Using out-of-sample mean squared prediction errors to test the martingale difference hypothesis
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 eq...
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| Published in | Journal of econometrics Vol. 135; no. 1; pp. 155 - 186 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Amsterdam
Elsevier B.V
01.11.2006
Elsevier Elsevier Sequoia S.A |
| Series | Journal of Econometrics |
| Subjects | |
| Online Access | Get full text |
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| Abstract | 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. |
|---|---|
| AbstractList | 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. 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. [PUBLICATION ABSTRACT] 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. All rights reserved, Elsevier |
| Author | Clark, Todd E. West, Kenneth D. |
| Author_xml | – sequence: 1 givenname: Todd E. surname: Clark fullname: Clark, Todd E. email: todd.e.clark@kc.frb.org organization: Economic Research Department, Federal Reserve Bank of Kansas City, 925 Grand Blvd., Kansas City, MO 64198, USA – sequence: 2 givenname: Kenneth D. surname: West fullname: West, Kenneth D. email: kdwest@wisc.edu organization: Department of Economics, University of Wisconsin, 1180 Observatory Drive, Madison, WI 53706-1393, USA |
| BackLink | http://econpapers.repec.org/article/eeeeconom/v_3a135_3ay_3a2006_3ai_3a1-2_3ap_3a155-186.htm$$DView record in RePEc |
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| Keywords | C530 C220 Efficient markets F370 Random walk Causality Exchange rate Forecasting Testing |
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| SubjectTerms | Causality Econometrics Economic efficiency Efficient markets Error analysis Exchange rate Exchange rates Forecasting Forecasts Market theory Parameter estimation Random walk Simulation Statistical analysis Studies Testing |
| Title | Using out-of-sample mean squared prediction errors to test the martingale difference hypothesis |
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