Estimating functions for discretely sampled diffusion-type models

TY - CHAP

T1 - Estimating functions for discretely sampled diffusion-type models

AU - Sørensen, Michael

AU - Jacobsen, Martin

AU - Bibby, Bo Martin

PY - 2010

Y1 - 2010

N2 - This chapter demonstrates that estimating functions can be found not only for ordinary diffusions but also for stochastic volatility models and diffusions with jumps. For stochastic volatility models, the estimating functions are constructed in such a way that asymptotic properties of the estimator can easily be established. The main advantage of the estimating functions discussed in this chapter is that they usually require less computation than the alternative methods. It is a particularly useful approach when quick estimators are needed. These simple estimators have a rather high efficiency when the estimating function is well chosen. The hallmark of the estimating functions approach is the use of a given collection of relations between observations at different time points to construct an optimal estimator, i.e., the most efficient estimator possible based on these relations. In a high-frequency sampling asymptotic scenario, optimal martingale estimating functions are, in fact, efficient for diffusion models.

AB - This chapter demonstrates that estimating functions can be found not only for ordinary diffusions but also for stochastic volatility models and diffusions with jumps. For stochastic volatility models, the estimating functions are constructed in such a way that asymptotic properties of the estimator can easily be established. The main advantage of the estimating functions discussed in this chapter is that they usually require less computation than the alternative methods. It is a particularly useful approach when quick estimators are needed. These simple estimators have a rather high efficiency when the estimating function is well chosen. The hallmark of the estimating functions approach is the use of a given collection of relations between observations at different time points to construct an optimal estimator, i.e., the most efficient estimator possible based on these relations. In a high-frequency sampling asymptotic scenario, optimal martingale estimating functions are, in fact, efficient for diffusion models.

M3 - Book chapter

SN - 978-0-444-50897-3

VL - 1

SP - 203

EP - 268

BT - Handbook of Financial Econometrics

A2 - Ait-Sahalia, Yacine

A2 - Hansen, Lars Peter

PB - North-Holland

CY - Oxford

ER -