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International audience; A simple method is proposed to estimate stochastic volatility models with Markov-switching. It relies on a nested structure of filters (a Hamilton filter and several particle filters) to approximate unobserved regimes and state variables, respectively. Smooth resampling is used to keep the computational complexity constant over time and to implement a standard likelihood-based inference on parameters. A bootstrap and an adapted version of the filter are described and their performance are assessed using simulation experiments. The volatility of US and French markets is characterized over the last decade using a three-regime stochastic volatility model extended to include a leverage effect.

This paper estimates the Brazilian NAIRU (Nonaccelerating Inflation Rate of Unemployment) and investigates several empirical questions: the stability of coefficients of the Brazilian price Phillips curve, the behavior of the NAIRU along time, and error bands for the NAIRU. This article innovates, with respect to previous research work done for Brazil, because it estimates error bands for the NAIRU and adopts econometric models that, in our judgment, deal more adequately with the still recent instability of the Brazilian economy. We estimate two different state-space models: one with a time-varying NAIRU and another in which the NAIRU is changing over time according to a hidden Markov chain specification. The study presents some new evidence on several questions. It shows that while the slope of the Brazilian price Phillips curve is stable the NAIRU has not been stable. It concludes that there is a statistically significant relationship, with correct sign, between deviations of unemployment from the NAIRU and inflation. It also shows that, after the second semester of 1995, there is no significant evidence that the NAIRU has been different from the observed unemployment rate.Neste artigo estima-se a NAIRU (a taxa de desemprego que mantém estável a taxa de inflação) do Brasil e investiga-se diversas questões empíricas: a estabilidade dos coeficientes da Curva de Phillips (para preços) brasileira , o comportamento da NAIRU ao longo do tempo, e os intervalos de confiança para a NAIRU. O presente trabalho inova, em relação aos anteriores, ao adotar modelos econométricos que, acredita-se, são mais adequados para lidar com as instabilidades defrontadas pela economia brasileira em período recente. Estimam-se dois modelos diferentes em espaço-de-estados: um com uma NAIRU que muda ao longo do tempo e outro no qual a NAIRU muda, ao longo do tempo, de acordo com a especificação de uma cadeia de Markov oculta. Obtém-se novas evidências sobre diversas questões empíricas. Mostra-se que a inclinação da Curva de Phillips do Brasil é estável mas que a NAIRU brasileira vem se alterando ao longo do tempo. Conclui-se que existe uma relação estatisticamente significante, e com o sinal correto, entre os desvios da taxa de desemprego em relação à NAIRU e a taxa de inflação. No entanto, devido à imprecisão das suas estimativas, não há evidência significativa de que a NAIRU, depois do segundo trimestre de 1995, tenha sido diferente da taxa de desemprego observada.

The evolution of commodity markets calls for advanced models to capture and analyze complex properties of the markets. This dissertation focuses on a large sector: the US natural gas market, and consists of three papers where three stochastic models are proposed to investigate the distinct characteristics of the market. Model parameters are estimated by maximizing the likelihood functions with the aid of the Kalman filter and the Kim filter. The first paper explores the multi-factor structure and risk premiums implied from the natural gas spot and futures. The model features a two-short-term/one-long-term structure, time-varying risk premiums and a seasonal risk premium. We find that three factors and the seasonal risk premium are needed to accurately describe the term structure of the natural gas futures. The coefficients for the time-varying risk premiums are significant. We also reveal a negative correlation between the seasonal risk premium and the uncertainty of the natural gas total consumption. The second paper deals with the changing slope of the natural gas futures long-end curve. We develop a Markov regime-switching model with a regime-dependent drift term under the equivalent martingale measure. The model has two factors and three regimes to capture three basic cases of the changing slope. The estimation results show that the model is able to produce a downward/flat/upward slope in each regime and classifies the regime status generally consistent with the observation. Through detailed model comparisons, we find that models without the regimes or the two factors lead to poor results. The third paper considers the variance dynamics of the natural gas futures returns. We directly model and estimate the variance dynamics. The model incorporates two variance factors, the Samuelson effect and seasonality. The estimation is implemented using a dataset of synthesized variance swap rates on the futures across the term-structure dimension. The rates are computed by integrating prices of relevant futures options across the strike dimension. The results indicate the existence of the Samuelson effect, seasonal variance and a negative variance risk premium. In addition, the two-factor setup exhibits its advantage along the term-structure dimension.