Comparing estimation methods of non-stationary errors-in-variables models

Japanese Journal of Statistics and Data Science - 2020
Naoto Kunitomo1, Naoki Awaya2, Daisuke Kurisu3
1School of Political Science and Economics, Meiji University, Sarugakucho 3rd Building C-106, 1-1 Kanda-Surugadai, Chiyoda-ku, Tokyo, 101-8301, Japan
2Department of Statistical Science, Duke University, P.O. Box 90251 Durham, NC 27708-0251, USA
3School of Engineering, Tokyo Institute of Technology, Meguro-ku, Ôokayama 2-12-1 W9-74, Tokyo, 152-8552, Japan

Tóm tắt

AbstractWe investigate the estimation methods of the multivariate non-stationary errors-in-variables models when there are non-stationary trend components and the measurement errors or noise components. We compare the maximum likelihood (ML) estimation and the separating information maximum likelihood (SIML) estimation. The latter was proposed by Kunitomo and Sato (Trend, seasonality and economic time series: the nonstationary errors-in-variables models. MIMS-RBP-SDS-3, MIMS, Meiji University. http://www.mims.meiji.ac.jp/, 2017) and Kunitomo et al. (Separating information maximum likelihood method for high-frequency financial data. Springer, Berlin, 2018). We have found that the Gaussian likelihood function can have non-concave shape in some cases and the ML method does work only when the Gaussianity of non-stationary and stationary components holds with some restrictions such as the signal–noise variance ratio in the parameter space. The SIML estimation has the asymptotic robust properties in more general situations. We explore the finite sample and asymptotic properties of the ML and SIML methods for the non-stationary errors-in variables models.

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Tài liệu tham khảo

Akaike, H. (1989). Choosing priors and its applications. In Y. Suzuki & N. Kunitomo (Eds.), Bayesian statistics and applications. Tokyo: Tokyo University Press (in Japanese).

Amemiya, T. (1985). Advanced econometrics. Oxford: Blackwell.

Anderson, T. W. (1971). The statistical analysis of time series. New York: Wiley.

Anderson, T. W. (1984). Estimating linear statistical relationships. Annals of Statistics, 12, 1–45.

Anderson, T. W. (2003). An introduction to statistical multivariate analysis (3rd ed.). New York: Wiley.

Anderson, T. W., & Takemura, A. (1986). Why do non-invertible moving average occur? Journal of Time Series Analysis, 7–4, 235–254.

Anderson, T. W., Kunitomo, N., & Morimune, K. (1986). Comparing single-equation estimators in a simultaneous equation system. Econometric Theory, 2, 1–32.

Andrews, D. K. (1999). Estimation with a parameter is on a boundary. Econometrica, 67, 1341–1383.

Box, G. E. P., & Jenkins, G. M. (1970). Time series analysis, forecasting and control. San Francisco: Holden-Day.

Chang, Y., Jiang, B., & Park, J. (2008). Using Kalman filter to extract and test for common stochastic trends. Unpublished manuscript.

Engle, R., & Granger, C. W. J. (1987). Co-integration and error correction. Econometrica, 55, 251–276.

Fuller, W. (1987). Measurement error models. New York: Wiley.

Granger, C. W. J., & Newbold, P. (1977). Forecasting economic time series. Cambridge: Academic Press.

Hayashi, F. (2000). Econometrics. Princeton: Princeton University Press.

Johansen, S. (1995). Likelihood based inference in cointegrated vector autoregressive models. Oxford: Oxford University Press.

Kitagawa, G. (2010). Introduction to time series modeling. Boca Raton: CRC Press.

Kunitomo, N., & Sato, S. (2017). Trend, seasonality and economic time series: The nonstationary errors-in-variables models. MIMS-REB-SDS-9, MIMS, Meiji University. https://mims.meiji.ac.jp/publications/datascience-e.html.

Kunitomo, N., & Sato, S. (2019). A robust-filtering method for noisy non-stationary time series with an application to Japanese macro-consumption. Unpublished manuscript. MIMS-RBP-SDS-9, MIMS, Meiji University

Kunitomo, N., Sato, S., & Kurisu, D. (2018). Separating information maximum likelihood method for high-frequency financial data. Berlin: Springer.

Morgenstern, O. (1950). On the accuracy of economic observations, (1966, revised edition). Princeton: Princeton University Press.

Nerlove, M., Grether, D. M., & Carvalho, J. L. (1995). Analysis of economic time series: A synthesis (Revised ed.). New York: Academic Press.

Rothenberg, T. (1971). Identification in parametric models. Econometrica, 39, 577–591.

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