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Particle learning for Bayesian semi-parametric stochasticvolatility model
(2019) Virbickaitė, Audronė; HEDIBERT FREITAS LOPES; Ausín, M. Concepción; Galeano, Pedro
This article designs a Sequential Monte Carlo (SMC) algorithm for estimation of Bayesian semi-parametric Stochastic Volatility model for financial data. In particular, it makes use of one of the most recent particle filters called Particle Learning (PL). SMC methods are especially well suited for state-space models and can be seen as a cost-efficient alternative to Markov Chain Monte Carlo (MCMC), since they allow for online type inference. The posterior distributions are updated as new data is observed, which is exceedingly costly using MCMC. Also, PL allows for consistent online model comparison using sequential predictive log Bayes factors. A simulated data is used in order to compare the posterior outputs for the PL and MCMC schemes, which are shown to be almost identical. Finally, a short real data application is included.
Ambiguity through confidence functions
(2009) Chateauneuf, Alain; JOSÉ HELENO FARO
We characterize preference relations over bounded below Anscombe and Aumann’s acts and give necessary and sufficient conditions that guarantee the existence of a utility function u on consequences, a confidence function ϕ on the set of all probabilities over states of nature, and a positive threshold level of confidence ˛0 such that our preference relation has a functional representation J, where given an act f J(f) = min p ∈ L˛0 ϕ 1 ϕ(p) S u(f) dp. The level set L˛0ϕ := {p : ϕ(p) ≥ ˛0} reflects the priors held by the decision maker and the valueϕ(p) captures the relevance of prior p for his decision. The combination ofϕ and˛0 may describe the decision maker’s subjective assessment of available information. An important feature of our representation is the characterization of the maximal confidence function which allows us to obtain results on comparative ambiguity aversion and on special cases, namely the subjective expected utility, the Choquet expected utility with convex capacity, and the maxmin expected utilit
On the Long-Run Volatility of Stocks
(2018) Carvalho, Carlos M.; HEDIBERT FREITAS LOPES; McCulloch, Robert E.
In this article, we investigate whether or not the volatility per period of stocks is lower over longer horizons.Taking the perspective of an investor, we evaluate the predictive variance of k-period returns under differentmodel and prior specifications. We adopt the state-space framework of Pástor and Stambaugh to model thedynamics of expected returns and evaluate the effects of prior elicitation in the resulting volatility estimates.Part of the developments includes an extension that incorporates time-varying volatilities and covariancesin a constrained prior information set-up. Our conclusion for the U.S. market, under plausible prior specifi-cations, is that stocks are less volatile in the long run. Model assessment exercises demonstrate the modelsand priors supporting our main conclusions are in accordance with the data. To assess the generality of theresults, we extend our analysis to a number of international equity indices. Supplementary materials for thisarticle are available online.
Walk on the Wild Side: Temporarily Unstable Paths and Multiplicative Sunspots
(2019) Ascari, Guido; Bonomolo, Paolo; HEDIBERT FREITAS LOPES
We propose a generalization of the rational expectations framework to allow for temporarily unstable paths. Our approach introduces multiplicative sunspot shocks and it yields drifting parameters and stochastic volatility. Then, we provide an econometric strategy to estimate this generalized model on the data. The methodology allows the data to choose between different possible alternatives: determinacy, indeterminacy, and temporary instability. We apply our methodology to US inflation dynamics in the 1970s through the lens of a simple New Keynesian model. When temporarily unstable paths are allowed, the data unambiguously select them to explain the stagflation period in the 1970s.

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