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Register a new userFast estimation of multivariate stochastic volatility
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In this paper we develop a Bayesian procedure for estimating multivariate stochastic volatility (MSV) using state space models. A multiplicative model based on inverted Wishart and multivariate singular beta distributions is proposed for the evolution of the volatility, and a flexible sequential volatility updating is employed. Being computationally fast, the resulting estimation procedure is particularly suitable for on-line forecasting. Three performance measures are discussed in the context of model selection: the log-likelihood criterion, the mean of standardized one-step forecast errors, and sequential Bayes factors. Finally, the proposed methods are applied to a data set comprising eight exchange rates vis-a-vis the US dollar.
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This paper is concerned with the estimation of the volatility process in a stochastic volatility model of the following form: $dX_t=a_tdt+sigma_tdW_t$, where $X$ denotes the log-price and $sigma$ is a c`adl`ag semi-martingale. In the spirit of a series of recent works on the estimation of the cumulated volatility, we here focus on the instantaneous volatility for which we study estimators built as finite differences of the textit{power variations} of the log-price. We provide central limit theorems with an optimal rate depending on the local behavior of $sigma$. In particular, these theorems yield some confidence intervals for $sigma_t$.
The leverage effect-- the correlation between an assets return and its volatility-- has played a key role in forecasting and understanding volatility and risk. While it is a long standing consensus that leverage effects exist and improve forecasts, empirical evidence paradoxically do not show that most individual stocks exhibit this phenomena, mischaracterizing risk and therefore leading to poor predictive performance. We examine this paradox, with the goal to improve density forecasts, by relaxing the assumption of linearity in the leverage effect. Nonlinear generalizations of the leverage effect are proposed within the Bayesian stochastic volatility framework in order to capture flexible leverage structures, where small fluctuations in prices have a different effect from large shocks. Efficient Bayesian sequential computation is developed and implemented to estimate this effect in a practical, on-line manner. Examining 615 stocks that comprise the S&P500 and Nikkei 225, we find that relaxing the linear assumption to our proposed nonlinear leverage effect function improves predictive performances for 89% of all stocks compared to the conventional model assumption.
Agents heterogeneity is recognized as a driver mechanism for the persistence of financial volatility. We focus on the multiplicity of investment strategies horizons, we embed this concept in a continuous time stochastic volatility framework and prove that a parsimonious, two-scale version effectively captures the long memory as measured from the real data. Since estimating parameters in a stochastic volatility model is challenging, we introduce a robust methodology based on the Generalized Method of Moments supported by a heuristic selection of the orthogonal conditions. In addition to the volatility clustering, the estimated model also captures other relevant stylized facts, emerging as a minimal but realistic and complete framework for modelling financial time series.
Volatility of financial stock is referring to the degree of uncertainty or risk embedded within a stocks dynamics. Such risk has been received huge amounts of attention from diverse financial researchers. By following the concept of regime-switching model, we proposed a non-parametric approach, named encoding-and-decoding, to discover multiple volatility states embedded within a discrete time series of stock returns. The encoding is performed across the entire span of temporal time points for relatively extreme events with respect to a chosen quantile-based threshold. As such the return time series is transformed into Bernoulli-variable processes. In the decoding phase, we computationally seek for locations of change points via estimations based on a new searching algorithm conjunction to the Bayesian information criterion applied on the observed collection of recurrence times upon the binary process. Besides the independence required for building the Geometric distributional likelihood function, the proposed approach can functionally partition the entire return time series into a collection of homogeneous segments without any assumptions of dynamic structure and underlying distributions. In the numerical experiments, our approach is found favorably compared with Viterbis under Hidden Markov Model (HMM) settings. In the real data applications, volatility dynamics of every single stock of S&P500 are computed and revealed. Then, a non-linear dependency of any stock-pair is derived by measuring through concurrent volatility states. Finally, various networks dealing with distinct financial implications are consequently established to represent different aspects of global connectivity among all stocks in S&P500.
We have presented a novel technique of detecting intermittencies in a financial time series of the foreign exchange rate data of U.S.- Euro dollar(US/EUR) using a combination of both statistical and spectral techniques. This has been possible due to Continuous Wavelet Transform (CWT) analysis which has been popularly applied to fluctuating data in various fields science and engineering and is also being tried out in finance and economics. We have been able to qualitatively identify the presence of nonlinearity and chaos in the time series of the foreign exchange rates for US/EURO (United States dollar to Euro Dollar) and US/UK (United States dollar to United Kingdom Pound) currencies. Interestingly we find that for the US-INDIA(United States dollar to Indian Rupee) foreign exchange rates, no such chaotic dynamics is observed. This could be a result of the government control over the foreign exchange rates, instead of the market controlling them.
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