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.