Choosing Conditional Least Squares for CIR Parameter Estimation

Summary

The document discusses estimating parameters in the Cox-Ingersoll-Ross model using conditional least squares (CLS). Its motivating example models cumulative capital calls for a private equity fund from quarterly observations, with a relatively short sample of about 40 quarters. It raises the practical question of how to calculate the CLS estimates from the data in R, referring to estimators derived in a paper by Overbeck and Ryden.

The document does not provide the estimator formulas, code, fitted parameters, or empirical results; it is a request for implementation guidance rather than a worked method. Its useful point is the proposed fit between a small sample and CLS in this application. Readers would need the cited derivation and additional implementation details to assess estimator assumptions, calculate uncertainty, or determine whether the model suits their data.

Key ideas

• The example applies a CIR model to cumulative private equity capital calls.
• The observations are quarterly and the sample is described as relatively short.
• Conditional least squares is proposed as an estimation approach for the small sample.
• The document asks how to implement the estimators in R but supplies no formulas or results.

Tags

# Estimating parameters of the Cox-Ingersoll-Ross model using CLS in R


# Estimating parameters of the Cox-Ingersoll-Ross model using CLS in R












I'm working on a project where I need to estimate the parameters of the CIR model. In the particular case, the CIR model is used to model cumulated capital calls for a private equity fund.

The data is quarterly, and runs for only 40 quarters or so, meaning that n is quite small. In this case, the CLS method should be the better choice for estimating the parameters.

The CLS estimators below are mathematically derived in the paper "Estimation in the Cox-Ingersoll-Ross model" by Overbeck and Ryden.

However, I am not confident on how to actually compute the specific estimates using these estimators and my data. Would you be so kind to help me in the right direction on this ? How would you go about this in R for example?

Best regards Kristian

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.