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Trend, Seasonality and Economic Time Series:the Nonstationary Errors-in-variables Models

Author

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  • Naoto Kunitomo

    (Faculty of Economics, The University of Tokyo)

  • Seisho Sato

    (Faculty of Economics, The University of Tokyo)

Abstract

The use of seasonally adjusted (official) data may have statistical problem because it is a common practice to use X-12-ARIMA in the official seasonal adjustment , which adopts the univariate ARIMA time series modeling with some renements. Instead of using the seasonally adjusted data, for estimating the structural parameters and relationships among non-stationary economic time series with seasonality and noise, we propose a new method called the Separating Information Maximum Likelihood (SIML) estimation. We show that the SIML estimation can identify the nonstationary trend, the seasonality and the noise components, which have been observed in many macro-economic time series, and recover the structural parameters and relationships among the non-stationary trends with seasonality. The SIML estimation is consistent and it has the asymptotic normality when the sample size is large. Based on simulations, we nd that the SIML estimator has reasonable nite sample properties and thus it would be useful for practice. --

Suggested Citation

  • Naoto Kunitomo & Seisho Sato, 2015. "Trend, Seasonality and Economic Time Series:the Nonstationary Errors-in-variables Models," CIRJE F-Series CIRJE-F-977, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2015cf977
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    References listed on IDEAS

    as
    1. Kunitomo, Naoto & Sato, Seisho, 2013. "Separating Information Maximum Likelihood estimation of the integrated volatility and covariance with micro-market noise," The North American Journal of Economics and Finance, Elsevier, vol. 26(C), pages 282-309.
    2. Findley, David F, et al, 1998. "New Capabilities and Methods of the X-12-ARIMA Seasonal-Adjustment Program: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(2), pages 169-177, April.
    3. Naoto Kunitomo & Seisho Sato, 2008. "Separating Information Maximum Likelihood Estimation of Realized Volatility and Covariance with Micro-Market Noise," CIRJE F-Series CIRJE-F-581, CIRJE, Faculty of Economics, University of Tokyo.
    4. Hirotugu Akaike, 1980. "Seasonal Adjustment By A Bayesian Modeling," Journal of Time Series Analysis, Wiley Blackwell, vol. 1(1), pages 1-13, January.
    5. Kunitomo, Naoto & Sato, Seisho, 2011. "The SIML estimation of realized volatility of the Nikkei-225 Futures and hedging coefficient with micro-market noise," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(7), pages 1272-1289.
    6. Findley, David F, et al, 1998. "New Capabilities and Methods of the X-12-ARIMA Seasonal-Adjustment Program," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(2), pages 127-152, April.
    7. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
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