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Model‐Based and Semiparametric Estimation of Time Series Components and Mean Square Error of Estimators

Daniel Pfeffermann, Richard B. Tiller, and M. Sverchkov


Wayne Fuller is known for his outstanding contributions to three main areas in statistics: Sample survey theory, Time series analysis and Measurements errors. This presentation will focus on time-series analysis and more specifically, on estimation of seasonally adjusted and trend components and the MSEs of the estimators. We shall compare the component estimators as obtained by application of the X-11 ARIMA and by fitting State-Space models that account more directly for correlated sampling errors. The classical model-based component estimators and variance estimators will be compared with a new procedure, which uses a different definition of the components that conforms to an original suggestion by Wayne Fuller. By this definition the unknown components are defined to be the hypothetical X-11 estimates if sufficient data was available for application of the symmetric filters imbedded in this procedure. We propose new MSE estimators with respect to this definition. The performance of the estimators is assessed by using simulated series that approximate a real series produced by the Bureau of Labor Statistics in the U.S.A.