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Testing for Nonlinear Autoregression

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  • Lobato, Ignacio N

Abstract

This article considers consistent testing the null hypothesis that the conditional mean of an economic time series is linear in past values. Two specific tests are discussed, the Cramer-von Mises and the Kolmogorov-Smirnov tests. The particular feature of the proposed tests is that the bootstrap is used to estimate the nonstandard asymptotic distributions of the test statistics considered. The tests are justified theoretically by asymptotics, and their finite-sample behaviors are studied by means of Monte Carlo experiments. The tests are applied to five U.S. monthly series, and evidence of nonlinearity is found for the first difference of the logarithm of the personal income and for the first difference of the unemployment rate. No evidence of nonlinearity is found for the first difference of the logarithm of the U.S. dollar/Japanese Yen exchange rate, for the first difference of the 3-month T-bill interest rate and for the first difference of the logarithm of the M2 money stock. Contrary to typically used tests, the proposed testing procedures are robust to the presence of conditional heteroscedasticity. This may explain the results for the exchange rate and the interest rate.

Suggested Citation

  • Lobato, Ignacio N, 2003. "Testing for Nonlinear Autoregression," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(1), pages 164-173, January.
    • Handle: RePEc:bes:jnlbes:v:21:y:2003:i:1:p:164-73
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    Cited by:

    1. Su, Liangjun & White, Halbert, 2007. "A consistent characteristic function-based test for conditional independence," Journal of Econometrics, Elsevier, vol. 141(2), pages 807-834, December.
    2. Shurojit Chatterji & Ignacio N. Lobato, 2010. "Transformations of the state variable and learning dynamics," International Journal of Economic Theory, The International Society for Economic Theory, vol. 6(4), pages 385-403, December.

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