ylefay / high_dimensional_vector_autoregression

Implementation of High-dimensional vector autoregression time series modeling via tensor decomposition, Di Wang, Yao Zheng, Heng Lian, Guodong Li. Written in JAX.

Efficient tensor implementation of vector autoregression (VAR) model written in Jax.

The VAR model of order $P\geq 1$ has the form:

$$y_t = A_1 y_{t-1} + \ldots + A_P y_{t-P} + \varepsilon_t$$

where the $y_t$'s are observed time series with $y_t\in\mathbb{R}^N$ and the $\varepsilon_t$'s are $N$-dimensional, centred and with finite variance, independent and identically distributed variables (called innovations). The $A_t$'s matrices are $N\times N$ transition matrices we want to estimate. The estimation process is both time and memory expensive. This package aims to implement the VAR model in a more efficient way by using tensor decomposition described in [@wang2020highdimensional].

It includes:

• An alternative least-square algorithm for VAR estimation via Tensor decomposition.
• An implementation of the SHORR algorithm, Lasso-penalized regression for VAR estimation via Tensor decomposition.
• An implementation of the Higher-order singular value decomposition (HOSVD) algorithm.
• A subroutine for sparse and orthogonal regressions.
• Multiple procedures to sample VAR models.
• Multiple tensor algebra related procedures.

References

• High-dimensional vector autoregressive time series modeling via tensor decomposition, by Di Wang, Yao Zheng, Heng Lian and Guodong Li.
• A splitting method for orthogonality constrainted problems, by Lai Rongjie and Osher Stanley.

See ref.bib.