Forecasting bubbles with mixed causal-noncausal autoregressive models

Abstract

This paper investigates one-step ahead density forecasts of mixed causalnoncausal models. We compare the sample-based and the simulations-based approaches respectively developed by Gouriéroux and Jasiak (2016) and Lanne, Luoto, and Saikkonen (2012). We focus on explosive episodes and therefore on predicting turning points of bubbles bursts. We suggest the use of both methods to construct investment strategies based on how much probabilities are induced by the assumed model and by past behaviours. We illustrate our analysis on Nickel prices series.

Conditional Moments of Noncausal Alpha-Stable Processes and the Prediction of Bubble Crash Odds

“…For practical econometric purposes, financial bubbles in stock prices, market indexes and price-dividend ratios are typically characterised as short-lived explosive episodes followed by abrupt or gradual collapses, and are analysed using reduced form models [Phillips and Shi (2018)]. An increasing body of literature documents, models and forecasts bubbles in various financial time series using heavy-tailed noncausal processes [Cavaliere et al (2020), Fries andZakoian (2019), Giancaterini and, Gouriéroux and Zakoian (2017), Hecq et al (2016), Hecq and Voisin (2020)]. In this section, we focus on the dynamics of noncausal processes during such explosive episodes, that is, when the conditioning level of the trajectory takes on large positive or negative values.…”

“…To encompass explosive exponential bubble patterns followed by more complex post-peak dynamics, the noncausal literature considered adding a causal component to the noncausal AR(1), resulting in the much-invoked MAR(1, q ) processes [see for instance Hecq and Voisin (2020), Gouriéroux et al (2019)]. We show here that whatever the form of the causal component adjoined to the noncausal AR(1), i.e., whatever the shape of the collapse after the exponential growth episode, the crash probability -or more accurately, the probability of reaching the end of the exponential growth-still follows from a geometric distribution with parameter   .…”

“…Taking notice of the absence of closed-form formulae for conditional moments and the predictive density Gouriéroux and Zakoian (2017) and Section 3 in Fries and Zakoian (2019)], two simulation-and sample-based methods have been proposed in the noncausal literature to approximate the conditional distribution of noncausal processes [Lanne et al (2012a), Gouriéroux and Jasiak (2016)]. While offering flexible alternatives for forecasting noncausal processes beyond the special cases, Hecq and Voisin (2020) find that these methods can become computationally intense for larger prediction horizons and that accurately capturing the dynamics during explosive episodes may prove challenging [see also Gouriéroux et al (2019)]. Partial results have been obtained by Gouriéroux and Zakoian (2017) on the conditional moments of noncausal AR(1) processes driven by independent and identically distributed (i.i.d.)…”

“…MAR processes with Cauchy errors (stable with α = 1 and β = 0) are a popular benchmark for speculative bubble modelling in the noncausal literature [e.g.,Hencic and Gouriéroux (2015),Hecq et al (2016),Fries and Zakoian (2019),Gouriéroux et al (2019),Cavaliere et al (2020),Hecq and Voisin (2020)]. An attractive feature of this class of models is that the Cauchy distribution is one of the special cases in the stable family for which a closed-form density is available.…”

Mixed causal–noncausal autoregressions with exogenous regressors

“…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).…”