Time Series: Theory and Methods

Brockwell, Peter J.; Davis, Richard A.

doi:10.1007/978-1-4419-0320-4

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“…If the parameter assumes values close to 1 the decline of the ACF is much slower. For a detailed discussion on autoregressive processes we refer the reader to the manuals of Hamilton (1994) and of Brockwell and Davis (1991).…”

Section: Definition: 1 Ar(1) the Discrete Time Stochastic Process (mentioning

confidence: 99%

Convolution Based Unit Root Processes: a Simulation Approach

Gobbi¹

2016

IJSP

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Section: Definition: 1 Ar(1) the Discrete Time Stochastic Process (mentioning

confidence: 99%

Convolution Based Unit Root Processes: a Simulation Approach

Gobbi¹

2016

IJSP

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“…On the contrary, Box and Jenkins'models are based on the assumption that di¤erenced series are stationary, which incorporates more rigidity. In this 35 Some examples of ARIMA models in State Space Form can be found in Harvey (1989), Brockwell and Davis (1991) and Hamilton (1994).…”

Section: Structural Models Versus Arimamentioning

confidence: 99%

“…context, with the structural approach forecasting is relatively straightforward 38 and missing observations are easier to treat 39 . Brockwell and Davis (1991) consider that state-space representation and recursive equations which characterize the Kalman Filter are ideal to analyse series with missing observations. 40 .…”

Section: Structural Models Versus Arimamentioning

confidence: 99%

Structural Time Series Models and the Kalman Filter: A Concise Review

Jalles

2009

SSRN Journal

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The continued increase in availability of economic data in recent years and, more importantly, the possibility to construct larger frequency time series, have fostered the use (and development) of statistical and econometric techniques to treat them more accurately. This paper presents an exposition of structural time series models by which a time series can be decomposed as the sum of a trend, seasonal and irregular components. In addition to a detailled analysis of univariate speci…cations we also address the SUTSE multivariate case and the issue of cointegration. Finally, the recursive estimation and smoothing by means of the Kalman …lter algorithm is described taking into account its di¤erent stages, from initialisation to parameter's estimation.Keywords: SUTSE, cointegration, ARIMA, smoothing, likelihood JEL Classi…cation Numbers: C10, C22, C32A special thanks goes to my Supervisor, Andrew Harvey for his guidance and support over the last year. The usual disclaimer applies, that is, all errors are mine alone.

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“…The second methodology to estimate this coefficient is the Geweke-Porter-Hudak's (henceforth GPH, 1983) method (see Brockwell and Davis (1991) for a formal presentation, or Corsi (2009) for a discussion). The GPH estimate is based on the regression of the logarithm of the periodogram estimate of the spectral density against ln(ω) over a range of frequencies ω with:…”

Section: Adf Test D(gp H)d From Regressionmentioning

confidence: 99%

On the realized volatility of the ECX CO2 emissions 2008 futures contract: distribution, dynamics and forecasting

Chevallier

Sévi

2009

Ann Finance

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Abstract:The recent implementation of the EU Emissions Trading Scheme (EU ETS) in January 2005 created new financial risks for emitting firms. To deal with these risks, options are traded since October 2006. Because the EU ETS is a new market, the relevant underlying model for option pricing is still a controversial issue. This article improves our understanding of this issue by characterizing the conditional and unconditional distributions of the realized volatility for the 2008 futures contract in the European Climate Exchange (ECX), which is valid during Phase II (2008)(2009)(2010)(2011)(2012) of the EU ETS. The realized volatility measures from naive, kernel-based and subsampling estimators are used to obtain inferences about the distributional and dynamic properties of the ECX emissions futures volatility. The distribution of the daily realized volatility in logarithmic form is shown to be close to normal. The mixture-of-distributions hypothesis is strongly rejected, as the returns standardized using daily measures of volatility clearly departs from normality. A simplified HAR-RV model (Corsi, 2009) with only a weekly component, which reproduces long memory properties of the series, is then used to model the volatility dynamics. Finally, the predictive accuracy of the HAR-RV model is tested against GARCH specifications using one-step-ahead forecasts, which confirms the HAR-RV superior ability. Our conclusions indicate that (i) the standard Brownian motion is not an adequate tool for option pricing in the EU ETS, and (ii) a jump component should be included in the stochastic process to price options, thus providing more efficient tools for risk-management activities.JEL Classification: C5, G1, Q4.

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Time Series: Theory and Methods

Abstract: Library of Congress Cataloging-in-Publication Data Brockwell, Peter J.Time series: theory and methods / Peter J. Brockwell, Richard A. Davis.p. cm. -(Springer series in statistics) "Second edition"-Pref. Inc1udes bibliographical references and index.

Cited by 3,927 publications

References 0 publications

Convolution Based Unit Root Processes: a Simulation Approach

Convolution Based Unit Root Processes: a Simulation Approach

Structural Time Series Models and the Kalman Filter: A Concise Review

On the realized volatility of the ECX CO2 emissions 2008 futures contract: distribution, dynamics and forecasting

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