gen_MEFM {MEFM}

Data generation of matrix time series with MEFM structure

Description

Generate a matrix time series with MEFM at each time t, with the first mode as the time mode, the second as the row mode and the third as the column mode

Usage

gen_MEFM(
  TT,
  d,
  r,
  re,
  eta,
  coef_f,
  coef_fe,
  coef_e,
  param_mu,
  param_alpha,
  param_beta,
  heavy_tailed = FALSE,
  t_df = 3,
  rademacher = FALSE,
  seed = 2024
)

Arguments

TT

Length of time series.

d

Dimensions of the matrix at time t, written in a vector of length 2 where the first number denotes the number of rows p and the second denoted the number of columns q.

r

Rank of the core factors, written in a vector of length 2.

re

re: Rank of the cross-sectional common error core factors, written in a vector of length 2.

eta

Quantities controlling factor strengths in each factor loading matrix, written in a list of 2 vectors.

coef_f

AR(5) coefficients for the factor series, written in a vector of length 5.

coef_fe

AR(5) coefficients for the common component in error series, written in a vector of length 5.

coef_e

AR(5) coefficients for the idiosyncratic component in error series, written in a vector of length 5.

param_mu

If rademacher = TRUE, represent parameters of normal distribution to generate grand mean series mu_t, written in a vector of length 2 representing the mean and standard deviation. Otherwise written in a scalar multiplied by the generated Rademacher random variable.

param_alpha

If rademacher = TRUE, represent parameters of normal distribution to generate row effect series alpha_t, written in a vector of length 2 representing the mean and standard deviation. Otherwise written in a scalar multiplied by the generated Rademacher random variable.

param_beta

If rademacher = TRUE, represent parameters of normal distribution to generate column effect series beta_t, written in a vector of length 2 representing the mean and standard deviation. Otherwise written in a scalar multiplied by the generated Rademacher random variable.

heavy_tailed

Whether to generate data from heavy-tailed distribution. If FALSE, generate from N(0,1); if TRUE, generate from t-distribution. Default is FALSE.

t_df

The degree of freedom for t-distribution if heavy_tailed = TRUE. Default is 3.

rademacher

Mechanism to generate mu, alpha and beta. If FALSE, generate from normal with param_mu, param_alpha and param_beta; if TRUE, generate from Rademacher distribution and scaled by param_mu, param_alpha and param_beta. Default is FALSE.

seed

Random seed required for reproducibility. Default is 2024.

Value

A list containing the following: mu: the generated time-varying grand mean series, as a vector of length TT; alpha: the generated time-varying row effect series, as a matrix of dimension (TT,p); beta: the generated time-varying column effect series, as a matrix of dimension (TT,q); A: a list of 2 factor loading matrices; C: the generated common component time series, as multi-dimensional array with dimension 3, where mode-1 is the time mode, mode-2 is for rows and mode-3 is for columns; Ft: the generated core factor series, as multi-dimensional array with dimension 3, where mode-1 is the time mode, mode-2 is for rows and mode-3 is for columns; MEFM: the generated matrix time series with MEFM structure, as multi-dimensional array with dimension 3, where mode-1 is the time mode, mode-2 is for rows and mode-3 is for columns; FM: the generated matrix time series with only traditional factor structure, as multi-dimensional array with dimension 3, where mode-1 is the time mode, mode-2 is for rows and mode-3 is for columns; E: the generated error time series with factor structure, as multi-dimensional array with dimension 3, where mode-1 is the time mode, mode-2 is for rows and mode-3 is for columns;

Examples

TT = 40;
d = c(40,40);
r = c(2,2);
re = c(2,2);
eta = list(c(0,0), c(0,0));
coef_f = c(0.7, 0.3, -0.4, 0.2, -0.1);
coef_fe = c(-0.7, -0.3, -0.4, 0.2, 0.1);
coef_e = c(0.8, 0.4, -0.4, 0.2, -0.1);
param_mu = c(0,1);
param_alpha = c(0,1);
param_beta = c(0,1);
gen_MEFM(TT,d,r,re,eta, coef_f, coef_fe, coef_e, param_mu, param_alpha, param_beta);