Resampling Benefits for Investment Simulation
This article summarizes the benefits of resampling methods for high-dimensional investment market simulation.
A core market simulation model from the Portfolio Construction and Risk Management book is the Fully Flexible Resampling (FFR) method introduced in Chapter 3.
While resampling has the benefit of being able to capture the cross-sectional dependencies no matter how complex they are, resampling methods require additional work to capture the time series dependencies.
This is why we introduced the class of Time- and State-Dependent Resampling methods, which presents the mild necessary conditions for a particular resampling method to have nice properties, for example, preserving stationarity.
In the cover image to this article, you see an example of the state-dependent resampling probabilities from the Multi-Asset Macro Model, where we use VIX, 5y breakeven inflation, and 5y real rate as the state variables.
Another, perhaps overlooked, benefit of resampling is that we can simulate markets in a highly computationally effective way, because we are essentially just resampling the index of the historical observations.
Stationary transformations
As explained in the Multi-Asset Simulation article, we usually have to preprocess the raw investment data into something that is (approximately and locally) stationary to make it easier for our statistical models to learn.
Some of these stationary transformations already reduce the magnitude of the time series dependencies, for example, there is a lot less autocorrelation in return series compared to price series.
However, the returns are likely to exhibit autocorrelation in higher movements, as explained in Chapter 2 of the Portfolio Construction and Risk Management book, which our resampling method has to capture for realistic future path simulation.
While we do not have to worry about the cross-sectional dependencies when using resampling, capturing the time series dependencies is our main challenge.
Filtering
If there is still significant time series dependency after we have performed our stationary transformations, we can resort to what is commonly referred to as “filtering”.
This means specifically estimating a model for a particular univariate time series that makes it easier for us to capture its time dependencies.
Filtering can also be applied if we think a particular time series has a long-term value that we want to capture or adjust in our simulations.
Finally, some time series might already be stationary but highly persistent, in which case filtering also makes it easier for us.
You can read more about resampling of persistent time series in the article below:
Resampling Persistent Time Series
Continuing the analysis from the Multi-Asset Macro Model and Multi-Asset Simulation posts, this article presents perspectives on how we can handle persistent time series in resampling models, such as the
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