TY  - JOUR
AU  - Durlauf,Steven N.
TI  - Spectral Based Testing of the Martingale Hypothesis
JF  - National Bureau of Economic Research Technical Working Paper Series
VL  - No. 90
PY  - 1992
Y2  - April 1992
UR  - http://www.nber.org/papers/t0090
L1  - http://www.nber.org/papers/t0090.pdf
N1  - Author contact info:
Steven N. Durlauf
Department of Economics
University of Wisconsin
1180 Observatory Drive
Madison, WI  53706-1393
Tel: 608/263-3859
Fax: 608/262-2033
E-Mail: sdurlauf@ssc.wisc.edu
AB  - This paper proposes a method of testing whether a time series is a martingale. The procedure develops an asymptotic theory for the shape of the spectral distribution function of the first differences. Under the null hypothesis, this shape should be a diagonal line. several tests are developed which determine whether the deviation of the sample spectral distribution function from a diagonal line, when treated as an element of a function space, is too erratic to be attributable to sampling error. These tests are consistent against all moving average alternatives. The testing procedure possesses the additional advantage that it eliminates discretion in choosing a particular H[sub 1] by the researcher and therefore guards against data mining, The tests may further be adjusted to analyze subsets of frequencies in isolation, which can enhance power against particular alternatives. Application of the test to stock prices finds some evidence against the random walk theory.
ER  -