Journal article
Predicting integrals of diffusion processes
Journal of statistical planning and inference, Vol.90(2), pp.183-193
2000
DOI: 10.1016/S0378-3758(00)00121-X
Abstract
Consider predicting the integral of a diffusion process
Z in a bounded interval
A, based on the observations
Z(
t
1
n
),…,
Z(
t
nn
), where
t
1
n
,…,
t
nn
is a dense triangular array of points (the step of discretization tends to zero as
n increases) in the bounded interval. The best linear predictor is generally not asymptotically optimal. Instead, we predict
∫
A
Z(t)
dt
using the conditional expectation of the integral of the diffusion process, the optimal predictor in terms of minimizing the mean squared error, given the observed values of the process. We obtain that, conditioning on the observed values, the order of convergence in probability to zero of the mean squared prediction error is O
p(
n
−2). We prove that the standardized conditional prediction error is approximately Gaussian with mean zero and unit variance, even though the underlying diffusion is generally non-Gaussian. Because the optimal predictor is hard to calculate exactly for most diffusions, we present an easily computed approximation that is asymptotically optimal. This approximation is a function of the diffusion coefficient.
Details
- Title: Subtitle
- Predicting integrals of diffusion processes
- Creators
- Montserrat Fuentes - Statistics Department, North Carolina State University, Patterson Hall 210C, Box 8203, Raleigh, NC 27695, USA
- Resource Type
- Journal article
- Publication Details
- Journal of statistical planning and inference, Vol.90(2), pp.183-193
- Publisher
- Elsevier B.V
- DOI
- 10.1016/S0378-3758(00)00121-X
- ISSN
- 0378-3758
- eISSN
- 1873-1171
- Language
- English
- Date published
- 2000
- Academic Unit
- Statistics and Actuarial Science; President; Biostatistics
- Record Identifier
- 9984065885202771
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