Noncausal Bayesian Vector Autoregression

Abstract

SUMMARYWe consider Bayesian analysis of the noncausal vector autoregressive model that is capable of capturing nonlinearities and effects of missing variables. Specifically, we devise a fast and reliable posterior simulator that yields the predictive distribution as a by-product. We apply the methods to postwar US inflation and GDP growth. The noncausal model is found superior in terms of both in-sample fit and out-of-sample forecasting performance over its conventional causal counterpart. Economic shocks based on the noncausal model turn out to be highly anticipated in advance. We also find the GDP growth to have predictive power for future inflation, but not vice versa.

A new unique impulse response function in linear vector autoregressive models

“…Relative to early attempts of unique measures, such as GIRF, the superiority of MIRF includes the non‐extreme identification and explainable associated FEVD. Compared to unique measures based on more recent developments, such as that investigated in Lanne and Luoto (2016), MIRF only requires the general VAR model, and thus the estimation is computationally efficient. As for unique OIRF computed over averages of all VAR permutations, MIRF can reduce the computational insensitivity to a minimum level.…”

“…Moreover, the associated FEVD of GIRF does not always add to 100% for each response, which causes difficulty in explanation. In a more recent attempt, Lanne and Luoto (2016) derive a unique identification based on a more complicated Bayesian structural VAR model investigated by Lanne et al (2017). The related computational intensity, however, is much higher than the usual VAR system, especially when the dimensionality is high, and/or the sample size is large.…”

Parallelization Experience with Four Canonical Econometric Models Using ParMitISEM

“…Several recent papers use and extend the MitISEM algorithm for Bayesian inference. Reference [10] incorporates the MitISEM algorithm to the estimation of non-Gaussian state space models, [11] uses MitISEM for Value-at-Risk estimation, [12,13] estimates non-causal models using MitISEM and [14] uses MitISEM for Bayesian inference of latent variable models. Recently, [15] provided the R package MitISEM, together with routines to use MitISEM and its sequential extension for Bayesian inference of model parameters and model probabilities.…”

Filtering, Prediction and Simulation Methods for Noncausal Processes

“…In recent literature, there has been a growing number of applications involving economic time series models with causal and noncausal components. The time series modelled as noncausal processes range from the macroeconomic data (Lanne and Saikkonen, ; Davis and Song, ; Chen et al ., ; Lanne and Luoto, ; Nyberg and Saikkonen, ) to the Standard and Poor (S & P) market index (Gourieroux and Zakoïan, ), the commodity prices and electronic currency exchange rates (Gourieroux and Hencic, ). The empirical results reported in the literature suggest that the traditional Box–Jenkins methodology that restricts the temporal dependence in linear autoregressive processes to the past only has been often found insufficient.…”

“…We show that the two proposed methods are equivalent and can accommodate any unconstrained partition of the roots of the autoregressive polynomial matrix inside and outside the unit circle. In this aspect, our approach differs from Lanne and Saikkonen () and Lanne and Luoto (), where the autoregressive polynomial matrix is defined as a product of a causal and a noncausal components of predetermined orders.…”