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154
Filtering Via Simulation: Auxiliary Particle Filters
, 1997
"... This paper analyses the recently suggested particle approach to filtering time series. We suggest that the algorithm is not robust to outliers for two reasons: the design of the simulators and the use of the discrete support to represent the sequentially updating prior distribution. Both problems ar ..."
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Cited by 519 (15 self)
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This paper analyses the recently suggested particle approach to filtering time series. We suggest that the algorithm is not robust to outliers for two reasons: the design of the simulators and the use of the discrete support to represent the sequentially updating prior distribution. Both problems are tackled in this paper. We believe we have largely solved the first problem and have reduced the order of magnitude of the second. In addition we introduce the idea of stratification into the particle filter which allows us to perform online Bayesian calculations about the parameters which index the models and maximum likelihood estimation. The new methods are illustrated by using a stochastic volatility model and a time series model of angles. Some key words: Filtering, Markov chain Monte Carlo, Particle filter, Simulation, SIR, State space. 1 1
Likelihood Inference for Discretely Observed NonLinear Diffusions
 Econometrica
, 1998
"... This paper is concerned with the Bayesian estimation of nonlinear stochastic differential equations when only discrete observations are available. The estimation is carried out using a tuned MCMC method, in particular a blocked MetropolisHastings algorithm, by introducing auxiliary points and usin ..."
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Cited by 155 (18 self)
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This paper is concerned with the Bayesian estimation of nonlinear stochastic differential equations when only discrete observations are available. The estimation is carried out using a tuned MCMC method, in particular a blocked MetropolisHastings algorithm, by introducing auxiliary points and using the EulerMaruyama discretisation scheme. Techniques for computing the likelihood function, the marginal likelihood and diagnostic measures (all based on the MCMC output) are presented. Examples using simulated and real data are presented and discussed in detail.
Modelling asymmetric exchange rate dependence
 International Economic Review
"... We test for asymmetry in a model of the dependence between the Deutsche mark and the yen, in the sense that a different degree of correlation is exhibited during joint appreciations against the U.S. dollar versus during joint depreciations. We consider an extension of the theory of copulas to allow ..."
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Cited by 103 (4 self)
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We test for asymmetry in a model of the dependence between the Deutsche mark and the yen, in the sense that a different degree of correlation is exhibited during joint appreciations against the U.S. dollar versus during joint depreciations. We consider an extension of the theory of copulas to allow for conditioning variables, and employ it to construct flexible models of the conditional dependence structure of these exchange rates. We find evidence that the mark–dollar and yen–dollar exchange rates are more correlated when they are depreciating against the dollar than when they are appreciating. 1.
Multivariate Density Forecast Evaluation and Calibration
 in Financial Risk Management: HighFrequency Returns on Foreign Exchange,” Review of Economics and Statistics
, 1999
"... educational and research purposes, so long as it is not altered, this copyright notice is reproduced with it, and it is not sold for profit. Abstract: We provide a framework for evaluating and improving multivariate density forecasts. Among other things, the multivariate framework lets us evaluate t ..."
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Cited by 72 (15 self)
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educational and research purposes, so long as it is not altered, this copyright notice is reproduced with it, and it is not sold for profit. Abstract: We provide a framework for evaluating and improving multivariate density forecasts. Among other things, the multivariate framework lets us evaluate the adequacy of density forecasts involving crossvariable interactions, such as timevarying conditional correlations. We also provide conditions under which a technique of density forecast “calibration ” can be used to improve deficient density forecasts. Finally, motivated by recent advances in financial risk management, we provide a detailed application to multivariate highfrequency exchange rate density forecasts.
Density Forecasting: A Survey
 Journal of Forecasting
, 2000
"... A density forecast of the realization of a random variable at some future time is an estimate of the probability distribution of the possible future values of that variable. This chapter presents a selective survey of applications of density forecasting in macroeconomics and finance, and discusses s ..."
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Cited by 65 (9 self)
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A density forecast of the realization of a random variable at some future time is an estimate of the probability distribution of the possible future values of that variable. This chapter presents a selective survey of applications of density forecasting in macroeconomics and finance, and discusses some issues concerning the production, presentation, and evaluation of density forecasts. This chapter first appeared as an article with the same title in Journal of Forecasting, 19 (2000), 235254. The helpful comments and suggestions of Frank Diebold, Stewart Hodges and two anonymous referees are gratefully acknowledged. Subsequent editorial changes have been made following suggestions from the editors of this volume. Responsibility for errors remains with the authors. 2 1. INTRODUCTION A density forecast of the realization of a random variable at some future time is an estimate of the probability distribution of the possible future values of that variable. It thus provides a complet...
Dependence Structures for Multivariate HighFrequency Data in Finance. Quantitative Finance 3
, 2003
"... www.math.ethz.ch/finance Stylised facts for univariate high–frequency data in finance are well–known. They include scaling behaviour, volatility clustering, heavy tails, and seasonalities. The multivariate problem, however, has scarcely been addressed up to now. In this paper, bivariate series of hi ..."
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Cited by 54 (4 self)
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www.math.ethz.ch/finance Stylised facts for univariate high–frequency data in finance are well–known. They include scaling behaviour, volatility clustering, heavy tails, and seasonalities. The multivariate problem, however, has scarcely been addressed up to now. In this paper, bivariate series of high–frequency FX spot data for major FX markets are investigated. First, as an indispensable prerequisite for further analysis, the problem of simultaneous deseasonalisation of high–frequency data is addressed. In the bulk of the paper we analyse in detail the dependence structure as a function of the time scale. Particular emphasis is put on the tail behaviour, which is investigated by means of copulas and spectral measures. 1
2003): “Forecast uncertainties in macroeconometric modelling: an application to the UK economy
 Journal of the American Statistical Association
"... This paper argues that probability forecasts convey information on the uncertainties that surround macroeconomic forecasts in a straightforward manner which is preferable to other alternatives, including the use of confidence intervals. Probability forecasts obtained using a small benchmark macroec ..."
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Cited by 44 (14 self)
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This paper argues that probability forecasts convey information on the uncertainties that surround macroeconomic forecasts in a straightforward manner which is preferable to other alternatives, including the use of confidence intervals. Probability forecasts obtained using a small benchmark macroeconometric model as well as a number of other alternatives are presented and evaluated using recursive forecasts generated over the period 1999q12001q1. Out of sample probability forecasts of inflation and output growth are also provided over the period 2001q22003q1, and their implications discussed in relation to the Bank of England’s inflation target and the need to avoid recessions, both as separate events and jointly. The robustness of the results to parameter and model uncertainties is also investigated by a pragmatic implementation of the Bayesian model averaging approach.
PairCopula Constructions of Multiple Dependence
"... Building on the work of Bedford, Cooke and Joe, we show how multivariate data, which exhibit complex patterns of dependence in the tails, can be modelled using a cascade of paircopulae, acting on two variables at a time. We use the paircopula decomposition of a general multivariate distribution an ..."
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Cited by 42 (12 self)
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Building on the work of Bedford, Cooke and Joe, we show how multivariate data, which exhibit complex patterns of dependence in the tails, can be modelled using a cascade of paircopulae, acting on two variables at a time. We use the paircopula decomposition of a general multivariate distribution and propose a method to perform inference. The model construction is hierarchical in nature, the various levels corresponding to the incorporation of more variables in the conditioning sets, using paircopulae as simple building blocs. Paircopula decomposed models also represent a very exible way to construct higherdimensional coplulae. We apply the methodology to a nancial data set. Our approach represents the rst step towards developing of an unsupervised algorithm that explores the space of possible paircopula models, that also can be applied to huge data sets automatically.
Probabilistic forecasts, calibration and sharpness
 Journal of the Royal Statistical Society Series B
, 2007
"... Summary. Probabilistic forecasts of continuous variables take the form of predictive densities or predictive cumulative distribution functions. We propose a diagnostic approach to the evaluation of predictive performance that is based on the paradigm of maximizing the sharpness of the predictive dis ..."
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Cited by 38 (15 self)
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Summary. Probabilistic forecasts of continuous variables take the form of predictive densities or predictive cumulative distribution functions. We propose a diagnostic approach to the evaluation of predictive performance that is based on the paradigm of maximizing the sharpness of the predictive distributions subject to calibration. Calibration refers to the statistical consistency between the distributional forecasts and the observations and is a joint property of the predictions and the events that materialize. Sharpness refers to the concentration of the predictive distributions and is a property of the forecasts only. A simple theoretical framework allows us to distinguish between probabilistic calibration, exceedance calibration and marginal calibration. We propose and study tools for checking calibration and sharpness, among them the probability integral transform histogram, marginal calibration plots, the sharpness diagram and proper scoring rules. The diagnostic approach is illustrated by an assessment and ranking of probabilistic forecasts of wind speed at the Stateline wind energy centre in the US Pacific Northwest. In combination with crossvalidation or in the time series context, our proposal provides very general, nonparametric alternatives to the use of information criteria for model diagnostics and model selection.
Particle Methods for Bayesian Modelling and Enhancement of Speech Signals
, 2000
"... This paper applies timevarying autoregressive (TVAR) models with stochastically evolving parameters to the problem of speech modelling and enhancement. The stochastic evolution models for the TVAR parameters are Markovian diusion processes. The main aim of the paper is to perform online estimation ..."
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Cited by 36 (5 self)
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This paper applies timevarying autoregressive (TVAR) models with stochastically evolving parameters to the problem of speech modelling and enhancement. The stochastic evolution models for the TVAR parameters are Markovian diusion processes. The main aim of the paper is to perform online estimation of the clean speech and model parameters, and to determine the adequacy of the chosen statistical models. Ecient particle methods are developed to solve the optimal ltering and xedlag smoothing problems. The algorithms combine sequential importance sampling (SIS), a selection step and Markov chain Monte Carlo (MCMC) methods. They employ several variance reduction strategies to make the best use of the statistical structure of the model. It is also shown how model adequacy may be determined by combining the particle lter with frequentist methods. The modelling and enhancement performance of the models and estimation algorithms are evaluated in simulation studies on both synthetic and re...