Measurement error models for time series
Estimation for multivariate linear measurement error models with serially correlated observations is addressed;The asymptotic properties of some standard linear errors-in-variables regression parameter estimators are developed under an ultrastructural model in which the random components of the model follow a linear process. Under the same assumptions, the asymptotic properties of weighted method-of-moments estimators are derived. The large-sample results rest on the asymptotic properties of the sum of a linear function and a quadratic function of a sequence of serially correlated random vectors;Maximum likelihood estimation for the normal structural and functional models is addressed. For each model, first- and second-derivative matrices of the log-likelihood functions are given and Newton-Raphson maximum likelihood estimation procedures are considered. For the structural model, the assumption that the random components follow a multivariate autoregressive moving average process is used to develop autoregressive moving average and state-space models for the observation sequence. The state-space representation of the structural model leads to innovation sequences and associated derivative sequences that provide the basis for a Newton-Raphson procedure for the estimation of regression parameters and autocovariance parameters of the structural model. A modified state-space approach leads to a similar procedure for the estimation for the functional model. An extension of the state-space approach to maximum likelihood estimation for a structural model with combined time series and cross-sectional data is given.