Midterm 1 Financial Econometrics University of Notre Dame Fall - - PDF document

Midterm 1 Financial Econometrics University of Notre Dame Fall 2018 Professor Mark Write clearly, legibly, and efficiently in black or dark blue ink. Think before writing. Don’t leave any question blank. Think before writing. Each question worth 10 points.

• 1. What are the properties of a stationary time series?
• 2. Why is the concept of stationarity important in econometrics?
• 3. How would you use the ADF test to test the hypothesis that a time series {yt}T

t=1 has a unit

root (i.e., is nonstationary)? 1

• 4. Let ǫt be i.i.d. with mean 0 and variance σ2

ǫ , and |ρ1 + ρ2| < 1 in the AR(2) model, ,

yt = ρ1yt−1 + ρ2yt−2 + ǫt (a) What is the optimal (best) forecast of yt+1 conditional on information known at t? (b) What is the optimal (best) forecast of yt+2 conditional on information known at t? (c) Assume y0 = y−1 = 0. What is the impulse response for y1,y2, and y3 for a one-time shock ǫ1 = 1? 2

• 5. Suppose you are trying to choose between an AR(1) model and an MA(1) model. How can

you use AIC, BIC, and HQIC to help?

• 6. Let

xt = ρxt−1 + ut where ut

iid

˜

• 0, σ2

u

• , and 0 < ρ < 1. Assume the truth is,

rt+1 = βxt + ǫt+1 where ǫt

iid

˜

• 0, σ2

ǫ

• , where rt is the one-period return on some asset. You ask if xt helps predict

the 2-period return, rt+1 + rt+2 by running the regression rt+1 + rt+2 = γxt + vt+2 (a) Show that the population slope γ is bigger than the population slope β. 3

(b) Express the regression error vt+2 in terms of ǫt+1, ǫt+2 and ut+1, and show that vt+2 is correlated with vt+1.

• 7. Let pt be the log dividend-adjusted price of a stock, where

pt = pt−1 + ǫt where ǫt

iid

˜

• 0, σ2

ǫ

• .What is the optimal (best) predictor of pt+20, conditional on information

available at t? 4