Filtering, Prediction and Simulation Methods for Noncausal Processes

Abstract

This article discusses filtering, prediction and simulation in univariate and multivariate noncausal processes. A closed-form functional estimator of the predictive density for noncausal and mixed processes is introduced that provides prediction intervals up to a finite horizon H. A state-space representation of a noncausal and mixed multivariate vector autoregressive process is derived in two ways-by the partial fraction decomposition or from the real Jordan canonical form. A recursive BHHH algorithm for the maximization of the approximate log-likelihood function is proposed, which calculates the filtered values of the unobserved causal and noncausal components of the process. The new methods are illustrated by a simulation study involving a univariate noncausal process with infinite variance.

Local Explosion Modelling by Non-Causal Process

“…Therefore, it is possible to predict the date of a bubble collapse by considering the extreme behaviour of non‐causal innovations . (The predictive distributions at any horizon can be estimated and used to predict the dates and magnitudes of downturns at given horizons (see Gouriéroux and Jasiak ()).) At time t , we can compute the probability of a bubble collapse at t + h as , for some extreme critical level c .…”

Mixed causal–noncausal autoregressions with exogenous regressors

“…The process t exists almost surely under rather weak conditions, such as (Gouriéroux & Jasiak, 2016). We observe that t has a two-sided moving average representation augmented with a second part involving linear combinations of past, current, and future values of X t .…”

“…Hence, if we want to represent the MARX by an MAR model, the dynamics of z t , which are determined by the fluctuations in X t , might increase the degree of the causal and noncausal polynomial of the MAR. In other words, given the dynamics of z t , we have that deg (1), we can construct unobserved noncausal and causal components (u, v) similar to Lanne and Saikkonen (2011) and Gouriéroux and Jasiak (2016) and obtain…”

“…We study both forecasting setups by simulation in the next section. An alternative forecasting procedure for noncausal models is the sample-based method proposed by Gouriéroux and Jasiak (2016), and an extensive comparison of the two methods can be found in Hecq and Voisin (2019).…”

Noncausal Affine Processes with Applications to Derivative Pricing

“…There is a recent growing literature on noncausal processes, which seem to better fit financial and economic time series [see e.g. Lanne, Saikkonen (2013), Gourieroux, Jasiak (2016), Gourieroux, Zakoian (2017)]. Indeed noncausal processes are appropriate for modelling sequences of speculative bubbles, that are increasing patterns followed by a burst, and such patterns are frequently encountered in financial series such as commodity prices and cryptocurrencies series [see e.g.…”