Selecting Mean-Reverting Asset Spreads with Frequency Analysis
Summary
The document describes a proposed statistical arbitrage workflow: enumerate combinations of assets, estimate hedge weights by regressing one asset on the others, and seek a spread with substantial high-frequency variation but little low-frequency drift. A long-term exponential moving average is used as a stop that reduces exposure when the spread moves too far from its reference level. The author asks whether Fourier analysis can identify suitable spreads and what tools are common in the industry.
The text provides a conceptual objective and an example of fitting weights, but no tested results or comparison of Fourier methods with other approaches. It leaves open important design questions, including how to define frequency-band scores, normalize candidate spreads, account for changing relationships, and validate the strategy out of sample. The proposed hedge regression fixes one asset's coefficient to avoid the trivial all-zero solution; the document does not establish that this produces an optimal or stable trading portfolio.
Key ideas
- The proposed strategy searches for linear combinations of assets that behave like mean-reverting spreads.
- The author fits hedge weights by regressing one asset on the remaining assets in a candidate combination.
- The selection goal is high-frequency variation with limited low-frequency movement.
- A long-term exponential moving average is used as a stop reference for reducing exposure.
- The document raises Fourier analysis as a possible selection tool but supplies no empirical evaluation.
Tags
Full text
# StatArb : Fourier transform to find the perfect factor? # StatArb : Fourier transform to find the perfect factor? We have a basic mean reverting strategy. Given a bench of assets, we are looking for the best linear combination of them such as the resulting normalized time series would be noisy at high frequencies (in order to have opportunities), but with very few directional (or low frequency) because we run with a long-timed EMA that acts as a stop loss (if that EMA goes too far away from the current price, we reduce the position even at a loss, to avoid further loss). We implemented a script that outputs all the possible combinations from a bench of assets. For example : BTC, ETH, SOL, ADA : ``` BTC - ETH BTC - SOL BTC - ADA ETH - SOL ETH - ADA SOL - ADA BTC - ETH - SOL BTC - ETH - ADA ETH - SOL - ADA BTC - ETH - SOL - ADA ``` Then we run a Tensorflow adam algorithm on each factor to have the weights that minimize : (for example with ETH - SOL - ADA) : ``` find A and B minimizing 1 ETH - A * SOL - B * ADA ``` Basically, it's just like an OLS. We couldn't tell the optimizer to minimize ``` A * ETH + B * SOL + C * ADA ``` Because it would just output A = 0, B = 0 and C = 0. I couldn't really get rid of this problem so I stick one asset multiplier to 1 and make the others hedging perfectly with it by running this OLS But anyway, now that we have all these linear combinations of assets, the goal is to take the one that have the higher amplitude in high frequency, and the lowest possible directional, lowest possible low frequency. My question is : Do you think using Fourier transform could be an answer to that problem ? Why is it so sparsely documented in statistical arbitrage papers while it looks like the perfect mathematical tool for statistical arbitrage? I'm basically quite new to statistical arbitrage so I'm looking for the mathematical tools that are usually used in the industry.
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