# The Pearson Diffusions: A Class of Statistically Tractable Diffusion Processes

@article{Forman2007ThePD, title={The Pearson Diffusions: A Class of Statistically Tractable Diffusion Processes}, author={Julie Lyng Forman and Michael S{\O}rensen}, journal={Scandinavian Journal of Statistics}, year={2007}, volume={35} }

Abstract. The Pearson diffusions form a flexible class of diffusions defined by having linear drift and quadratic squared diffusion coefficient. It is demonstrated that for this class explicit statistical inference is feasible. A complete model classification is presented for the ergodic Pearson diffusions. The class of stationary distributions equals the full Pearson system of distributions. Well‐known instances are the Ornstein–Uhlenbeck processes and the square root (CIR) processes. Also…

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## References

SHOWING 1-10 OF 89 REFERENCES

### Diffusion-type models with given marginal distribution and autocorrelation function

- Mathematics
- 2005

Flexible stationary diffusion-type models are developed that can fit both the marginal distribution and the correlation structure found in many time series from e.g. finance and turbulence. Diffusion…

### Simple and Explicit Estimating Functions for a Discretely Observed Diffusion Process

- Mathematics
- 2000

We consider a one‐dimensional diffusion process X, with ergodic property, with drift b(x, θ) and diffusion coefficient a(x, θ) depending on an unknown parameter θ that may be multidimensional. We are…

### Estimating Functions for Discretely Observed Diffusions: A Review

- Mathematics
- 1997

Several estimating functions for discretely observed diffusion processes are reviewed. First we discuss simple explicit estimating functions based on Gaussian approximations to the transition…

### Inference for Observations of Integrated Diffusion Processes

- Mathematics
- 2004

Abstract. Estimation of parameters in diffusion models is investigated when the observations are integrals over intervals of the process with respect to some weight function. This type of…

### Estimating equations based on eigenfunctions for a discretely observed diffusion process

- Mathematics
- 1999

A new type of martingale estimating function is proposed for inference about classes of diffusion processes based on discrete-time observations. These estimating functions can be tailored to a…

### Efficient Estimation for Ergodic Diffusions Sampled at High Frequency

- Mathematics
- 2007

A general theory of efficient estimation for ergodic diffusions sampled at high fre- quency is presented. High frequency sampling is now possible in many applications, in particular in finance. The…

### Spectral GMM Estimation of Continuous-Time Processes

- Economics, Mathematics
- 1999

This paper derives a methodology for the exact estimation of continuous-time stochastic models based on the characteristic function. The estimation method does not require discretization of the…

### Martingale estimation functions for discretely observed diffusion processes

- Mathematics
- 1995

We consider three different martingale estimating functions based on discrete-time observations of a diffusion process. One is the discretized continuous-time score function adjusted by its…

### Stochastic volatility models

- Economics
- 2007

In this chapter we discuss continuous-time stochastic volatility models. By this we mean two-dimensional diffusion models where only one of the coordinates is observable and where the stochastic…

### Efficient Estimation of Jump Diffusions and General Dynamic Models with a Continuum of Moment Conditions

- Mathematics
- 2002

A general estimation approach combining the attractive features of method of moments with the efficiency of ML is proposed. The moment conditions are computed via the characteristic function. The two…