This paper considers estimation and hypothesis testing in linear time series when some or all of the variables have (possibly multiple) unit roots. The motivating example is a vector autoregression with some unit roots in the companion matrix, which might include polynomials in time as...

Efficient estimators of cointegrating vectors are presented for systems involving deterministic components and variables of differing, higher orders of integration. The estimators are computed using GLS or OLS, and Wald statistics constructed from these estimators have asymptotic x [superscript]...

‘Iterated’ multiperiod ahead time series forecasts are made using a one-period ahead model, iterated forward for the desired number of periods, whereas ‘direct’ forecasts are made using a horizon-specific estimated model, where the dependent variable is the multi-period ahead value being...

Average postwar expansions are twice as long as prewar expansions and contractions are one-half as long. This paper investigates three possible explanations. The first explanation is that shocks to the economy have been smaller in the postwar period. The second explanation is that the...

This paper uses a dynamic factor model for the quarterly changes in consumption goods’ prices to separate them into three components: idiosyncratic relative-price changes, aggregate relative-price changes, and changes in the unit of account. The model identifies a measure of “pure”...

This paper suggests a new procedure for evaluating the fit of a dynamic structural economic model. The procedure begins by augmenting the variables in the model with just enough stochastic error so that the model can exactly match the second moments of the actual data. Measures of fit for the...