I have a question regarding possible ways to simulate realized variance (the sum of squared intraday returns) for testing different realized variance forecasting models.
I'm aware of several approaches to model stock prices, such as Geometric Brownian Motion and the Merton model. Recently, I was told that a simpler and more direct approach to simulate realized variance could involve using a HAR/AR model (for linear dependencies) something like this: $$ RV_{t+1} = \phi_{1} RV_{t} + \phi_{2} RV_{t-1}+ ... + \phi_n RV_{t-n} + \epsilon_{t}$$ with $\epsilon$ following some distribution.
Additionally, I was told that an exponential model could be used for simulating non-linear dependencies. The goal of this simulation study is to evaluate how different realized variance forecasting models perform under both linear and non-linear dependency assumptions. However, I’ve struggled to find much literature explaining this specific approach to simulating realized variance.
This is why I wanted to ask:
- How would you approach simulating realized variance for a simulation study
- What kind of exponential model would be most appropriate for capturing non-linear dependencies in realized variance?
- Can you recommend any literature that explores these or similar approaches?
Thanks a lot in advance!
