Abstract
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.
Highlights
Academic Editor: Lijun Pei e non-linear market microstructure (MM) model for financial time series modeling is a flexible stochastic volatility model with demand surplus and market liquidity. e estimation of the model is difficult, since the unobservable surplus demand is a timevarying 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
To demonstrate the computation performance of the precision-based simulation smoother, a Kalman filter-based Markov Chain Monte Carlo (MCMC) method for stochastic volatility (SV) model and stochastic volatility-in-mean (SVM) model is developed. e Kalman filterbased simulation smoother algorithm and the auxiliary mixture sampler method are compared with our precision-based simulation smoother method on the SV model
We studied the more general MM and microstructure model plus Student-t heavy tails (MMt) models compared to the MM type models researched in previous works and proposed a new approach for efficiently estimating the general MM type models, which are nonlinear non-Gaussian models
Summary
Academic Editor: Lijun Pei e non-linear market microstructure (MM) model for financial time series modeling is a flexible stochastic volatility model with demand surplus and market liquidity. e estimation of the model is difficult, since the unobservable surplus demand is a timevarying 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. Academic Editor: Lijun Pei e non-linear market microstructure (MM) model for financial time series modeling is a flexible stochastic volatility model with demand surplus and market liquidity. Rough 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. E estimation of the MM model is not straightforward, since the market liquidity appears both in the mean term and in the variance term of Discrete Dynamics in Nature and Society the model, and the surplus demand is time-varying stochastic variable. Unlike the non-linear Kalman filter and maximum likelihood method-based estimation way for the MM model (see, e.g., Peng et al [5]; Peng et al [6]; Peng et al [7]; and Qin et al [9]), we develop an efficient MCMC method to estimate the market microstructure model. The status of the chain after a huge number of steps is used as a sample of the desired distribution, which may lead to complex desired distribution and an inaccurate estimate result. us, the modification of the simulation smoother algorithm is required for the estimation of the MM model
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