ASSESSING AND TESTING FOR THRESHOLD NONLINEARITY IN STOCK RETURNS

This paper proposes a test for threshold nonlinearity in a time series with generalized autore‐gressive conditional heteroscedasticity (GARCH) volatility dynamics. This test is used to examine whether financial returns on market indices exhibit asymmetric mean and volatility around a threshold value, using a double‐threshold GARCH model. The test adopts the reversible‐jump Markov chain Monte Carlo idea of Green, proposed in 1995, to calculate the posterior probabilities for a conventional GARCH model and a double‐threshold GARCH model. Posterior evidence favouring the threshold GARCH model indicates threshold nonlinearity with asymmetric behaviour of the mean and volatility. Simulation experiments demonstrate that the test works very well in distinguishing between the conventional GARCH and the double‐threshold GARCH models. In an application to eight international financial market indices, including the G‐7 countries, clear evidence supporting the hypothesis of threshold nonlinearity is discovered, simultaneously indicating an uneven mean‐reverting pattern and volatility asymmetry around a threshold return value.     

A Survey of Sequential Monte Carlo Methods for Economics and Finance

This article serves as an introduction and survey for economists to the field of sequential Monte Carlo methods which are also known as particle filters. Sequential Monte Carlo methods are simulation-based algorithms used to compute the high-dimensional and/or complex integrals that arise regularly in applied work. These methods are becoming increasingly popular in economics and finance; from dynamic stochastic general equilibrium models in macro-economics to option pricing. The objective of this article is to explain the basics of the methodology, provide references to the literature, and cover some of the theoretical results that justify the methods in practice.     

Inference for Lévy‐Driven Stochastic Volatility Models via Adaptive Sequential Monte Carlo

Abstract. We investigate simulation methodology for Bayesian inference in Lévy‐driven stochastic volatility (SV) models. Typically, Bayesian inference from such models is performed using Markov chain Monte Carlo (MCMC); this is often a challenging task. Sequential Monte Carlo (SMC) samplers are methods that can improve over MCMC; however, there are many user‐set parameters to specify. We develop a fully automated SMC algorithm, which substantially improves over the standard MCMC methods in the literature. To illustrate our methodology, we look at a model comprised of a Heston model with an independent, additive, variance gamma process in the returns equation. The driving gamma process can capture the stylized behaviour of many financial time series and a discretized version, fit in a Bayesian manner, has been found to be very useful for modelling equity data. We demonstrate that it is possible to draw exact inference, in the sense of no time‐discretization error, from the Bayesian SV model.     

COMPOSITIONAL TIME SERIES ANALYSIS OF MORTALITY PROPORTIONS

Compositional time series are multivariate time series which at each time point are proportions that sum to a constant. Accurate inference for such series which occur in several disciplines such as geology, economics and ecology is important in practice. Usual multivariate statistical procedures ignore the inherent constrained nature of these observations as parts of a whole and may lead to inaccurate estimation and prediction. In this article, a regression model with vector autoregressive moving average (VARMA) errors is fit to the compositional time series after an additive log ratio (ALR) transformation. Inference is carried out in a hierarchical Bayesian framework using Markov chain Monte Carlo techniques. The approach is illustrated on compositional time series of mortality events in Los Angeles in order to investigate dependence of different categories of mortality on air quality.     

LONG-RANGE DEPENDENT COMMON FACTOR MODELS: A BAYESIAN APPROACH

We propose a simulation-based Bayesian approach to analyze multivariate time series with possible common long-range dependent factors. A state-space approach is used to represent the likelihood function in a tractable manner. The approach taken here allows for extension to fit a non-Gaussian multivariate stochastic volatility (MVSV) model with common long-range dependent components. The method is illustrated for a set of stock returns for companies having similar annual sales.     

Inference for Adaptive Time Series Models: Stochastic Volatility and Conditionally Gaussian State Space Form

In this paper we model the Gaussian errors in the standard Gaussian linear state space model as stochastic volatility processes. We show that conventional MCMC algorithms for this class of models are ineffective, but that the problem can be alleviated by reparameterizing the model. Instead of sampling the unobserved variance series directly, we sample in the space of the disturbances, which proves to lower correlation in the sampler and thus increases the quality of the Markov chain.

Using our reparameterized MCMC sampler, it is possible to estimate an unobserved factor model for exchange rates between a group of n countries. The underlying n + 1 country-specific currency strength factors and the n + 1 currency volatility factors can be extracted using the new methodology. With the factors, a more detailed image of the events around the 1992 EMS crisis is obtained.

We assess the fit of competitive models on the panels of exchange rates with an effective particle filter and find that indeed the factor model is strongly preferred by the data.     

Markov Chain Monte Carlo Methods for Fitting Spatiotemporal Stochastic Models in Plant Epidemiology

Strategies for controlling plant epidemics are investigated by fitting continuous time spatiotemporal stochastic models to data consisting of maps of disease incidence observed at discrete times. Markov chain Monte Carlo methods are used for fitting two such models to data describing the spread of citrus tristeza virus (CTV) in an orchard. The approach overcomes some of the difficulties encountered when fitting stochastic models to infrequent observations of a continuous process. The results of the analysis cast doubt on the effectiveness of a strategy identified from a previous spatial analysis of the CTV data. Extensions of the approaches to more general models and other problems are also considered.     

SPACE–TIME MODELLING OF SYDNEY HARBOUR WINDS

This paper develops a space‐time statistical model for local forecasting of surface‐level wind fields in a coastal region with complex topography. The statistical model makes use of output from deterministic numerical weather prediction models which are able to produce forecasts of surface wind fields on a spatial grid. When predicting surface winds at observing stations , errors can arise due to sub‐grid scale processes not adequately captured by the numerical weather prediction model , and the statistical model attempts to correct for these influences. In particular , it uses information from observing stations within the study region as well as topographic information to account for local bias. Bayesian methods for inference are used in the model , with computations carried out using Markov chain Monte Carlo algorithms. Empirical performance of the model is described , illustrating that a structured Bayesian approach to complicated space‐time models of the type considered in this paper can be readily implemented and can lead to improvements in forecasting over traditional methods.     

Forecasting interest rates volatilities by GARCH (1,1) and stochastic volatility models

In this paper, we compare the forecast ability of GARCH(1,1) and stochastic volatility models for interest rates. The stochastic volatility is estimated using Markov chain Monte Carlo methods. The comparison is based on daily data from 1994 to 1996 for the ten year swap rates for Deutsch Mark, Japanese Yen, and Pound Sterling. Various forecast horizons are considered. It turns out that forecasts based on stochastic volatility models are in most cases superiour to those obtained by GARCH(1,1) models.     

SABR随机波动率LIBOR市场模型的参数校准估计方法与实证模拟

针对标准化Libor市场模型（LMM）和Heston随机波动率Libor市场模型（Heston-LMM）的应用局限,首先将SABR代替Heston过程引入标准化Libor市场模型框架,建立非标准化的SABR随机波动率Libor市场模型（SABR-LMM）;在此基础上,运用利率上限期权（Cap）、利率互换期权（Swaption）和自适应马尔科夫链蒙特卡罗模拟方法（MCMC）对模型参数进行有效市场校准与模拟估计;最后,针对三个月美元Libor远期利率实际数据,对上述三类Libor市场模型的实际运行效果进行了实证模拟计算与比较分析。研究结论认为,基于模拟利差计算结果,针对短期Libor利率模拟而言,与LMM和Heston -LMM两类模型而言,加入SABR波动项的SABR-LMM模型具有更小的模拟误差,因而具有更好的模拟效果。     

Uniform Ergodicity of the Particle Gibbs Sampler

The particle Gibbs sampler is a systematic way of using a particle filter within Markov chain Monte Carlo. This results in an off‐the‐shelf Markov kernel on the space of state trajectories, which can be used to simulate from the full joint smoothing distribution for a state space model in a Markov chain Monte Carlo scheme. We show that the particle Gibbs Markov kernel is uniformly ergodic under rather general assumptions, which we will carefully review and discuss. In particular, we provide an explicit rate of convergence, which reveals that (i) for fixed number of data points, the convergence rate can be made arbitrarily good by increasing the number of particles and (ii) under general mixing assumptions, the convergence rate can be kept constant by increasing the number of particles superlinearly with the number of observations. We illustrate the applicability of our result by studying in detail a common stochastic volatility model with a non‐compact state space.     

A Stochastic Geometry Model for Functional Magnetic Resonance Images

In functional magnetic resonance imaging, spatial activation patterns are commonly estimated using a non-parametric smoothing approach. Significant peaks or clusters in the smoothed image are subsequently identified by testing the null hypothesis of lack of activation in every volume element of the scans. A weakness of this approach is the lack of a model for the activation pattern; this makes it difficult to determine the variance of estimates, to test specific neuroscientific hypotheses or to incorporate prior information about the brain area under study in the analysis. These issues may be addressed by formulating explicit spatial models for the activation and using simulation methods for inference. We present one such approach, based on a marked point process prior. Informally, one may think of the points as centres of activation, and the marks as parameters describing the shape and area of the surrounding cluster. We present an MCMC algorithm for making inference in the model and compare the approach with a traditional non-parametric method, using both simulated and visual stimulation data. Finally we discuss extensions of the model and the inferential framework to account for non-stationary responses and spatio-temporal correlation.     

Monte Carlo Kalman filter and smoothing for multivariate discrete state space models

The author studies state space models for multivariate binomial time series, focussing on the development of the Kalman filter and smoothing for state variables. He proposes a Monte Carlo approach employing the latent variable representation which transplants the classical Kalman filter and smoothing developed for Gaussian state space models to discrete models and leads to a conceptually simple and computationally convenient approach. The method is illustrated through simulations and concrete examples.     

SV模型下中国股票型开放式基金杠杆效应分析

针对中国股票型开放式基金收益波动中是否存在杠杆效应的问题,在对该类基金整体及所选取的三支具有代表性的单个基金分析的基础上,运用一个带杠杆效应的SV模型对其收益的波动性建模,并利用MCMC方法对模型进行参数估计。结果显示：不同于一般对股票市场的研究结论,无论股票型开放式基金整体还是单个基金,其收益率序列的波动中均不存在显著的杠杆效应。     

Structural learning with time-varying components: tracking the cross-section of financial time series

Summary.  When modelling multivariate financial data, the problem of structural learning is compounded by the fact that the covariance structure changes with time. Previous work has focused on modelling those changes by using multivariate stochastic volatility models. We present an alternative to these models that focuses instead on the latent graphical structure that is related to the precision matrix. We develop a graphical model for sequences of Gaussian random vectors when changes in the underlying graph occur at random times, and a new block of data is created with the addition or deletion of an edge. We show how a Bayesian hierarchical model incorporates both the uncertainty about that graph and the time variation thereof.     

A Bayesian kriged Kalman model for short-term forecasting of air pollution levels

Summary.  Short-term forecasts of air pollution levels in big cities are now reported in news-papers and other media outlets. Studies indicate that even short-term exposure to high levels of an air pollutant called atmospheric particulate matter can lead to long-term health effects. Data are typically observed at fixed monitoring stations throughout a study region of interest at different time points. Statistical spatiotemporal models are appropriate for modelling these data. We consider short-term forecasting of these spatiotemporal processes by using a Bayesian kriged Kalman filtering model. The spatial prediction surface of the model is built by using the well-known method of kriging for optimum spatial prediction and the temporal effects are analysed by using the models underlying the Kalman filtering method. The full Bayesian model is implemented by using Markov chain Monte Carlo techniques which enable us to obtain the optimal Bayesian forecasts in time and space. A new cross-validation method based on the Mahalanobis distance between the forecasts and observed data is also developed to assess the forecasting performance of the model implemented.     

Hierarchical priors for Bayesian CART shrinkage

The Bayesian CART (classification and regression tree) approach proposed by Chipman, George and McCulloch (1998) entails putting a prior distribution on the set of all CART models and then using stochastic search to select a model. The main thrust of this paper is to propose a new class of hierarchical priors which enhance the potential of this Bayesian approach. These priors indicate a preference for smooth local mean structure, resulting in tree models which shrink predictions from adjacent terminal node towards each other. Past methods for tree shrinkage have searched for trees without shrinking, and applied shrinkage to the identified tree only after the search. By using hierarchical priors in the stochastic search, the proposed method searches for shrunk trees that fit well and improves the tree through shrinkage of predictions.     

A class of models for aggregated traffic volume time series

Summary. The development of time series models for traffic volume data constitutes an important step in constructing automated tools for the management of computing infrastructure resources. We analyse two traffic volume time series: one is the volume of hard disc activity, aggregated into half-hour periods, measured on a workstation, and the other is the volume of Internet requests made to a workstation. Both of these time series exhibit features that are typical of network traffic data, namely strong seasonal components and highly non-Gaussian distributions. For these time series, a particular class of non-linear state space models is proposed, and practical techniques for model fitting and forecasting are demonstrated.     

Foreign Exchange Intervention by the Bank of Japan: Bayesian Analysis Using a Bivariate Stochastic Volatility Model

A bivariate stochastic volatility model is employed to measure the effect of intervention by the Bank of Japan (BOJ) on daily returns and volume in the USD/YEN foreign exchange market. Missing observations are accounted for, and a data-based Wishart prior for the precision matrix of the errors to the transition equation that is in line with the likelihood is suggested. Empirical results suggest there is strong conditional heteroskedasticity in the mean-corrected volume measure, as well as contemporaneous correlation in the errors to both the observation and transition equations. A threshold model is used for the BOJ reaction function, which is estimated jointly with the bivariate stochastic volatility model via Markov chain Monte Carlo. This accounts for endogeneity between volatility in the market and the BOJ reaction function, something that has hindered much previous empirical analysis in the literature on central bank intervention. The empirical results suggest there was a shift in behavior by the BOJ, with a movement away from a policy of market stabilization and toward a role of support for domestic monetary policy objectives. Throughout, we observe “leaning against the wind” behavior, something that is a feature of most previous empirical analysis of central bank intervention. A comparison with a bivariate EGARCH model suggests that the bivariate stochastic volatility model produces estimates that better capture spikes in in-sample volatility. This is important in improving estimates of a central bank reaction function because it is at these periods of high daily volatility that central banks more frequently intervene.     

Foreign Exchange Intervention by the Bank of Japan: Bayesian Analysis Using a Bivariate Stochastic Volatility Model

A bivariate stochastic volatility model is employed to measure the effect of intervention by the Bank of Japan (BOJ) on daily returns and volume in the USD/YEN foreign exchange market. Missing observations are accounted for, and a data-based Wishart prior for the precision matrix of the errors to the transition equation that is in line with the likelihood is suggested. Empirical results suggest there is strong conditional heteroskedasticity in the mean-corrected volume measure, as well as contemporaneous correlation in the errors to both the observation and transition equations. A threshold model is used for the BOJ reaction function, which is estimated jointly with the bivariate stochastic volatility model via Markov chain Monte Carlo. This accounts for endogeneity between volatility in the market and the BOJ reaction function, something that has hindered much previous empirical analysis in the literature on central bank intervention. The empirical results suggest there was a shift in behavior by the BOJ, with a movement away from a policy of market stabilization and toward a role of support for domestic monetary policy objectives. Throughout, we observe “leaning against the wind” behavior, something that is a feature of most previous empirical analysis of central bank intervention. A comparison with a bivariate EGARCH model suggests that the bivariate stochastic volatility model produces estimates that better capture spikes in in-sample volatility. This is important in improving estimates of a central bank reaction function because it is at these periods of high daily volatility that central banks more frequently intervene.