TY  - JOUR
AU  - Clark,Todd E.
AU  - West,Kenneth D.
TI  - Using Out-of-Sample Mean Squared Prediction Errors to Test the Martingale Difference
JF  - National Bureau of Economic Research Technical Working Paper Series
VL  - No. 305
PY  - 2005
Y2  - January 2005
UR  - http://www.nber.org/papers/t0305
L1  - http://www.nber.org/papers/t0305.pdf
N1  - Author contact info:
Todd Clark
Research Department
Federal Reserve Bank of Kansas City
1 Memorial Drive
Kansas City, MO  64198
Tel: 816 881 2575
E-Mail: todd.clark@clev.frb.org

Kenneth D. West
Department of Economics
University of Wisconsin
1180 Observatory Drive
Madison, WI  53706
Tel: 608/262-0033
Fax: 608/262-2033
E-Mail: kdwest@wisc.edu
AB  - We consider using out-of-sample mean squared prediction errors (MSPEs) to evaluate the null that a given series follows a zero mean martingale difference against the alternative that it is linearly predictable. Under the null of no predictability, the population MSPE of the null "no change" model equals that of the linear alternative. We show analytically and via simulations that despite this equality, the alternative model's sample MSPE is expected to be greater than the null's. For rolling regression estimators of the alternative model's parameters, we propose and evaluate an asymptotically normal test that properly accounts for the upward shift of the sample MSPE of the alternative model. Our simulations indicate that our proposed procedure works well.
ER  -