Construct observation and covariate matrices for a vector autoregressive model

nmfkc.ar generates the observation matrix and covariate matrix corresponding to a specified autoregressive lag order.

If the input Y is a ts object, its time properties are preserved in the "tsp_info" attribute, adjusted for the lag. Additionally, the column names of Y and A are set to the corresponding time points.

Usage

nmfkc.ar(Y, degree = 1, intercept = TRUE)

Arguments

Y: An observation matrix (P x N) or a ts object. If Y is a ts object (typically N x P), it is automatically transposed to match the (P x N) format.
degree: The lag order of the autoregressive model. The default is 1.
intercept: Logical. If TRUE (default), an intercept term is added to the covariate matrix.

Value

A list containing:

Y: Observation matrix (P x N_A) used for NMF. Includes adjusted "tsp_info" attribute and time-based column names.
A: Covariate matrix (R x N_A) constructed according to the specified lag order. Includes adjusted "tsp_info" attribute and time-based column names.
A.columns: Index matrix used to generate A.
degree.max: Maximum lag order.

References

Satoh, K. (2025). Applying non-negative matrix factorization with covariates to multivariate time series data as a vector autoregression model. Japanese Journal of Statistics and Data Science. arXiv:2501.17446. doi:10.1007/s42081-025-00314-0

Examples

# Example using AirPassengers (ts object)
d <- AirPassengers
ar_data <- nmfkc.ar(d, degree = 2)
dim(ar_data$Y)
#> [1]   1 142
dim(ar_data$A)
#> [1]   3 142

# Example using matrix input
Y <- matrix(1:20, nrow = 2)
ar_data <- nmfkc.ar(Y, degree = 1)
ar_data$degree.max
#> [1] 9