300 research outputs found
High-frequency Estimation of the L\'evy-driven Graph Ornstein-Uhlenbeck process
We consider the Graph Ornstein-Uhlenbeck (GrOU) process observed on a
non-uniform discrete time grid and introduce discretised maximum likelihood
estimators with parameters specific to the whole graph or specific to each
component, or node. Under a high-frequency sampling scheme, we study the
asymptotic behaviour of those estimators as the mesh size of the observation
grid goes to zero. We prove two stable central limit theorems to the same
distribution as in the continuously-observed case under both finite and
infinite jump activity for the L\'evy driving noise. When a graph structure is
not explicitly available, the stable convergence allows to consider
purpose-specific sparse inference procedures, i.e. pruning, on the edges
themselves in parallel to the GrOU inference and preserve its asymptotic
properties. We apply the new estimators to wind capacity factor measurements,
i.e. the ratio between the wind power produced locally compared to its rated
peak power, across fifty locations in Northern Spain and Portugal. We show the
superiority of those estimators compared to the standard least squares
estimator through a simulation study extending known univariate results across
graph configurations, noise types and amplitudes
Nonparametric estimation of the jump component in financial time series
In this thesis, we analyze nonparametric estimation of Lévy-based models using wavelets methods. As the considered class is restricted to pure-jump Lévy processes, it is sufficient to estimate their Lévy densities. For implementing a wavelet density estimator, it is necessary to setup a preliminary histogram estimator. Simulation studies show that there is an improvement of the wavelet estimator by invoking an optimally selected histogram. The wavelet estimator is based on block-thresholding of empirical coefficients. We conclude with two empirical applications which show that there is a very high arrival rate of small jumps in financial data sets
Parameter estimation and model testing for Markov processes via conditional characteristic functions
Markov processes are used in a wide range of disciplines, including finance.
The transition densities of these processes are often unknown. However, the
conditional characteristic functions are more likely to be available,
especially for L\'{e}vy-driven processes. We propose an empirical likelihood
approach, for both parameter estimation and model specification testing, based
on the conditional characteristic function for processes with either continuous
or discontinuous sample paths. Theoretical properties of the empirical
likelihood estimator for parameters and a smoothed empirical likelihood ratio
test for a parametric specification of the process are provided. Simulations
and empirical case studies are carried out to confirm the effectiveness of the
proposed estimator and test.Comment: Published in at http://dx.doi.org/10.3150/11-BEJ400 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Jump-diffusion model of exchange rate dynamics : estimation via indirect inference
This paper investigates asymmetric effects of monetary policy over the business cycle. A two-state Markov Switching Model is employed to model both recessions and expansions. For the United States and Germany, strong evidence is found that monetary policy is more effective in a recession than during a boom. Also some evidence is found for asymmetry in the United Kingdom and Belgium. In the Netherlands, monetary policy is not very effective in either regime.
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