est_FM function

Estimation of factor models on matrix time series

Estimate the FM structure on the given matrix time series

est_FM(Yt, r = 0, delta = 0.2)

Arguments

• Yt: demeaned matrix time series, written in an array with dimension 3 and the first dimension for time.
• r: Rank of core factors for the common component, written in a vector of length 2. First value as 0 is to denote unknown rank which would be automatically estimated using ratio-based estimators. Default is 0.
• delta: Non-negative number as the correction parameter for rank estimation. Default is 0.2.

Returns

A list containing the following: r: a vector representing either the given rank or the estimated rank, with length 2; A: a list of the estimated row and column factor loading matrices; Ft: the estimated core factor series, as multi-dimensional array with dimension 3, where mode-1 is the time mode; Ct: the estimated common component time series, as multi-dimensional array with dimension 3, where mode-1 is the time mode; covMatrix: a list of the estimated row and column covariance matrices which are used to estimate loading matrices;

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);
data_example = gen_MEFM(TT,d,r,re,eta, coef_f, coef_fe, coef_e, param_mu, param_alpha, param_beta);
est_FM(data_example$FM);