iter_proj {TensorPreAve}

Iterative Projection Estimator.

Description

Function for Iterative Projection Direction Refinement to re-estimate the factor loading matrices.

Usage

iter_proj(X, initial_direction, proj_N = 30, z = rep(1, X@num_modes - 1))

Arguments

X

A 'Tensor' object defined in package rTensor with K+1 modes. Mode-1 should correspond to the time mode.

initial_direction

Initial direction for projection, written in a list of K vectors. This can be obtained from the pre-averaging procedure by using function pre_est.

proj_N

Number of iterations, should be a positive integer. Default is 30.

z

(Estimated) Rank of the core tensor, written as a vector of length K. Can be set as 1's when we only need to do rank estimation based on projected data. Default is 1's.

Details

Input a tensor time series and initial estimated directions corresponding to the strongest factors, return the estimated factor loading matrices (or directions) using the Algorithm for Iterative Projection Direction Refinement.

Value

A list of K estimated factor loading matrices.

Examples

# Example of a real data set
set.seed(10)
Q_PRE = pre_est(value_weight_tensor)
Q_PROJ = iter_proj(value_weight_tensor, initial_direction = Q_PRE)
Q_PROJ

set.seed(10)
Q_PRE = pre_est(value_weight_tensor)
Q_PROJ_2 = iter_proj(value_weight_tensor, initial_direction = Q_PRE, z = c(2,2))
Q_PROJ_2


# Example using generated data
K = 2
T = 100
d = c(40,40)
r = c(2,2)
re = c(2,2)
eta = list(c(0,0),c(0,0))
u = list(c(-2,2),c(-2,2))
set.seed(10)
Data_test = tensor_data_gen(K,T,d,r,re,eta,u)
X = Data_test$X
Q_PRE = pre_est(X)
Q_PROJ = iter_proj(X, initial_direction = Q_PRE, z = r)
Q_PROJ