Time Series Simulations: Signature Transformation Method in Python. Part 2

Author(s): Pavel Zapolskii

Originally published on Towards AI.

In this article, we continue to explore a powerful tool for compressing Time Series information known as the Signature.

Please read the first part if you want to learn more about math and calculation of Signatures:

I will propose a strong mathematical method for converting multidimensional time series into information-preserving…

pub.towardsai.net

The purpose of the second part of our journey is to practice data augmentation. We will enrich the dataset with a large number of vectors distributed in the same way as the original ones, for which I will be using a method that has no restrictions on the dimensionality of the original dataset — the evolutionary method of recovery.

Following the plan above, we are now moving to the left part, which includes two separate tasks: inversion and sampling.

The results of this work can be used for:

Calculating of sample statistics across a dataset (confidence intervals, probabilities)Enriching a small dataset for further training of complex ML modelsAnonymizing data while preserving the general properties of time series

I will show you the implementation using financial market data: Gold ETF with ticker GLD and mining company Barrick Gold with ticker GOLD.

We are going to

Recover path from the SignatureSimulate new Time Series sample in order to increase the robustness… Read the full blog for free on Medium.

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Published via Towards AI