Post-crash distributions inferred from S

Temporal textures are textures with motion. Examples include wavy water, rising steam and fire. We model image sequences of temporal textures using the spatio-temporal autoregressive model (STAR). This model expresses each pixel as a linear combination of surrounding pixels lagged both in space and in time. The model provides a base for both recognition and synthesis. We show how the least squares method can accurately estimate model parameters for large, causal neighborhoods with more than 1000 parameters. Synthesis results show that the model can adequately capture the spatial and temporal characteristics of many temporal textures. A 95% recognition rate is achieved for a 135 element database with 15 texture classes. 1.

Abstract—An overview of statistical and information-theoretic aspects of hidden Markov processes (HMPs) is presented. An HMP is a discrete-time finite-state homogeneous Markov chain observed through a discrete-time memoryless invariant channel. In recent years, the work of Baum and Petrie on finite-state finite-alphabet HMPs was expanded to HMPs with finite as well as continuous state spaces and a general alphabet. In particular, statistical properties and ergodic theorems for relative entropy densities of HMPs were developed. Consistency and asymptotic normality of the maximum-likelihood (ML) parameter estimator were proved under some mild conditions. Similar results were established for switching autoregressive processes. These processes generalize HMPs. New algorithms were developed for estimating the state, parameter, and order of an HMP, for universal coding and classification of HMPs, and for universal decoding of hidden Markov channels. These and other related topics are reviewed in this paper. Index Terms—Baum–Petrie algorithm, entropy ergodic theorems, finite-state channels, hidden Markov models, identifiability, Kalman filter, maximum-likelihood (ML) estimation, order estimation, recursive parameter estimation, switching autoregressive processes, Ziv inequality. I.

We propose using the price range in the estimation of stochastic volatility models. We show theoretically, numerically, and empirically that range-based volatility proxies are not only highly efficient, but also approximately Gaussian and robust to microstructure noise. Hence range-based Gaussian quasi-maximum likelihood estimation produces highly efficient estimates of stochastic volatility models and extractions of latent volatility. We use our method to examine the dynamics of daily exchange rate volatility and find the evidence points strongly toward two-factor models with one highly persistent factor and one quickly mean-reverting factor. VOLATILITY IS A CENTRAL CONCEPT in finance, whether in asset pricing, portfolio choice, or risk management. Not long ago, theoretical models routinely assumed constant volatility ~e.g., Merton ~1969!, Black and Scholes ~1973!!. Today, however, we widely acknowledge that volatility is both time varying and predictable ~e.g., Andersen and Bollerslev ~1997!!, andstochastic volatility models are commonplace. Discrete- and continuous-time stochastic volatility models are extensively used in theoretical finance, empirical finance, and financial econometrics, both in academe and industry ~e.g., Hull and

this paper: ftp://ftp.cs.colorado.edu/pub/Time-Series/MyPapers/experts.ps.Z,

411 144 ecb d All rights reserved. Photocopying for educational and non-commercial purposes permitted provided that the source is acknowledged. ISSN 1607-1484Table of contents Abstract 5 1 Introduction: general aspects of the reference value for monetary growth in the context of the ECB’s monetary policy strategy 7 2 A first look at the data 10 2.1 The concept of M3 income velocity and its behaviour in the euro area 10 2.2 Data and aggregation issues 12

This paper is concerned with finite mixture models in which the populations from one observation to the next are selected according to an unobserved Markov process. A new, full Bayesian approach based on the method of Gibbs sampling is developed. Calculations are simplified by data augmentation, achieved by introducing a population index variable into the list of unknown parameters. It is shown that the latent variables, one for each observation, can be simulated from their joint distribution given the data and the remaining parameters. This result serves to accelerate the convergence of the Gibbs sample. Modal estimates are also computed by stochastic versions of the EM algorithm. These provide an alternative to a lull Bayesian approach and to existing methods of locating the maximum likelihood estimate. The ideas are applied in detail to Poisson data, mixtures of rnultivariate normal distributions, and autoregressivc time series.

Often, researchers wish to analyze nonlinear dynamic discrete-time stochastic models. This chapter provides a toolkit for solving such models easily, building on log-linearizing the necessary equations characterizing the equilibrium and solving for the recursive equilibrium law of motion with the method of undetermined coefficients. This chapter contains nothing substantially new. Instead, the chapter simplifies and unifies existing approaches to make them accessible for a wide audience, showing how to log-linearizing the nonlinear equations without the need for explicit di erentiation, how to use the method of undetermined coefficients for models with a vector of endogenous state variables, to provide a general solution by characterizing the solution with a matrix quadratic equation and solving it, and to provide frequency-domain techniques to calculate the second order properties of the model in its HP-filtered version without resorting to simulations. Since the method is an Euler-equation based approach rather than an approach based on solving a social planners problem, models with externalities or distortionary taxation do not pose additional problems. MATLAB programs to carry out the calculations in this chapter are made available. This chapter should be useful for researchers and Ph.D. students alike.

A number of panel unit root tests that allow for cross section dependence have been proposed in the literature that use orthogonalization type procedures to asymptotically eliminate the cross dependence of the series before standard panel unit root tests are applied to the transformed series. In this paper we propose a simple alternative where the standard ADF regressions are augmented with the cross section averages of lagged levels and first-differences of the individual series. New asymptotic results are obtained both for the individual cross sectionally augmented ADF (CADF) statistics, and their simple averages. It is shown that the individual CADF statistics are asymptotically similar and do not depend on the factor loadings. The limit distribution of the average CADF statistic is shown to exist and its critical values are tabulated. Small sample properties of the proposed test are investigated by Monte Carlo experiments. The proposed test is applied to a panel of 17 OECD real exchange rate series as well as to log real earnings of households in the PSID data.

This paper examines the importance of the regular patterns in the behavior of electricity prices, and its implications for the purposes of derivative pricing. We analyze the Nordic Power Exchange's spot, futures, and forward prices. We conclude that the seasonal systematic pattern throughout the year, in particular, is of crucial importance in explaining the shape of the futures/forward curve. Moreover, in the context of the one factor models analyzed in this paper, actual futures and forward prices are best explained by a sinusoidal function in order to capture the seasonal behavior directly implied by spot electricity prices. 1 Respectively, Dpto. Economa Financiera y Matemtica, Universidad de Valencia, Avda. de los Naranjos s/n, 46022-Valencia, Spain, and The Anderson School at UCLA, Box 951481, Los Angeles, CA 90095-1481, USA. We are grateful to Felipe Aguerrevere, M. Dolores Furi, Javier Gmez Biscarri, and Vicente Meneu for helpful comments. This paper was completed while...