Simulating Realized Variance for Forecasting Model Tests

Summary

The document asks how to generate realized variance (the sum of squared intraday returns) for simulation studies that compare forecasting models. It contrasts simulating underlying prices with directly modeling the variance series, suggesting an autoregressive specification for linear dependence and asking whether an exponential model could represent nonlinear dependence.

The text does not settle on a simulation method, provide model parameters, or report empirical results. Instead, it identifies design questions: how to construct realistic variance paths, which nonlinear specification to choose, and where to find relevant literature. Any proposed simulation would need to define the innovation distribution and ensure generated variance remains nonnegative; the document itself does not address those details. Its value is as a research question framing alternative data-generating assumptions, rather than as a worked procedure or evidence-based recommendation.

Key ideas

• A simulation study can model realized variance directly instead of simulating prices first.
• An autoregressive model is proposed as a way to represent linear dependence in realized variance.
• The document asks whether an exponential model can capture nonlinear dependence.
• The choice of data-generating process affects how forecasting models are evaluated.
• No specific nonlinear model, parameterization, or literature recommendation is provided.

Tags

# Simulating realized variance


# Simulating realized variance












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!

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