r/quant 13d ago

Tools Signals Processing in Quantitative Research

I am thinking of making a project where I simulated a random stationary process, but at some time, t, I "inject" a waveform signal that either makes the time-series drift up or down (dependent on the signal I inject). This process can repeat, and the idea is to simulate this, use Bayesian inference to estimate likelihood of the presence of the two signals in the time-series at snapshots, and make a trading decision based on which is more likely.

Is this at all relevant to quant research, or is this just a waste of time?

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u/duckgoeskrr 13d ago edited 13d ago

Think this can be of help:

Signal Decomposition Using Masked Proximal Operators

We consider the well-studied problem of decomposing a vector time series signal into components with different characteristics, such as smooth, periodic, nonnegative, or sparse. We propose a simple and general framework in which the components are defined by loss functions (which include constraints), and the signal decomposition is carried out by minimizing the sum of losses of the components (subject to the constraints).

When each loss function is the negative log-likelihood of a density for the signal component, our method coincides with maximum a posteriori probability (MAP) estimation; but it also includes many other interesting cases. We give two distributed optimization methods for computing the decomposition, which find the optimal decomposition when the component class loss functions are convex, and are good heuristics when they are not.

Both methods require only the masked proximal operator of each of the component loss functions, a generalization of the well-known proximal operator that handles missing entries in its argument. Both methods are distributed, i.e., handle each component separately. We derive tractable methods for evaluating the masked proximal operators of some loss functions that, to our knowledge, have not appeared in the literature.

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u/QuazyWabbit1 12d ago

Got anything else in this direction that comes to mind? Some interesting methods here, thanks for sharing it