We introduce a new method for Bayesian estimation of fractionally integrated vector autoregressions (FIVARs). The FIVAR, which nests a standard VAR as a special case, allows each series to exhibit long memory, meaning that low frequencies can play a dominant role — a salient feature of many macroeconomic and financial time series. Although the parameter space is typically high-dimensional, our inferential procedure is computationally tractable and relatively easy to implement. We apply our methodology to the identification of technology shocks, an empirical problem in which business-cycle predictions depend on carefully accounting for low-frequency fluctuations.

We discuss posterior sampling for two distinct multivariate generalizations of the univariate ARIMA model with fractional integration. The existing approach to Bayesian estimation, introduced by Ravishanker and Ray (1997), claims to provide a posterior-sampling algorithm for fractionally integrated vector autoregressive moving averages (FIVARMAs). We show that this algorithm produces posterior draws for vector autoregressive fractionally integrated moving averages (VARFIMAs), a model of independent interest that has not previously received attention in the Bayesian literature.

In this paper we show that the problem of demand inversion in multinomial choice models is equivalent to the determination of stable outcomes in matching models. This result is very general and applies to random utility models that are not necessarily additive or smooth. Based on this equivalence, we argue that the algorithms for the determination of stable matchings can provide effective computational methods to inverse multinomial choice models, and we give a numerical benchmark of these algorithms. Our approach allows to estimate models that were previously difficult to estimate, such as the pure characteristics model, as well as nonadditive random utility models. The equivalence also allows to exploit the theory of stable matchings in order to describe important properties of the set of utilities solution to the demand inversion problem, and to study the cases of existence and uniqueness of identified utilities, as well as obtain consistency results.