# ARISE: ApeRIodic SEmi-parametric Process for Efficient Markets without Periodogram and Gaussianity Assumptions

arXiv: https://arxiv.org/abs/2111.06222 · HTML: https://mlsanity.com/paper/2111.06222/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 68 references that are in the map.
- First posted on arXiv 8 Nov 2021.

## Builds on (most cited first, 15 of 15)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
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- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [Unitary Evolution Recurrent Neural Networks](https://mlsanity.com/paper/1511.06464/) (2015)
- [Financial Time Series Forecasting with Deep Learning : A Systematic Literature Review: 2005-2019](https://mlsanity.com/paper/1911.13288/) (2019)
- [Long Short-Term Memory-Networks for Machine Reading](https://mlsanity.com/paper/1601.06733/) (2016)
- [A Refined Laser Method and Faster Matrix Multiplication](https://mlsanity.com/paper/2010.05846/) (2020)
- [Do RNN and LSTM have Long Memory?](https://mlsanity.com/paper/2006.03860/) (2020)
- [Causal Discovery and Forecasting in Nonstationary Environments with State-Space Models](https://mlsanity.com/paper/1905.10857/) (2019)
- [Minimal Gated Unit for Recurrent Neural Networks](https://mlsanity.com/paper/1603.09420/) (2016)
- [Deriving Neural Architectures from Sequence and Graph Kernels](https://mlsanity.com/paper/1705.09037/) (2017)
- [A Statistical Investigation of Long Memory in Language and Music](https://mlsanity.com/paper/1904.03834/) (2019)
- [Long Short-Term Memory as a Dynamically Computed Element-wise Weighted Sum](https://mlsanity.com/paper/1805.03716/) (2018)
- [Flexible Transmitter Network](https://mlsanity.com/paper/2004.03839/) (2020)

## Built on by (most cited first, 1 of 1)

- [A Unified Kernel for Neural Network Learning](https://mlsanity.com/paper/2403.17467/) (2024)

## Abstract (arXiv)

Mimicking and learning the long-term memory of efficient markets is a fundamental problem in the interaction between machine learning and financial economics to sequential data. Despite the prominence of this issue, current treatments either remain largely limited to heuristic techniques or rely significantly on periodogram or Gaussianty assumptions. In this paper, we present the ApeRIodic SEmi-parametric (ARISE) process for investigating efficient markets. The ARISE process is formulated as an infinite-sum function of some known processes and employs the aperiodic spectrum estimation to determine the key hyper-parameters, thus possessing the power and potential of modeling the price data with long-term memory, non-stationarity, and aperiodic spectrum. We further theoretically show that the ARISE process has the mean-square convergence, consistency, and asymptotic normality without periodogram and Gaussianity assumptions. In practice, we apply the ARISE process to identify the efficiency of real-world markets. Besides, we also provide two alternative ARISE applications: studying the long-term memorability of various machine-learning models and developing a latent state-space model for inference and forecasting of time series. The numerical experiments confirm the superiority of our proposed approaches.