"Semiparametric
Estimation of A Nonlinear Error-Correction Model" (with A. Rahbek)
ABSTRACT: We consider a nonlinear cointegration model where the transfer function (or
loadings) of the stationary relationships is unknown and potentially nonlinear.
We propose estimators of the parameters for the linear stationary relationships
and the nonparametric transfer function, and derive their asymptotic
properties.
"Estimation of Stochastic
Volatility Models By Nonparametric Filtering" (with S. Kanaya)
ABSTRACT: A new estimation method of
stochastic volatility models is proposed based on the nonparametric filter of
the instantaneous volatility process of Kristensen (2006). We propose to use
standard estimation methods for fully observed diffusion processes but with the
filtered volatility process replacing the latent process. The estimator will
carry a bias due to the use of the filtered volatility instead of the actual
volatility, but under regularity conditons this
vanishes asymptotically and our estimators inherit the asymptotic properties of
the infeasible estimators based on observations of the volatility process. The
estimation strategy is applicable both for parametric and nonparametric
stochastic volatility models, and we give theoretical results for both. A
simulation study examines the estimators finite-sample
properties.
"Higher Order Improvements for
Approximate Estimators" (with Bernard Salanié)
ABSTRACT: We propose two methods to improve on
the precision of approximate estimators. Both of these methods only carry a
small additional computation burden. The first method is targeted at estimators
based on stochastic approximators, such as
simulation-based estimators. It consists of a general formula that corrects the
objective function and eliminates the leading order of the additional bias of
the approximate estimator. Our second proposed improvement is a two-step method
which applies quite generally. In the first step, we compute the approximate
estimator, using an approximator that may be coarser
than what is usually done; and in the second step we run one or several Newton-Raphson iterations based on the same objective function,
but with a much finer degree of approximation. The second step removes some or
all of the additional bias and variance of the initial approximate estimator.
"Stochastic Demand and
Revealed Preferences" (with R. Blundell and
R.
Matzkin)
ABSTRACT: In the econometric analysis of Engel
curves it is standard to assume an additive relationship between the
expenditure share, the total expenditure and the error term. In this paper, we
relax this assumption and instead consider non-separable relations between the
three variables. Furthermore, we impose revealed preferences restrictions in
the estimation. A nonparametric sieve estimator is developed, and its
asymptotic properties derived. We apply our estimator the UK Family Expenditure
Survey data.
"Estimation of Hidden Markov
Models with Nonparametric Simulated Maximum Likelihood" (with C. Brownlees and Y. Shin)
ABSTRACT: We extend the nonparametric
simulated maximum-likelihood estimator (NPSMLE) of Kristensen and Shin (2006)
to include built-in nonlinear filtering. By recursively approximating the
unknown conditional densities, our method enables calculation of simulated
version of the MLE of general dynamic models with latent variables---including
time-inhomogeneous and non-stationary processes. We establish the asymptotic
properties of the NPSMLE’s for hidden Markov
models, and then demonstrate the usefulness of our proposed method with