Volatility persistence is a stylized statistical property of financial time-series data such as exchange rates and stock returns. The purpose of this letter is to investigate the relationship between volatility persistence and predictability of squared returns.

This paper points out that the ARMA models followed by GARCH squares are volatile and gives explicit and general forms of their dependent and volatile innovations. The volatility function of the ARMA innovations is shown to be the square of the corresponding GARCH volatility function. The prediction of GARCH squares is facilitated by the ARMA structure and predictive intervals are considered. Further, the developments suggest families of volatile ARMA processes.

The s-period ahead Value-at-Risk (VaR) for a portfolio of dimension n is considered and its Bayesian analysis is discussed. The VaR assessment can be based either on the n-variate predictive distribution of future returns on individual assets, or on the univariate Bayesian model for the portfolio value (or the return on portfolio). In both cases Bayesian VaR takes into account parameter uncertainty and non-linear relationship between ordinary and logarithmic returns. In the case of a large portfolio, the applicability of the n-variate approach to Bayesian VaR depends on the form of the statistical model for asset prices. We use the n-variate type I MSF-SBEKK(1,1) volatility model proposed specially to cope with large n. We compare empirical results obtained using this multivariate approach and the much simpler univariate approach based on modelling volatility of the value of a given portfolio.

The aim of the study is to formally compare the explanatory power of Copula-GARCH and MGARCH models. The models are estimated for logarithmic daily rates of return of two exchange rates: EUR/PLN, USD/PLN and stock market indices: SP500, BUX. The analysis is performed within the Bayesian framework. The posterior model probabilities point to AR(1)-tSBEKK(1,1) for the exchange rates and VAR(1)-tCopula-GARCH(1,1) for the stock market indices, as the superior specifications. If the marginal sampling distributions are different in terms of tail thickness, the Copula-GARCH models have higher explanatory power than the MGARCH models.

In the paper we present robust estimation methods based on bounded innovation propagation filters and quantile regression, applied to measure Value at Risk. To illustrate advantage connected with the robust methods, we compare VaR forecasts of several group of instruments in the period of high uncertainty on the financial markets with the ones modelled using traditional quasi-likelihood estimation. For comparative purpose we use three groups of tests i.e. based on Bernoulli trial models, on decision making aspect, and on the expected shortfall.

In the article the author analyses the impact of the Financial Crisis, especially the Greek fiscal one, on the sCDS prices in Europe. The aim of the article is to assess the ability of the sCDS premia to price the risk of countries before and during the Greek crisis. The author analyses sCDS premia of maturity 10 years together with the so called bond-spreads, i.e. the spreadsbetween the countries’ bond indexes and the risk free rate of the region (in our case it was the yield of German bonds of corresponding maturity – 10 years).The idea was to check whether there occurred any discrepancies in the risk valuation via the two measures, as a consequence of the Greek crisis. The data is taken daily and covers the period of 2008‒2012. Based upon the results obtained in the research we conclude that the Greek crisis indeed influenced the relationships between the two measures of risk, however the degree of the influence was different in different countries. The relationships between the two measures of risk were totally broken only in the case of Greece, while in the other countries the relationships either were not distorted or had been broken already at the beginning of the financial crisis (2008/2009). The Greek problems were indeed reflected in volatilities of all analysed instruments; however triggering the credit event affected only Greek bonds dynamics.

We discuss the empirical importance of long term cyclical effects in the volatility of financial returns. Following Amado and Teräsvirta (2009), ČiŽek and Spokoiny (2009) and others, we consider a general conditionally heteroscedastic process with stationarity property distorted by a deterministic function that governs the possible time variability of the unconditional variance. The function proposed in this paper can be interpreted as a finite Fourier approximation of an Almost Periodic (AP) function as defined by Corduneanu (1989). The resulting model has a particular form of a GARCH process with time varying parameters, intensively discussed in the recent literature.

In the empirical analyses we apply a generalisation of the Bayesian AR(1)-GARCH model for daily returns of S&P500, covering the period of sixty years of US postwar economy, including the recently observed global financial crisis. The results of a formal Bayesian model comparison clearly indicate the existence of significant long term cyclical patterns in volatility with a strongly supported periodic component corresponding to a 14 year cycle. Our main results are invariant with respect to the changes of the conditional distribution from Normal to Student-tand to the changes of the volatility equation from regular GARCH to the Asymmetric GARCH.

The aim of this paper is to examine the empirical usefulness of two new MSF – Scalar BEKK(1,1) models of n-variate volatility. These models formally belong to the MSV class, but in fact are some hybrids of the simplest MGARCH and MSV specifications. Such hybrid structures have been proposed as feasible (yet non-trivial) tools for analyzing highly dimensional financial data (large n). This research shows Bayesian model comparison for two data sets with n = 2, since in bivariate cases we can obtain Bayes factors against many (even unparsimonious) MGARCH and MSV specifications. Also, for bivariate data, approximate posterior results (based on preliminary estimates of nuisance matrix parameters) are compared to the exact ones in both MSF-SBEKK models. Finally, approximate results are obtained for a large set of returns on equities (n = 34).

This paper develops a new model of market abuse detection in real time. Market abuse is detected, as Minenna (2003) proposed, on the basis of prediction intervals. The model structure is based on the discrete-time, extended market model introduced by Monteiro, Zaman, Leitterstorf (2007) to analyze the market cleanliness. Parameters of the expected return equation are assumed, however, to be time-varying and estimated under the state-space framework using the extended Kalman filter postulated by Chou, Engle, Kane (1992) to capture the GARCH effect in returns. QML estimation is performed on intraday data; its utilization is proposed as an alternative to the continuous time modeling by Minenna (2003). This framework is generalized to the bivariate case which enables the analysis of daily open/close data. The paper also extends procedures of the statistical verification of the estimated state-space model to include the uncertainty arising from time-invariant parameters.

In empirical research on financial market microstructure and in testing some predictions from the market microstructure literature, the behavior of some characteristics of trading process can be very important and useful. Among all characteristics associated with tick-by-tick data, the trading time and the price seem the most important. The very first joint model for prices and durations, the so-called UHF-GARCH, has been introduced by Engle (2000). The main aim of this paper is to propose a simple, novel extension of Engle’s specification based on trade-to-trade data and to develop and apply the Bayesian approach to estimation of this model. The intraday dynamics of the return volatility is modelled by an EGARCH-type specification adapted to irregularly time-spaced data. In the analysis of price durations, the Box-Cox ACD model with the generalized gamma distribution for the error term is considered. To the best of our knowledge, the UHF-GARCH model with such a combination of the EGARCH and the Box-Cox ACD structures has not been studied in the literature so far. To estimate the model, the Bayesian approach is adopted. Finally, the methodology developed in the paper is employed to analyze transaction data from the Polish Stock Market.

The purpose of this paper is to model daily returns of the WIG20 index. The idea is to consider a model that explicitly takes changes in the amplitude of the clusters of volatility into account. This variation is modelled by a positive-valued deterministic component. A novelty in specification of the model is that the deterministic component is specified before estimating the multiplicative conditional variance component. The resulting model is subjected to misspecification tests and its forecasting performance is compared with that of commonly applied models of conditional heteroskedasticity.