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Efficient computation of the quasi likelihood function for discretely observed diffusion processes

Höök, Lars Josef and Lindström, Erik LU (2016) In Computational Statistics & Data Analysis 103. p.426-437
Abstract
An efficient numerical method for nearly simultaneous computation of all conditional moments needed for quasi maximum likelihood estimation of parameters in discretely observed stochastic differential equations is presented. The method is not restricted to any particular dynamics of the stochastic differential equation and is virtually insensitive to the sampling interval. The key contribution is that computational complexity is sublinear in terms of expensive operations in the number of observations as all moments can be computed offline in a single operation. Simulations show that the bias of the method is small compared to the random error in the estimates, and to the bias of comparable methods. Furthermore the computational cost is... (More)
An efficient numerical method for nearly simultaneous computation of all conditional moments needed for quasi maximum likelihood estimation of parameters in discretely observed stochastic differential equations is presented. The method is not restricted to any particular dynamics of the stochastic differential equation and is virtually insensitive to the sampling interval. The key contribution is that computational complexity is sublinear in terms of expensive operations in the number of observations as all moments can be computed offline in a single operation. Simulations show that the bias of the method is small compared to the random error in the estimates, and to the bias of comparable methods. Furthermore the computational cost is comparable (actually faster for moderate and large data sets) to the simple, but in some applications badly biased, the Euler–Maruyama approximation. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Computational Statistics & Data Analysis
volume
103
pages
12 pages
publisher
Elsevier
external identifiers
  • Scopus:84976550980
ISSN
0167-9473
DOI
10.1016/j.csda.2016.05.014
language
English
LU publication?
yes
id
90e54057-4718-429e-a657-09122fbc29fc
date added to LUP
2016-08-24 14:04:51
date last changed
2016-10-25 09:40:16
@misc{90e54057-4718-429e-a657-09122fbc29fc,
  abstract     = {An efficient numerical method for nearly simultaneous computation of all conditional moments needed for quasi maximum likelihood estimation of parameters in discretely observed stochastic differential equations is presented. The method is not restricted to any particular dynamics of the stochastic differential equation and is virtually insensitive to the sampling interval. The key contribution is that computational complexity is sublinear in terms of expensive operations in the number of observations as all moments can be computed offline in a single operation. Simulations show that the bias of the method is small compared to the random error in the estimates, and to the bias of comparable methods. Furthermore the computational cost is comparable (actually faster for moderate and large data sets) to the simple, but in some applications badly biased, the Euler–Maruyama approximation.},
  author       = {Höök, Lars Josef and Lindström, Erik},
  issn         = {0167-9473},
  language     = {eng},
  pages        = {426--437},
  publisher    = {ARRAY(0x5da18e8)},
  series       = {Computational Statistics & Data Analysis},
  title        = {Efficient computation of the quasi likelihood function for discretely observed diffusion processes},
  url          = {http://dx.doi.org/10.1016/j.csda.2016.05.014},
  volume       = {103},
  year         = {2016},
}