Forecasting VaR using analytic higher moments for GARCH processes

It is widely accepted that some of the most accurate Value-at-Risk (VaR) estimates are based on an appropriately specified GARCH process. But when the forecast horizon is greater than the frequency of the GARCH model, such predictions have typically required time-consuming simulations of the aggregated returns distributions. This paper shows that fast, quasi-analytic GARCH VaR calculations can be based on new formulae for the first four moments of aggregated GARCH returns. Our extensive empirical study compares the Cornish–Fisher expansion with the Johnson SU distribution for fitting distributions to analytic moments of normal and Student t, symmetric and asymmetric (GJR) GARCH processes to returns data on different financial assets, for the purpose of deriving accurate GARCH VaR forecasts over multiple horizons and significance levels.

The finite-sample size of the BDS test for GARCH standardized residuals

This paper uses a multivariate response surface methodology to analyze the size distortion of the BDS test when applied to standardized residuals of rst-order GARCH processes. The results show that the asymptotic standard normal distribution is an unreliable approximation, even in large samples. On the other hand, a simple log-transformation of the squared standardized residuals seems to correct most of the size problems. Nonethe-less, the estimated response surfaces can provide not only a measure of the size distortion, but also more adequate critical values for the BDS test in small samples.

An Empirical Study of the Mixture of Time and Movements in Prices

This paper investigates the persistent pattern in the Helsinki Exchanges. The persistent pattern is analyzed using a time and a price approach. It is hypothesized that arrival times are related to movements in prices. Thus, the arrival times are defined as durations and formulated as an Autoregressive Conditional Duration (ACD) model as in Engle and Russell (1998). The prices are defined as price changes and formulated as a GARCH process including duration measures. The research question follows from market microstructure predictions about price intensities defined as time between price changes. The microstructure theory states that long transaction durations might be associated with both no news and bad news. Accordingly, short durations would be related to high volatility and long durations to low volatility. As a result, the spread will tend to be larger under intensive moments. The main findings of this study are 1) arrival times are positively autocorrelated and 2) long durations are associated with low volatility in the market.

Prediction in dynamic models with time-dependent conditional variances

This paper considers forecasting the conditional mean and variance from a single-equation dynamic model with autocorrelated disturbances following an ARMA process, and innovations with time-dependent conditional heteroskedasticity as represented by a linear GARCH process. Expressions for the minimum MSE predictor and the conditional MSE are presented. We also derive the formula for all the theoretical moments of the prediction error distribution from a general dynamic model with GARCH(1, 1) innovations. These results are then used in the construction of ex ante prediction confidence intervals by means of the Cornish-Fisher asymptotic expansion. An empirical example relating to the uncertainty of the expected depreciation of foreign exchange rates illustrates the usefulness of the results. © 1992.

Modelos estocásticos com heterocedasticidade: Uma abordagem Bayesiana para os retornos do Ibovespa

Current research compares the Bayesian estimates obtained for the parameters of processes of ARCH family with normal and Student's t distributions for the conditional distribution of the return series. A non-informative prior distribution was adopted and a reparameterization of models under analysis was taken into account to map parameters' space into real space. The procedure adopts a normal prior distribution for the transformed parameters. The posterior summaries were obtained by Monte Carlo Markov Chain (MCMC) simulation methods. The methodology was evaluated by a series of Bovespa Index returns and the predictive ordinate criterion was employed to select the best adjustment model to the data. Results show that, as a rule, the proposed Bayesian approach provides satisfactory estimates and that the GARCH process with Student's t distribution adjusted better to the data.

Distribuição de funções de variáveis aleatórias dependentes e R-Vines cópulas

Dissertação (mestrado)—Universidade de Brasília, Instituto de Ciências Exatas, Departamento de Estatística, 2015.

Testing for a unit root in a process exhibiting a structural break in the presence of GARCH errors

This paper considers the effect of GARCH errors on the tests proposed byPerron (1997) for a unit root in the presence of a structural break. We assessthe impact of degeneracy and integratedness of the conditional varianceindividually and find that, apart from in the limit, the testing procedure isinsensitive to the degree of degeneracy but does exhibit an increasingover-sizing as the process becomes more integrated. When we consider the GARCHspecifications that we are likely to encounter in empirical research, we findthat the Perron tests are reasonably robust to the presence of GARCH and donot suffer from severe over-or under-rejection of a correct null hypothesis.

Strong Consistency of the Conditional Least Squares Estimator for a Nonstationary Process. Example of the Garch Model

2000 Mathematics Subject Classification: Primary: 62M10, 62J02, 62F12, 62M05, 62P05, 62P10; secondary: 60G46, 60F15.

Technology, design and process innovation in the built environment

Buildings and infrastructure represent principal assets of any national economy as well as prime sources of environmental degradation. Making them more sustainable represents a key challenge for the construction, planning and design industries and governments at all levels; and the rapid urbanisation of the 21st century has turned this into a global challenge. This book embodies the results of a major research programme by members of the Australia Co-operative Research Centre for Construction Innovation and its global partners, presented for an international audience of construction researchers, senior professionals and advanced students. It covers four themes, applied to regeneration as well as to new build, and within the overall theme of Innovation: Sustainable Materials and Manufactures, focusing on building material products, their manufacture and assembly – and the reduction of their ecological ‘fingerprints’, the extension of their service lives, and their re-use and recyclability. It also explores the prospects for applying the principles of the assembly line. Virtual Design, Construction and Management, viewed as increasing sustainable development through automation, enhanced collaboration (such as virtual design teams), real time BL performance assessment during design, simulation of the construction process, life-cycle management of project information (zero information loss) risk minimisation, and increased potential for innovation and value adding. Integrating Design, Construction and Facility Management over the Project Life Cycle, by converging ICT, design science engineering and sustainability science. Integration across spatial scales, enabling building–infrastructure synergies (such as water and energy efficiency). Convergences between IT and design and operational processes are also viewed as a key platform increased sustainability.

Fracture process zone size and true fracture energy of concrete using acoustic emission

Acoustic emission (AE) energy, instead of amplitude, associated with each of the event is used to estimate the fracture process zone (FPZ) size. A steep increase in the cumulative AE energy of the events with respect to time is correlated with the formation of FPZ. Based on the AE energy released during these events and the locations of the events, FPZ size is obtained. The size-independent fracture energy is computed using the expressions given in the boundary effect model by least squares method since over-determined system of equations are obtained when data from several specimens are used. Instead of least squares method a different method is suggested in which the transition ligament length, measured from the plot of histograms of AE events plotted over the un-cracked ligament, is used directly to obtain size-independent fracture energy. The fracture energy thus calculated seems to be size-independent.

In Situ Scanning Tunneling Microscopy on the Dynamic Process of the Replacement of Coronene on Au (111) by 6-Mercapto-1-Hexanol

The replacement of coronene monolayer on Au (111) by 6-mercapto-1-hexanol (MHO) was studied by in situ scanning tunneling microscopy (STM) in solutions. It was found that the rate of replacement depends strongly on the concentration of MHO. The replacement finished within a second at a higher concentration of MHO. At a lower concentration, the slow replacement could be followed by in situ STM. The replacement occurred initially near the elbow position of reconstructed Au (111) with the formation of pits in a single or several missing molecules. With the proceeding of replacement, these small pits expanded, and the surrounding coronene molecules were gradually substituted by MHO, which developed into ordered domains within a spatial confined environment. Meanwhile, the reconstruction of Au (111) was lifted. The replacement expanded fast along the reconstruction lines in the domain. For the fast replacement, a (root 3 x root 3) R30 degrees adlattice was observed, while a c(4 x 2) superlattice was observed for the slow replacement.

The Shape of the Risk Premium: Evidence from a Semiparametric Garch Model.

We examine the relationship between the risk premium on the S&P 500 index return and its conditional variance. We use the SMEGARCH - Semiparametric-Mean EGARCH - model in which the conditional variance process is EGARCH while the conditional mean is an arbitrary function of the conditional variance. For monthly S&P 500 excess returns, the relationship between the two moments that we uncover is nonlinear and nonmonotonic. Moreover, we find considerable persistence in the conditional variance as well as a leverage effect, as documented by others. Moreover, the shape of these relationships seems to be relatively stable over time.

American option valuation: implied calibration of GARCH pricing models

This study analyzes the issue of American option valuation when the underlying exhibits a GARCH-type volatility process. We propose the usage of Rubinstein's Edgeworth binomial tree (EBT) in contrast to simulation-based methods being considered in previous studies. The EBT-based valuation approach makes an implied calibration of the pricing model feasible. By empirically analyzing the pricing performance of American index and equity options, we illustrate the superiority of the proposed approach.