Estimating Parameters in Complex Time-Series and Volatility Models

Summary

The document asks how to estimate parameters in models such as GARCH, Heston, and stochastic volatility with jumps, and whether standard methods like maximum likelihood or least squares can be applied. It also asks about general-purpose estimation without specialist libraries and the roles of Kalman filters, Monte Carlo simulation, and martingale measures.

No answers, worked examples, or evidence are provided; the text is a request for guidance rather than an explanation of an estimation method. Its useful framing is the distinction between fitting a familiar ARIMA model and handling more complex models with latent variables or multiple stochastic components. The questions also connect model estimation to the practical needs of testing mid-frequency strategies. Readers should not treat the document as a tutorial or infer that one estimation procedure applies to every model: the choice depends on the model structure and available observations.

Key ideas

• The document raises parameter estimation for GARCH, Heston, and stochastic volatility models with jumps.
• It asks whether maximum likelihood or least squares can handle models with multiple random components.
• It asks how Kalman filtering, Monte Carlo simulation, and martingale measures relate to parameter estimation.
• It provides questions rather than answers, procedures, or empirical evidence.

Tags

# Parameter Estimation of any model


# Parameter Estimation of any model












I am new to time series modelling.I cant get my head around parameter estimation and its methods. My question consists of 3 parts :

1st : Lets say i have a model like Garch or Heston model or a SVJD model having multiple terms and multiple iid random variables.How do i estimate the parameters with simple methods like mle or OLS (or its not possible) possibly in R using inbuilt functions for mle(i can do for estimating Arima).

2nd : Is there a general approach i can use to estimate the parameters of any complex model without relying on any external library.

3rd : How does Kalman filters , Monte-carlo simulation, martingale measures can estimate parameters .(It would be very helpful if you could cite a book or a tutorial).

(Do i need to know all the estimation methods or a simple few would do for testing mid-frequency strategies).

(I have read the source code of custom libraries in R and i could not understand anything (implementation) beyond Arima.)

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.