Are output growth‐rate distributions fat‐tailed? some evidence from OECD countries

This work explores some distributional properties of aggregate output growth‐rate time series. We show that, in the majority of OECD countries, output growth‐rate distributions are well approximated by symmetric exponential power densities with tails much fatter than those of a Gaussian (but with finite moments of any order). Fat tails robustly emerge in output growth rates independently of: (i) the way we measure aggregate output; (ii) the family of densities employed in the estimation; (iii) the length of time lags used to compute growth rates. We also show that fat tails still characterize output growth‐rate distributions even after one washes away outliers, autocorrelation and heteroscedasticity. Copyright © 2008 John Wiley & Sons, Ltd.     

Realising the future: forecasting with high‐frequency‐based volatility (HEAVY) models

This paper studies in some detail a class of high‐frequency‐based volatility (HEAVY) models. These models are direct models of daily asset return volatility based on realised measures constructed from high‐frequency data. Our analysis identifies that the models have momentum and mean reversion effects, and that they adjust quickly to structural breaks in the level of the volatility process. We study how to estimate the models and how they perform through the credit crunch, comparing their fit to more traditional GARCH models. We analyse a model‐based bootstrap which allows us to estimate the entire predictive distribution of returns. We also provide an analysis of missing data in the context of these models. Copyright © 2010 John Wiley & Sons, Ltd.     

Stochastic volatility models with ARMA innovations: An application to G7 inflation forecasts

We introduce a new class of stochastic volatility models with autoregressive moving average (ARMA) innovations. The conditional mean process has a flexible form that can accommodate both a state space representation and a conventional dynamic regression. The ARMA component introduces serial dependence, which results in standard Kalman filter techniques not being directly applicable. To overcome this hurdle, we develop an efficient posterior simulator that builds on recently developed precision-based algorithms. We assess the usefulness of these new models in an inflation forecasting exercise across all G7 economies. We find that the new models generally provide competitive point and density forecasts compared to standard benchmarks, and are especially useful for Canada, France, Italy, and the U.S.     

Stochastic volatility with leverage: Fast and efficient likelihood inference

This paper is concerned with the Bayesian analysis of stochastic volatility (SV) models with leverage. Specifically, the paper shows how the often used Kim et al. [1998. Stochastic volatility: likelihood inference and comparison with ARCH models. Review of Economic Studies 65, 361–393] method that was developed for SV models without leverage can be extended to models with leverage. The approach relies on the novel idea of approximating the joint distribution of the outcome and volatility innovations by a suitably constructed ten-component mixture of bivariate normal distributions. The resulting posterior distribution is summarized by MCMC methods and the small approximation error in working with the mixture approximation is corrected by a reweighting procedure. The overall procedure is fast and highly efficient. We illustrate the ideas on daily returns of the Tokyo Stock Price Index. Finally, extensions of the method are described for superposition models (where the log-volatility is made up of a linear combination of heterogenous and independent autoregressions) and heavy-tailed error distributions (student and log-normal).     

Common correlated effect cross‐sectional dependence corrections for nonlinear conditional mean panel models

This paper provides an approach to estimation and inference for nonlinear conditional mean panel data models, in the presence of cross‐sectional dependence. We modify Pesaran's (Econometrica, 2006, 74(4), 967–1012) common correlated effects correction to filter out the interactive unobserved multifactor structure. The estimation can be carried out using nonlinear least squares, by augmenting the set of explanatory variables with cross‐sectional averages of both linear and nonlinear terms. We propose pooled and mean group estimators, derive their asymptotic distributions, and show the consistency and asymptotic normality of the coefficients of the model. The features of the proposed estimators are investigated through extensive Monte Carlo experiments. We also present two empirical exercises. The first explores the nonlinear relationship between banks' capital ratios and riskiness. The second estimates the nonlinear effect of national savings on national investment in OECD countries depending on countries' openness.     

Forecasting realized volatility: a Bayesian model‐averaging approach

How to measure and model volatility is an important issue in finance. Recent research uses high‐frequency intraday data to construct ex post measures of daily volatility. This paper uses a Bayesian model‐averaging approach to forecast realized volatility. Candidate models include autoregressive and heterogeneous autoregressive specifications based on the logarithm of realized volatility, realized power variation, realized bipower variation, a jump and an asymmetric term. Applied to equity and exchange rate volatility over several forecast horizons, Bayesian model averaging provides very competitive density forecasts and modest improvements in point forecasts compared to benchmark models. We discuss the reasons for this, including the importance of using realized power variation as a predictor. Bayesian model averaging provides further improvements to density forecasts when we move away from linear models and average over specifications that allow for GARCH effects in the innovations to log‐volatility. Copyright © 2009 John Wiley & Sons, Ltd.     

Estimation methods for stochastic volatility models: a survey

Abstract.  Although stochastic volatility (SV) models have an intuitive appeal, their empirical application has been limited mainly due to difficulties involved in their estimation. The main problem is that the likelihood function is hard to evaluate. However, recently, several new estimation methods have been introduced and the literature on SV models has grown substantially. In this article, we review this literature. We describe the main estimators of the parameters and the underlying volatilities focusing on their advantages and limitations both from the theoretical and empirical point of view. We complete the survey with an application of the most important procedures to the S&P 500 stock price index.     

Calibration of stochastic volatility models: A Tikhonov regularization approach

We aim to calibrate stochastic volatility models from option prices. We develop a Tikhonov regularization approach with an efficient numerical algorithm to recover the risk neutral drift term of the volatility (or variance) process. In contrast to most existing literature, we do not assume that the drift term has any special structure. As such, our algorithm applies to calibration of general stochastic volatility models. An extensive numerical analysis is presented to demonstrate the efficiency of our approach. Interestingly, our empirical study reveals that the risk neutral variance processes recovered from market prices of options on S&P 500 index and EUR/USD exchange rate are indeed linearly mean-reverting.     

Econometric estimation in long-range dependent volatility models: Theory and practice

It is commonly accepted that some financial data may exhibit long-range dependence, while other financial data exhibit intermediate-range dependence or short-range dependence. These behaviours may be fitted to a continuous-time fractional stochastic model. The estimation procedure proposed in this paper is based on a continuous-time version of the Gauss–Whittle objective function to find the parameter estimates that minimize the discrepancy between the spectral density and the data periodogram. As a special case, the proposed estimation procedure is applied to a class of fractional stochastic volatility models to estimate the drift, standard deviation and memory parameters of the volatility process under consideration. As an application, the volatility of the Dow Jones, S&P 500, CAC 40, DAX 30, FTSE 100 and NIKKEI 225 is estimated.     

Multi‐state Stochastic Processes: A Statistical Flowgraph Perspective

Two‐state models (working/failed or alive/dead) are widely used in reliability and survival analysis. In contrast, multi‐state stochastic processes provide a richer framework for modeling and analyzing the progression of a process from an initial to a terminal state, allowing incorporation of more details of the process mechanism. We review multi‐state models, focusing on time‐homogeneous semi‐Markov processes (SMPs), and then describe the statistical flowgraph framework, which comprises analysis methods and algorithms for computing quantities of interest such as the distribution of first passage times to a terminal state. These algorithms algebraically combine integral transforms of the waiting time distributions in each state and invert them to get the required results. The estimated transforms may be based on parametric distributions or on empirical distributions of sample transition data, which may be censored. The methods are illustrated with several applications.     

Realized extreme quantile: A joint model for conditional quantiles and measures of volatility with EVT refinements

We propose a new framework exploiting realized measures of volatility to estimate and forecast extreme quantiles. Our realized extreme quantile (REQ) combines quantile regression with extreme value theory and uses a measurement equation that relates the realized measure to the latent conditional quantile. Model estimation is performed by quasi maximum likelihood, and a simulation experiment validates this estimator in finite samples. An extensive empirical analysis shows that high‐frequency measures are particularly informative of the dynamic quantiles. Finally, an out‐of‐sample forecast analysis of quantile‐based risk measures confirms the merit of the REQ.     

Simulating non‐normal distributions with specified L‐moments and L‐correlations

This paper derives a procedure for simulating continuous non‐normal distributions with specified L‐moments and L‐correlations in the context of power method polynomials of order three. It is demonstrated that the proposed procedure has computational advantages over the traditional product‐moment procedure in terms of solving for intermediate correlations. Simulation results also demonstrate that the proposed L‐moment‐based procedure is an attractive alternative to the traditional procedure when distributions with more severe departures from normality are considered. Specifically, estimates of L‐skew and L‐kurtosis are superior to the conventional estimates of skew and kurtosis in terms of both relative bias and relative standard error. Further, the L‐correlation also demonstrated to be less biased and more stable than the Pearson correlation. It is also shown how the proposed L‐moment‐based procedure can be extended to the larger class of power method distributions associated with polynomials of order five.     

US‐style contingent fees and UK‐style conditional fees: agency problems and the supply of legal services

Under contingent fees, the attorney gets a share of the judgment; under conditional fees, the lawyer gets an upscale premium if the case is won which is, however, unrelated to the adjudicated amount. We compare conditional and contingent fees in a principal–agent framework where the lawyer chooses unobservable effort after she has observed the amount at stake. Contingent fees provide better incentives than conditional fees independently of whether upfront payments are restricted to be non‐negative or not. Under contingent fees, the attorney uses her information about what is at stake more efficiently. Copyright © 2006 John Wiley & Sons, Ltd.     

Mixed‐frequency models with moving‐average components

Temporal aggregation in general introduces a moving‐average (MA) component in the aggregated model. A similar feature emerges when not all but only a few variables are aggregated, which generates a mixed‐frequency (MF) model. The MA component is generally neglected, likely to preserve the possibility of ordinary least squares estimation, but the consequences have never been properly studied in the MF context. In this paper we show, analytically, in Monte Carlo simulations and in a forecasting application on US macroeconomic variables, the relevance of considering the MA component in MF mixed‐data sampling (MIDAS) and unrestricted MIDAS models (MIDAS–autoregressive moving average (ARMA) and UMIDAS‐ARMA). Specifically, the simulation results indicate that the short‐term forecasting performance of MIDAS‐ARMA and UMIDAS‐ARMA are better than that of, respectively, MIDAS and UMIDAS. The empirical applications on nowcasting US gross domestic product (GDP) growth, investment growth, and GDP deflator inflation confirm this ranking. Moreover, in both simulation and empirical results, MIDAS‐ARMA is better than UMIDAS‐ARMA.     

An alternative approach to estimating demand: Neural network regression with conditional volatility for high frequency air passenger arrivals

In this paper we provide an alternative approach to analyze the demand for international tourism in the Balearic Islands, Spain, by using a neural network model that incorporates time-varying conditional volatility. We consider daily air passenger arrivals to Palma de Mallorca, Ibiza and Mahon, which are located in the islands of Mallorca, Ibiza and Menorca, respectively, as a proxy for international tourism demand for the Balearic Islands. Spain is a world leader in terms of total international tourist arrivals and receipts, and Mallorca is one of the most popular destinations in Spain. For tourism management and marketing, it is essential to forecast high frequency international tourist demand accurately. As it is important to provide sensible international tourism demand forecast intervals, it is also necessary to model their variances accurately. Moreover, time-varying variances provide useful information regarding the risks associated with variations in international tourist arrivals.     

A note on mean testing for high dimensional multivariate data under non‐normality

A test statistic is considered for testing a hypothesis for the mean vector for multivariate data, when the dimension of the vector, p, may exceed the number of vectors, n, and the underlying distribution need not necessarily be normal. With n,p→∞, and under mild assumptions, but without assuming any relationship between n and p, the statistic is shown to asymptotically follow a chi‐square distribution. A by product of the paper is the approximate distribution of a quadratic form, based on the reformulation of the well‐known Box's approximation, under high‐dimensional set up. Using a classical limit theorem, the approximation is further extended to an asymptotic normal limit under the same high dimensional set up. The simulation results, generated under different parameter settings, are used to show the accuracy of the approximation for moderate n and large p.     

Bayesian model comparison for time‐varying parameter VARs with stochastic volatility

We develop importance sampling methods for computing two popular Bayesian model comparison criteria, namely, the marginal likelihood and the deviance information criterion (DIC) for time‐varying parameter vector autoregressions (TVP‐VARs), where both the regression coefficients and volatilities are drifting over time. The proposed estimators are based on the integrated likelihood, which are substantially more reliable than alternatives. Using US data, we find overwhelming support for the TVP‐VAR with stochastic volatility compared to a conventional constant coefficients VAR with homoskedastic innovations. Most of the gains, however, appear to have come from allowing for stochastic volatility rather than time variation in the VAR coefficients or contemporaneous relationships. Indeed, according to both criteria, a constant coefficients VAR with stochastic volatility outperforms the more general model with time‐varying parameters.     

Stochastic models for risky choices: A comparison of different axiomatizations

For a long time researchers have recognized the need for applying stochastic models for analyzing data generated from agents’ choice under risk. This paper compares and discusses recent axiomatizations of stochastic models for risky choice given by Blavatskyy (2008) and Dagsvik (2008). We show that some of Blavatskyy’s axioms are equivalent to some of Dagsvik’s axioms. We also propose new axioms and derive their implications. Specifically, we show that some of the results of Dagsvik (2008) can be derived under weaker axioms than those he proposed originally.     

Crack spread hedging: accounting for time‐varying volatility spillovers in the energy futures markets

Crude oil, heating oil, and unleaded gasoline futures contracts are simultaneously analysed for their effectiveness in reducing price volatility for an energy trader. A conceptual model is developed for a trader hedging the ‘crack spread’. Various hedge ratio estimation techniques are compared to a Multivariate GARCH model that directly incorporates the time to maturity effect often found in futures markets. Modelling of the time‐variation in hedge ratios via the Multivariate GARCH methodology, and thus taking into account volatility spillovers between markets is shown to result in significant reductions in uncertainty even while accounting for trading costs. Copyright © 2002 John Wiley & Sons, Ltd.