Seasonal Adjustment with Measurement Error Present
National Bureau of Economic Research, 1983 - Seasonal variations (Economics) - 40 pages
Seasonal adjustment procedures attempt to estimate the sample realizations of an unobservable economic time series in the presence of both seasonal factors and irregular factors. In this paper we consider a factor which has not been considered explicitly in previous treatments of seasonal adjustment: measurement error. Because of the sample design used in the CPS, measurement error will not be a white noise process, but instead it will be characterized by serial correlation of a known form. We first consider what effect the serially correlated measurement error has on estimation of the non-seasonal component in seasonal adjustment models. We also consider the effect of measurement error on the widely used seasonal adjustment process X11. X11 which is the seasonal adjust procedure used by the BLS will implicitly reduce the effect of measurement error because of the averaging process used. However, this treatment will not be optimal in general. We therefore specify a seasonal adjustment model which takes explicit account of the measurement error. For examples on the unemployment rate, we find that X11 does almost as well as the optimal filter on some series but its efficiency is less than 10% for the teenage unemployment series. We also find that optimal treatment of the measurement error which accounts for the serial correlation can reduce the overall mean square error of the seasonally adjusted series below the variance of the measurement error which is often used as the benchmark for the sampling procedure
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ADJUSTMENT WITH MEASUREMENT arises autoregressive autoregressive process calculated Chart civilian rate civilian unemployment rate complete realization composite series constructing seasonal adjustment Deterministic adjustment deterministic component economic time series effect of measurement equation estimate models estimated parameters filter constructed filter V(B filter which ignores Hausman ignores measurement error increase in m.s.e. increase in mean Kalman filter Lars E.O. Svensson likelihood function Mark Watson mean square error meas measured with error measurement error component MEASUREMENT ERROR PRESENT Model 1 filter Monetary Policy non-seasonal component non-seasonal processes normally distributed observed series optimal estimate optimal seasonal adjustment overall unemployment rate parameter uncertainty parameters of Model present the r.m.s.e. relative efficiency root mean square sample design sampling error seasonal adjustment error seasonal adjustment filters seasonal adjustment procedures seasonally adjusted series serially correlated signal extraction stochastic component sub-sample teenage rate teenage unemployment rate Torsten Persson unknown parameters variance white noise X-11 filter X11 procedure