LTAR {LTAR}

Tensor Autoregression (TAR) Model

Description

Fits a Tensor Autoregression (TAR) Model to historical 3D tensor data and returns the coefficient tensor (A) and the constant matrix (C).

\mathbf{A}=[A_1 | A_2 | \ldots | A_p], \mathbf{C}

Usage

LTAR(p,tnsr,type = c("const", "trend", "both", "none"),season=NULL)

Arguments

p

: Number of lags

tnsr

: A 3D tensor

type

:Type of deterministic regressors to include.

season

: Inclusion of centered seasonal dummy variables (integer value of frequency).

Value

The coefficient tensor

\mathbf{A}=[A_1 | A_2 | \ldots | A_p]

and the constant matrix

C

for the LTAR model:

\mathbf{y}_t = A_1\mathbf{y}_{t-1}+\ldots+A_p\mathbf{y}_p+CD_t+\mathbf{u}_t.

Author(s)

Kyle Caudle

Randy Hoover

Jackson Cates

References

Cates, J., Hoover, R. C., Caudle, K., Kopp, R., & Ozdemir, C. (2021, December). Transform-Based Tensor Auto Regression for Multilinear Time Series Forecasting. In 2021 20th IEEE International Conference on Machine Learning and Applications (ICMLA) (pp. 461-466). IEEE.

Examples

require(rTensor)
data(tensor)
tnsr <- as.tensor(tensor)
# an LTAR(1) model with trend
model <- LTAR(p=1,tnsr,type="trend")