model Yt = 0 + 1Yt - 1 + ut. Suppose the process is stationary. a. Show that E (Yt) = E (Yt – 1). b. Show that E (Yt) = 0 / (1 - 1).

Q: A researcher carries out a QLR test using 30% trimming,

A researcher carries out a QLR test using 30% trimming, and there are q = 5 restrictions. Answer the following questions, using the values in Table 15.5 (“Critical Values of the QLR...

Q: Suppose ∆Yt follows the AR (1) model ∆Yt

Suppose ∆Yt follows the AR (1) model ∆Yt = 0 +∆Yt - 1 + ut. a. Show that Yt follows an AR (2) model. b. Derive the AR (2) coefficients for Yt as a function of 0 and 1.

Q: Consider the stationary AR (1) model Yt = b0 +

Consider the stationary AR (1) model Yt = b0 + b1Yt−1 + ut, where ut is i.i.d. with mean 0 and variance 2u. The model is estimated using data from time periods t = 1 through t = T, yielding the OLS e...

Q: Suppose Yt follows a random walk, Yt = Yt−1

Suppose Yt follows a random walk, Yt = Yt−1 + ut, for t = 1, ……, T, where Y0 = 0 and ut is i.i.d. with mean 0 and variance 2u. a. Compute the mean and variance of Yt. b. Compute the covariance betwee...

Q: The Index of Industrial Production (IPt) is a monthly time

The Index of Industrial Production (IPt) is a monthly time series that measures the quantity of industrial commodities produced in a given month. This problem uses data on this index for the United St...

Q: Using the same data as in Exercise 15.2, a

Using the same data as in Exercise 15.2, a researcher tests for a stochastic trend in ln (IPt), using the following regression: where the standard errors shown in parentheses are computed using the ho...

Q: The forecaster in Exercise 15.2 augments her AR (4

The forecaster in Exercise 15.2 augments her AR (4) model for IP growth to include four lagged values of ∆Rt, where Rt is the interest rate on three-month U.S. Treasury bills (measur...