38 research outputs found
Goodness-of-Fit Tests for Symmetric Stable Distributions -- Empirical Characteristic Function Approach
We consider goodness-of-fit tests of symmetric stable distributions based on
weighted integrals of the squared distance between the empirical characteristic
function of the standardized data and the characteristic function of the
standard symmetric stable distribution with the characteristic exponent
estimated from the data. We treat as an unknown parameter,
but for theoretical simplicity we also consider the case that is
fixed. For estimation of parameters and the standardization of data we use
maximum likelihood estimator (MLE) and an equivariant integrated squared error
estimator (EISE) which minimizes the weighted integral. We derive the
asymptotic covariance function of the characteristic function process with
parameters estimated by MLE and EISE. For the case of MLE, the eigenvalues of
the covariance function are numerically evaluated and asymptotic distribution
of the test statistic is obtained using complex integration. Simulation studies
show that the asymptotic distribution of the test statistics is very accurate.
We also present a formula of the asymptotic covariance function of the
characteristic function process with parameters estimated by an efficient
estimator for general distributions
Social networks and labour productivity in Europe: An empirical investigation
This paper uses firm-level data recorded in the AMADEUS database to
investigate the distribution of labour productivity in different European
countries. We find that the upper tail of the empirical productivity
distributions follows a decaying power-law, whose exponent is obtained
by a semi-parametric estimation technique recently developed by Clementi et al.
(2006). The emergence of "fat tails" in productivity distribution has already
been detected in Di Matteo et al. (2005) and explained by means of a model of
social network. Here we show that this model is tested on a broader sample of
countries having different patterns of social network structure. These
different social attitudes, measured using a social capital indicator, reflect
in the power-law exponent estimates, verifying in this way the existence of
linkages among firms' productivity performance and social network.Comment: LaTeX2e; 18 pages with 3 figures; Journal of Economic Interaction and
Coordination, in pres
Risk assessment of diesel exhaust and lung cancer: combining human and animal studies after adjustment for biases in epidemiological studies
T1 and extracellular volume mapping in the heart: estimation of error maps and the influence of noise on precision
Network meta-analysis of multiple outcome measures accounting for borrowing of information across outcomes
Models for Heavy-tailed Asset Returns
Many of the concepts in theoretical and empirical finance developed over the past decades – including the classical portfolio theory, the Black-Scholes-Merton option pricing model or the RiskMetrics variance-covariance approach to VaR – rest upon the assumption that asset returns follow a normal distribution. But this assumption is not justified by empirical data! Rather, the empirical observations exhibit excess kurtosis, more colloquially known as fat
tails or heavy tails. This chapter is intended as a guide to heavy-tailed models. We first describe the historically oldest heavy-tailed model – the stable laws. Next, we briefly characterize their recent lighter-tailed generalizations, the so-called truncated and tempered stable distributions. Then we study the class of generalized hyperbolic laws, which – like tempered stable distributions – can be classified somewhere between infinite variance stable laws and the Gaussian distribution. Finally, we provide numerical examples
Downside risk for European equity markets
This paper applies extreme value theory to measure downside risk for European equity markets. Two related measures, value at risk and the excess loss probability estimator provide a coherent approach to optimally protect investor wealth opportunities for low quantile and probability combinations. The fat-tailed characteristic of equity index returns is captured by explicitly modelling tail returns only. The paper finds the DAX100 is the most volatile index, and this generally becomes more pronounced as a move is made to lower quantile and probability estimates.