Abstract
We propose a method for obtaining maximum likelihood estimates of parameters
in diffusion models when the data is a discrete time sample of the integral of the
process, while no direct observations of the process itself are available. The data are,
moreover, assumed to be contaminated by measurement errors. Integrated volatility is
an example of this type of observations. Another example is ice-core data on oxygen
isotopes used to investigate paleo-temperatures.
The data can be viewed as incomplete observations of a model with a tractable likelihood
function. Therefore we propose a simulated EM-algorithm to obtain maximum
likelihood estimates of the parameters in the diffusion model. As part of the algorithm,
we use a recent simple method for approximate simulation of diffusion bridges. In simulation
studies for the Ornstein-Uhlenbeck process and the CIR process the proposed
method works well.
in diffusion models when the data is a discrete time sample of the integral of the
process, while no direct observations of the process itself are available. The data are,
moreover, assumed to be contaminated by measurement errors. Integrated volatility is
an example of this type of observations. Another example is ice-core data on oxygen
isotopes used to investigate paleo-temperatures.
The data can be viewed as incomplete observations of a model with a tractable likelihood
function. Therefore we propose a simulated EM-algorithm to obtain maximum
likelihood estimates of the parameters in the diffusion model. As part of the algorithm,
we use a recent simple method for approximate simulation of diffusion bridges. In simulation
studies for the Ornstein-Uhlenbeck process and the CIR process the proposed
method works well.
| Original language | English |
|---|---|
| Place of publication | Aarhus |
| Publisher | Institut for Økonomi, Aarhus Universitet |
| Number of pages | 16 |
| Publication status | Published - 2010 |
Keywords
- Diffusion bridge, discretely sampled diffusions, EM-algorithm, likelihood inference, measurement error, stochastic differential equation, stochastic volatility