40,518 research outputs found
A selective overview of nonparametric methods in financial econometrics
This paper gives a brief overview on the nonparametric techniques that are
useful for financial econometric problems. The problems include estimation and
inferences of instantaneous returns and volatility functions of
time-homogeneous and time-dependent diffusion processes, and estimation of
transition densities and state price densities. We first briefly describe the
problems and then outline main techniques and main results. Some useful
probabilistic aspects of diffusion processes are also briefly summarized to
facilitate our presentation and applications.Comment: 32 pages include 7 figure
Identification of time-varying systems using multiresolution wavelet models
Identification of linear and nonlinear time-varying systems is investigated and a new wavelet model identification algorithm is introduced. By expanding each time-varying coefficient using a multiresolution wavelet expansion, the time-varying problem is reduced to a time invariant problem and the identification reduces to regressor selection and parameter estimation. Several examples are included to illustrate the application of the new algorithm
The Parameter Houlihan: a solution to high-throughput identifiability indeterminacy for brutally ill-posed problems
One way to interject knowledge into clinically impactful forecasting is to
use data assimilation, a nonlinear regression that projects data onto a
mechanistic physiologic model, instead of a set of functions, such as neural
networks. Such regressions have an advantage of being useful with particularly
sparse, non-stationary clinical data. However, physiological models are often
nonlinear and can have many parameters, leading to potential problems with
parameter identifiability, or the ability to find a unique set of parameters
that minimize forecasting error. The identifiability problems can be minimized
or eliminated by reducing the number of parameters estimated, but reducing the
number of estimated parameters also reduces the flexibility of the model and
hence increases forecasting error. We propose a method, the parameter Houlihan,
that combines traditional machine learning techniques with data assimilation,
to select the right set of model parameters to minimize forecasting error while
reducing identifiability problems. The method worked well: the data
assimilation-based glucose forecasts and estimates for our cohort using the
Houlihan-selected parameter sets generally also minimize forecasting errors
compared to other parameter selection methods such as by-hand parameter
selection. Nevertheless, the forecast with the lowest forecast error does not
always accurately represent physiology, but further advancements of the
algorithm provide a path for improving physiologic fidelity as well. Our hope
is that this methodology represents a first step toward combining machine
learning with data assimilation and provides a lower-threshold entry point for
using data assimilation with clinical data by helping select the right
parameters to estimate
Asymmetric and time-varying error-correction: an application to labour demand in the UK
In this paper we compare the asymmetric and time-varying error-correction models that have recently been proposed, and apply these to the case of UK aggregate labour demand. The aim of the paper is to investigate the possible co-existence of time-varying adjustment on the one hand, and constant asymmetric error-correction on the other hand. We find that without allowing for time-varying adjustment variables, the asymmetric error-correction models of Granger and Lee (1989) and Escribano (1986) work well. But once the time-varying adjustment variables are included, the evidence for time-invariant asymmetric adjustment is marginal
Dimension reduction for systems with slow relaxation
We develop reduced, stochastic models for high dimensional, dissipative
dynamical systems that relax very slowly to equilibrium and can encode long
term memory. We present a variety of empirical and first principles approaches
for model reduction, and build a mathematical framework for analyzing the
reduced models. We introduce the notions of universal and asymptotic filters to
characterize `optimal' model reductions for sloppy linear models. We illustrate
our methods by applying them to the practically important problem of modeling
evaporation in oil spills.Comment: 48 Pages, 13 figures. Paper dedicated to the memory of Leo Kadanof
- …