Structural time series grammar over variable blocks

TL;DR

This paper introduces a formal grammar for structural time series models, enabling systematic reasoning about their components and extending to models with changepoints, with potential for simplifying model construction and analysis.

Contribution

The paper presents a novel formal grammar for structural time series models, including changepoint extensions, facilitating structured reasoning and model generation.

Findings

Preliminary implementation of the grammar demonstrates its practical potential.

The grammar can generate models with changepoints, expanding expressiveness.

Framework simplifies understanding and designing complex time series models.

Abstract

A structural time series model additively decomposes into generative, semantically-meaningful components, each of which depends on a vector of parameters. We demonstrate that considering each generative component together with its vector of parameters as a single latent structural time series node can simplify reasoning about collections of structural time series components. We then introduce a formal grammar over structural time series nodes and parameter vectors. Valid sentences in the grammar can be interpreted as generative structural time series models. An extension of the grammar can also express structural time series models that include changepoints, though these models are necessarily not generative. We demonstrate a preliminary implementation of the language generated by this grammar. We close with a discussion of possible future work.