1,721,017 research outputs found
Adaptive MCMC Methods for Inference on Discretely Observed Affine Jump Diffusion Models.
Full text linkIn the present paper we generalize in a Bayesian framework the inferential solution proposed by Eraker, Johannes & Polson (2003) for stochastic volatility models with jumps and affine structure. We will use an adaptive sampling methodology known as Delayed Rejection suggested in Tierney & Mira (1999) in a Markov Chain Monte Carlo settings in order to reduce the asymptotic variance of the estimates. Furthermore, the use of a particle filtering procedure allows to compute the Bayes factor
Volatility, Jumps and Predictability of Returns: a Sequential Analysis.
Full text linkIn this paper we propose a sequential Monte Carlo algorithm to estimate a stochastic volatility model with leverage effects and non constant conditional mean and jumps. We are interested in estimating the time invariant parameters and the non-observable dynamics involved in the model. Our idea relies on the auxiliary particle filter algorithm mixed together with Markov Chain Monte Carlo (MCMC) methodology. Adding an MCMC step to the auxiliary particle filter prevents numerical degeneracies in the sequential algorithm and allows sequential evaluation of the fixed parameters and the latent processes. Empirical evaluation on simulated and real data is presented to assess the performance of the algorithm
Comparing stochastic volatility models through Monte Carlo simulations
No full textStochastic volatility models are important tools for studying the behavior of many financial markets.
For this reason a number of versions have been introduced and studied in the recent literature. The
goal is to review and compare some of these alternatives by using Bayesian procedures. The quantity
used to assess the goodness-of-fit is the Bayes factor, whereas the ability to forecast the volatility has
been tested through the computation of the one-step-ahead value-at-risk (VaR). Model estimation has
been carried out through adaptive Markov chain Monte Carlo (MCMC) procedures. The marginal
likelihood, necessary to compute the Bayes factor, has been computed through reduced runs of the
same MCMC algorithm and through an auxiliary particle filter. The empirical analysis is based on
the study of three international financial indexes
Testing Rational Addiction: When Lifetime is Uncertain, One Lag is Enough
Full text linkThe rational addiction model is usually tested by estimating a linear second-order difference Euler equation, which may produce unreliable estimates. We show that a linear first-order difference equation is a better alternative. This empirical specification is appropriate under the reasonable assumption that people are uncertain about the time of their death, it is based on the same structural assumptions used in the literature, and it retains all policy implications of the deterministic rational addiction model. It is also empirically convenient because it is simple, it allows using efficient estimation strategies that do not require instrumental variables, and it is robust to the possible non-stationarity of the data. As an application we estimate the demand for smoking in the US from 1970 to 2016, and we show that it is consistent with the rational addiction model
Volatility, Jumps, and Predictability of Returns: A Sequential Analysis
Full text linkIn this article we propose a Monte Carlo algorithm for sequential parameter learning for a stochastic volatility model with leverage, nonconstant conditional mean and jumps. We are interested in estimating the time invariant parameters and the nonobservable dynamics involved in the model. Our simple but effective idea relies on the auxiliary particle filter algorithm mixed together with the Markov Chain Monte Carlo (MCMC) methodology. Adding an MCMC step to the auxiliary particle filter prevents numerical degeneracies in the sequential algorithm and allows sequential evaluation of the fixed parameters and the latent processes. Empirical evaluation on simulated and real data is presented to assess the performance of the algorithm. A numerical comparison with a full MCMC procedure is also provided. We also extend our methodology to superposition models in which volatility is obtained by a linear combination of independent processes.Auxiliary particle filters, Bayesian estimation, Leverage, MCMC, Return's predictability, Stochastic volatility with jumps,
Investigating asymmetry in US stock market indexes: evidence from a stochastic volatility model
No full textThis study provides empirical evidence on asymmetry in financial returns using a simple stochastic volatility model which allows a parsimonious yet flexible treatment of both skewness and heavy tails in the conditional distribution of returns. In particular, it is assumed that returns have a Skew-GED conditional distribution. Inference is conducted under a Bayesian framework using Markov Chain Monte Carlo methods for estimating the properties of the posterior distributions of the parameters. One is also able to perform some specification testing via Bayes factors. The data set consists of daily and weekly returns on the DJ30, S&P500 and Nasdaq US stock market indexes. The estimation results are consistent with the presence of substantial asymmetry and heavy tails in the distribution of US stock market indexes
Multiple Equilibria and the Phillips Curve: Do Agents Always Underreact?
Full text linkWe study a New Keynesian Phillips curve in which agents deviate from the rational expectation paradigm and forecast inflation using a simple, potentially misspecified autoregressive rule. Consistency criteria à la Hommes and Zhu (2014) between perceived and actual laws of motion of inflation might allow for multiple expectational equilibria. Unfortunately, multiple equilibria models pose challenges for empirical validation. This paper proposes a latent Markov chain process to dynamically separate such equilibria. Moreover, an original Bayesian inference approach based on hierarchical priors is introduced, which naturally offers the possibility of incorporating equilibrium-identifying constraints with various degrees of prior beliefs. Finally, an inference procedure is proposed to assess a posteriori the probability that the theoretical constraints are satisfied and to estimate the equilibrium changes over time. We show that common prior assumptions regarding structural parameters favor the separation of equilibria, thereby making the Bayesian inference a natural framework for Markov-switching Phillips curve models. Empirical evidence obtained from observed inflation, output gap, and the consensus expectations from the Survey of Professional Forecasters supports multiple equilibria, and we find evidence of temporal variation in over-and under-reaction patterns, which, to the best of our knowledge, have not been previously documented. Specifically, we observe that agents tend to underreact to shocks when inflation is high and persistent, whereas they behave substantially as fully informed forecasters when the inflation level is low and stable, i.e., after the mid-nineties. We also find that the model does not suffer from the missing disinflation puzzle during the Great Recession
Solving the Milk Addiction Paradox
Full text linkThe milk addiction paradox refers to an empirical finding in which commodities that are typically considered to be non addictive, such as milk, appear instead to be addictive. This result seems more likely when there is persistence in consumption and when using aggregate data, and it suggests that the AR(2) model typically used in the addiction literature is prone to produce spurious result in favor of rational addiction. Using both simulated and real data, we show that the milk addiction paradox disappears when estimating the data using an AR(1) linear specification that describes the saddle-path solution of the rational addiction model. The AR(1) specification is able to correctly discriminate between rational addiction and simple persistence in the data, to test for the main features of rational addiction, and to produce unbiased estimates of the short and long-run elasticity of demand. These results hold both with individual and aggregated data, and they suggest that, for testing rational addiction, the AR(1) model is a better empirical alternative than the canonical AR(2) model
MCMC Bayesian Estimation of a Skew-GED Stochastic Volatility Model
No full textIn this paper we present a stochastic volatility model assuming that the return shock has a Skew-GED distribution. This allows a parsimonious yet flexible treatment of asymmetry and heavy tails in the conditional distribution of returns. The Skew-GED distribution nests both the GED, the Skew-normal and the normal densities as special cases so that specification tests are easily performed. Inference is conducted under a Bayesian framework using Markov Chain MonteCarlo methods for computing the posterior distributions of the parameters. More precisely, our Gibbs-MH updating scheme makes use of the Delayed Rejection Metropolis-Hastings methodology as proposed by Tierney and Mira (1999), and of Adaptive-Rejection Metropolis sampling. We apply this methodology to a data set of daily and weekly exchange rates. Our results suggest that daily returns are mostly symmetric with fat-tailed distributions while weekly returns exhibit both significant asymmetry and fat tails
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