References for Estimating Continuous-Time Models from Discrete Data

Summary

The document asks where to learn econometric methods for continuous-time models when observations arrive at discrete times. It explains why the topic is relatively specialized: standard econometrics and time-series texts may give it little attention, and many option-pricing models are calibrated to option prices rather than estimated from historical observations. For statistical work, discrete-time models can also be a practical starting point when the data itself is discrete.

For a focused reference, the answer recommends a text on high-frequency financial econometrics that covers estimation of diffusion and jump models. The document offers a pointer rather than a tutorial: it does not compare estimation techniques, explain their assumptions, or provide empirical results. Its scope is therefore useful for finding an entry point, while further sources would be needed to learn implementation and assess which methods fit a particular model or sampling scheme.

Key ideas

• Continuous-time parameter estimation from discretely sampled data is a specialized econometrics topic.
• Many option-pricing models are fitted to options data instead of estimated from historical time series.
• Discrete-time models can be a practical alternative for statistical analysis of discrete observations.
• High-frequency financial econometrics references cover estimation of diffusion and jump models.

Tags

# Which references would be useful as an introduction to econometrics as it pertains to CONTINUOUS TIME models?


# Which references would be useful as an introduction to econometrics as it pertains to CONTINUOUS TIME models?












It seems like the problem of trying to estimate model parameters for continuous time models is not commonly covered in standard econometric textbooks, even those focusing on time series. I certainly am able to read and work on research pertaining to discrete time series models, but I have never encountered an introduction on how to estimate continuous time models using discretely sampled data and I would be curious to know if anyone has suggestions.

## Answer by fes (score 3)

https://quant.stackexchange.com/a/59045

This is seen as a bit of a niche field, which is likely why there are not so many books and these issues are not covered in standard econometrics texts. Options pricing models are usually fitted to options data rather than estimated econometrically from historical data. For statistical models, it is often more convenient to start from a discrete model as the data is discrete anyway.

However, there are some relevant books. You could check e.g. "High-Frequency Financial Econometrics" by Ait-Sahalia and Jacod, which covers the estimation of diffusion and jump models.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.