scholarly journals Particle Markov Chain Monte Carlo Techniques of Unobserved Component Time Series Models Using Ox

2014 ◽  
Author(s):  
Nima Nonejad
Keyword(s):  
Time Series ◽  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Time Series Models ◽  
Monte Carlo Techniques ◽  
Unobserved Component ◽  
Component Time

scholarly journals Particle Markov Chain Monte Carlo Techniques of Unobserved Component Time Series Models Using Ox

2016 ◽  
Vol 8 (1) ◽  
Author(s):  
Nima Nonejad
Keyword(s):  
Time Series ◽  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Time Series Models ◽  
Unobserved Component ◽  
Volatility Model ◽  
Component Time

AbstractThis paper details particle Markov chain Monte Carlo (PMCMC) techniques for analysis of unobserved component time series models using several economic data sets. The objective of this paper is to explain the basics of the methodology and provide computational applications that justify applying PMCMC in practice. For instance, we use PMCMC to estimate a stochastic volatility model with a leverage effect, Student-t distributed errors or serial dependence. We also model time series characteristics of monthly US inflation rate by considering a heteroskedastic ARFIMA model where heteroskedasticity is specified by means of a Gaussian stochastic volatility process.

scholarly journals Typical representatives of free homotopy classes in multi-punctured plane

2019 ◽  
Vol 11 (03) ◽  
pp. 623-659
Author(s):  
Maxim Arnold ◽  
Yuliy Baryshnikov ◽  
Yuriy Mileyko
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Probability Measure ◽  
Homotopy Class ◽  
Piecewise Linear ◽  
Homotopy Classes ◽  
Simple Method ◽  
Monte Carlo Techniques ◽  
Free Homotopy Class

We show that a uniform probability measure supported on a specific set of piecewise linear loops in a nontrivial free homotopy class in a multi-punctured plane is overwhelmingly concentrated around loops of minimal lengths. Our approach is based on extending Mogulskii’s theorem to closed paths, which is a useful result of independent interest. In addition, we show that the above measure can be sampled using standard Markov Chain Monte Carlo techniques, thus providing a simple method for approximating shortest loops.

scholarly journals A Fast and Efficient Markov Chain Monte Carlo Method for Market Microstructure Model

2021 ◽  
Vol 2021 ◽  
pp. 1-24
Author(s):  
Sun Yapeng ◽  
Peng Hui ◽  
Xie Wenbiao
Keyword(s):  
Time Series ◽  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Market Microstructure ◽  
Financial Time Series ◽  
Market Liquidity ◽  
Time Varying ◽  
Financial Time ◽  
Simulation Smoother

The non-linear market microstructure (MM) model for financial time series modeling is a flexible stochastic volatility model with demand surplus and market liquidity. The estimation of the model is difficult, since the unobservable surplus demand is a time-varying stochastic variable in the return equation, and the market liquidity arises both in the mean term and in the variance term of the return equation in the MM model. A fast and efficient Markov Chain Monte Carlo (MCMC) approach based on an efficient simulation smoother algorithm and an acceptance-rejection Metropolis–Hastings algorithm is designed to estimate the non-linear MM model. Since the simulation smoother algorithm makes use of the band diagonal structure and positive definition of Hessian matrix of the logarithmic density, it can quickly draw the market liquidity. In addition, we discuss the MM model with Student-t heavy tail distribution that can be utilized to address the presence of outliers in typical financial time series. Using the presented modeling method to make analysis of daily income of the S&P 500 index through the point forecast and the density forecast, we find clear support for time-varying volatility, volatility feedback effect, market microstructure theory, and Student-t heavy tails in the financial time series. Through this method, one can use the estimated market liquidity and surplus demand which is much smoother than the strong stochastic return process to assist the transaction decision making in the financial market.

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