# Pyramidal Hidden Markov Model For Multivariate Time Series Forecasting

arXiv: https://arxiv.org/abs/2310.14341 · HTML: https://mlsanity.com/paper/2310.14341/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 42 references that are in the map.
- First posted on arXiv 22 Oct 2023.

## Builds on (most cited first, 20 of 20)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Generalized Out-of-Distribution Detection: A Survey](https://mlsanity.com/paper/2110.11334/) (2021)
- [TS2Vec: Towards Universal Representation of Time Series](https://mlsanity.com/paper/2106.10466/) (2021)
- [The UCR Time Series Archive](https://mlsanity.com/paper/1810.07758/) (2018)
- [Anomaly Transformer: Time Series Anomaly Detection with Association Discrepancy](https://mlsanity.com/paper/2110.02642/) (2021)
- [Non-stationary Transformers: Exploring the Stationarity in Time Series Forecasting](https://mlsanity.com/paper/2205.14415/) (2022)
- [ROCKET: Exceptionally fast and accurate time series classification using random convolutional kernels](https://mlsanity.com/paper/1910.13051/) (2019)
- [The UEA multivariate time series classification archive, 2018](https://mlsanity.com/paper/1811.00075/) (2018)
- [MINIROCKET: A Very Fast (Almost) Deterministic Transform for Time Series Classification](https://mlsanity.com/paper/2012.08791/) (2020)
- [Recurrent Neural Networks for Time Series Forecasting: Current Status and Future Directions](https://mlsanity.com/paper/1909.00590/) (2019)
- [CoST: Contrastive Learning of Disentangled Seasonal-Trend Representations for Time Series Forecasting](https://mlsanity.com/paper/2202.01575/) (2022)
- [Multivariate LSTM-FCNs for Time Series Classification](https://mlsanity.com/paper/1801.04503/) (2018)
- [Domain Adaptation for Time Series Forecasting via Attention Sharing](https://mlsanity.com/paper/2102.06828/) (2021)
- [Multivariate Time Series Classification with WEASEL+MUSE](https://mlsanity.com/paper/1711.11343/) (2017)
- [Causal Hidden Markov Model for Time Series Disease Forecasting](https://mlsanity.com/paper/2103.16391/) (2021)
- [Neural HMMs are all you need (for high-quality attention-free TTS)](https://mlsanity.com/paper/2108.13320/) (2021)
- [Early Performance Prediction using Interpretable Patterns in Programming Process Data](https://mlsanity.com/paper/2102.05765/) (2021)
- [MrSQM: Fast Time Series Classification with Symbolic Representations](https://mlsanity.com/paper/2109.01036/) (2021)

## Abstract (arXiv)

The Hidden Markov Model (HMM) can predict the future value of a time series based on its current and previous values, making it a powerful algorithm for handling various types of time series. Numerous studies have explored the improvement of HMM using advanced techniques, leading to the development of several variations of HMM. Despite these studies indicating the increased competitiveness of HMM compared to other advanced algorithms, few have recognized the significance and impact of incorporating multistep stochastic states into its performance. In this work, we propose a Pyramidal Hidden Markov Model (PHMM) that can capture multiple multistep stochastic states. Initially, a multistep HMM is designed for extracting short multistep stochastic states. Next, a novel time series forecasting structure is proposed based on PHMM, which utilizes pyramid-like stacking to adaptively identify long multistep stochastic states. By employing these two schemes, our model can effectively handle non-stationary and noisy data, while also establishing long-term dependencies for more accurate and comprehensive forecasting. The experimental results on diverse multivariate time series datasets convincingly demonstrate the superior performance of our proposed PHMM compared to its competitive peers in time series forecasting.