||Trend, Seasonality, and Economic Time Series :
A New Approach Using Non-stationary Errors-in-Variables Models
||Naoto Kunitomo and Seisho Sato
||The use of seasonally adjusted (official) data may introduce statistical problem, particularly the use of X-12-ARIMA in the official seasonal adjustment, which adopts univariate ARIMA (autoregressive integrated moving average) time series modeling with some refinements. Instead of using 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 use an additive decomposition of components of multivariate time series to handle the measurement errors with non-stationary trends and seasonality. We will show that the SIML estimation can identify the non-stationary trend, the seasonality, and the noise components, and recover statistical relationships among the nonstationary trend and seasonality. The SIML estimator is consistent, and it has asymptotic normality when the sample size is large. Since the SIML estimator has also reasonable finite sample properties, it would be useful for practice.
||Non-stationary economic time series, Errors-variables models, trend and seasonality, Official Seasonal Adjustment, Additive decomposition of components, Structural relationships, SIML method, Asymptotic properties.
||Paper in English (42 pages)