Model Estimation, Prediction, and Signal Extraction for Nonstationary Stock and Flow Time Series Observed at Mixed Frequencies

An important practical problem for statistical agencies and central banks that publish economic data is the seasonal adjustment of mixed frequency stock and flow time series. This may arise in practice due to changes in funding of a particular survey. Mathematically, the problem can be reduced to the need to compute imputations, forecasts, and backcasts from a given model of the highest available frequency data. The nonstationarity of the economic time series coupled with the alteration of sampling frequency makes the problem of model estimation and imputation challenging. For flow data the analysis cannot be recast as a missing value problem, so that time series imputation methods are ineffective. We provide explicit formulas and algorithms that allow one to compute the log Gaussian likelihood of the mixed sample, as well as any imputations and forecasts. Formulas for the relevant mean squared error are also derived. We evaluate the methodology through simulations, and illustrate the techniques on some economic time series.