Continuous time volatility modelling: COGARCH versus Ornstein-Uhlenbeck models

We compare the probabilistic properties of the non-Gaussian Ornstein-Uhlenbeck based stochastic volatility model of Barndorff-Nielsen and Shephard (2001) with those of the COGARCH process. The latter is a continuous time GARCH process introduced by the authors (2004). Many features are shown to be shared by both processes, but differences are pointed out as well. Furthermore, it is shown that the COGARCH process has Pareto like tails under weak regularity conditions

Financial Time Series Analysis of SV Model by Hybrid Monte Carlo

We apply the hybrid Monte Carlo (HMC) algorithm to the financial time sires analysis of the stochastic volatility (SV) model for the first time. The HMC algorithm is used for the Markov chain Monte Carlo (MCMC) update of volatility variables of the SV model in the Bayesian inference. We compute parameters of the SV model from the artificial financial data and compare the results from the HMC algorithm with those from the Metropolis algorithm. We find that the HMC decorrelates the volatility variables faster than the Metropolis algorithm. We also make an empirical analysis based on the Yen/Dollar exchange rates.Comment: 8 pages, 3 figures, to be published in LNC

Monetary Policy Rules and Directions of Causality: a Test for the Euro Area

Using a VAR model in first differences with quarterly data for the euro zone, the study aims to ascertain whether decisions on monetary policy can be interpreted in terms of a “monetary policy rule” with specific reference to the so-called nominal GDP targeting rule (Hall and Mankiw, 1994; McCallum, 1988; Woodford, 2012). The results obtained indicate a causal relation proceeding from deviation between the growth rates of nominal gross domestic product (GDP) and target GDP to variation in the three-month market interest rate. The same analyses do not, however, appear to confirm the existence of a significant inverse causal relation from variation in the market interest rate to deviation between the nominal and target GDP growth rates. Similar results were obtained on replacing the market interest rate with the European Central Bank refinancing interest rate. This confirmation of only one of the two directions of causality does not support an interpretation of monetary policy based on the nominal GDP targeting rule and gives rise to doubt in more general terms as to the applicability of the Taylor rule and all the conventional rules of monetary policy to the case in question. The results appear instead to be more in line with other possible approaches, such as those based on post Keynesian analyses of monetary theory and policy and more specifically the so-called solvency rule (Brancaccio and Fontana, 2013, 2015). These lines of research challenge the simplistic argument that the scope of monetary policy consists in the stabilization of inflation, real GDP, or nominal income around a “natural equilibrium” level. Rather, they suggest that central banks actually follow a more complex purpose, which is the political regulation of the financial system with particular reference to the relations between creditors and debtors and the related solvency of economic units

An Adaptive Markov Chain Monte Carlo Method for GARCH Model

We propose a method to construct a proposal density for the Metropolis-Hastings algorithm in Markov Chain Monte Carlo (MCMC) simulations of the GARCH model. The proposal density is constructed adaptively by using the data sampled by the MCMC metho d itself. It turns out that autocorrelations between the data generated with our adaptive proposal density are greatly reduced. Thus it is concluded that the adaptive construction method is very efficient and works well for the MCMC simulations of the GARCH model.Comment: 11 pages, 6 figure

The effect of asymmetries on stock index return value-at-risk estimates

It is widely accepted that equity return volatility increases more following negative shocks rather than positive shocks. However, much of value-at-risk (VaR) analysis relies on the assumption that returns are normally distributed (a symmetric distribution). This article considers the effect of asymmetries on the evaluation and accuracy of VaR by comparing estimates based on various models

The non-random walk of stock prices: The long-term correlation between signs and sizes

We investigate the random walk of prices by developing a simple model relating the properties of the signs and absolute values of individual price changes to the diffusion rate (volatility) of prices at longer time scales. We show that this benchmark model is unable to reproduce the diffusion properties of real prices. Specifically, we find that for one hour intervals this model consistently over-predicts the volatility of real price series by about 70%, and that this effect becomes stronger as the length of the intervals increases. By selectively shuffling some components of the data while preserving others we are able to show that this discrepancy is caused by a subtle but long-range non-contemporaneous correlation between the signs and sizes of individual returns. We conjecture that this is related to the long-memory of transaction signs and the need to enforce market efficiency.Comment: 9 pages, 5 figures, StatPhys2

A study of orientational ordering in a fluid of dipolar Gay-Berne molecules using density-functional theory

Published versio

Cointegration analysis with state space models

Abstract: This paper presents and exemplifies results developed for cointegration analysis with state space models by Bauer and Wagner in a series of papers. Unit root processes, cointegration and polynomial cointegration are defined. Based upon these definitions the major part of the paper discusses how state space models, which are equivalent to VARMA models, can be fruitfully employed for cointegration analysis. By means of detailing the cases most relevant for empirical applications, the I(1), MFI(1) and I(2) cases, a canonical representation is developed and thereafter some available statistical results are briefly mentioned.