Testing for Noncausal Vector Autoregressive Representation

Hamidi Sahneh, Mehdi (2013): Testing for Noncausal Vector Autoregressive Representation.

Abstract

We propose a test for noncausal vector autoregressive representation generated by non-Gaussian shocks. We prove that in these models the Wold innovations are martingale difference if and only if the model is correctly specified. We propose a test based on a generalized spectral density to check for martingale difference property of the Wold innovations. Our approach does not require to identify and estimate the noncausal models. No specific estimation method is required, and the test has the appealing nuisance parameter free property. The test statistic uses all lags in the sample and it has a convenient asymptotic standard normal distribution under the null hypothesis. A Monte Carlo study is conducted to examine the �finite-sample performance of our test.

• Item Type: MPRA Paper
• Language: English
• Keywords: Explosive Bubble; Identification; Noncausal Process; Vector Autoregressive.
• Subjects: C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C32 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes ; State Space Models; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling

References

Box, G. E. and Pierce, D. A., 1970. Distribution of residual autocorrelations in autoregressive-integrated moving average time series models. Journal of the American Statistical Association, 65(332):1509{1526.

Breidt, F. J., Davis, R. A., Lh, K.-S., and Rosenblatt, M., 1991. Maximum likelihood estimation for noncausal autoregressive processes. Journal of Multivariate Analysis, 36(2):175{198.

Breidt, F. and Davis, R., 1992. Time-reversibility, identifiability and independence of innovations for stationary time series. Journal of Time Series Analysis, 13(5): 377{390.

Brockwell, P. and Davis, R., 1991. Time Series: Theory and Methods: Theory and Methods. Springer series in statistics. Springer.

Chan, K.-S., Ho, L.-H., and Tong, H., 2006. A note on time-reversibility of multivariate linear processes. Biometrika, 93(1):221{227.

Dominguez, M. A. and Lobato, I. N., 2003. Testing the martingale difference hypothesis. Econometric Reviews, 22(4):351{377.

Goncalves, S. and Kilian, L., 2004. Bootstrapping autoregressions with conditional heteroskedasticity of unknown form. Journal of Econometrics, 123(1):89{120.

Hamedani, G., 2013. Sub-independence: An expository perspective. Communications in Statistics-Theory and Methods, 42(20):3615{3638.

Hamidi Sahneh, M. Are the shocks obtained from svar fundamental? Technical report, University Library of Munich, Germany, June, 2015.

Harvey, C. R. and Siddique, A., 1999. Autoregressive conditional skewness. Journal of financial and quantitative analysis, 34(04):465{487. 22

Harvey, C. R. and Siddique, A., 2000. Conditional skewness in asset pricing tests. The Journal of Finance, 55(3):1263{1295.

Hong, Y., 1999. Hypothesis testing in time series via the empirical characteristic function: A generalized spectral density approach. Journal of the American Statistical Association, 94(448):1201{1220.

Hong, Y. and Lee, Y.-J., 2005. Generalized spectral tests for conditional mean models in time series with conditional heteroscedasticity of unknown form. The Review of Economic Studies, 72(2):499{541.

Jondeau, E. and Rockinger, M., 2003. Conditional volatility, skewness, and kurtosis: existence, persistence, and comovements. Journal of Economic Dynamics and Control, 27(10):1699{1737.

Lanne, M. and Saikkonen, P., 2011. Noncausal autoregressions for economic time series. Journal of Time Series Econometrics, 3(3).

Lii, K. and Rosenblatt, M., 1982. Deconvolution and estimation of transfer function phase and coefficients for nongaussian linear processes. The Annals of Statistics, pages 1195{1208.

Lippi, M. and Reichlin, L., 1994. Var analysis, nonfundamental representations, blaschke matrices. Journal of Econometrics, 63(1):307{325.

Ljung, G. M. and Box, G. E., 1978. On a measure of lack of fit in time series models. Biometrika, 65(2):297{303.

Rosenblatt, M., 2000. Gaussian and non-Gaussian linear time series and random fields. Springer.