IPCA factor extraction

Usage

ipca_est(ret, Z, nfac, max_iter = 100, tol = 1e-06, factor_mean = "zero")

Arguments

ret: Numeric matrix (T x N) of asset returns. Use NA for missing observations (unbalanced panel).
Z: Numeric array (T x N x L) of asset characteristics. NAs must mirror ret exactly.
nfac: Positive integer; number of latent factors K to extract.
max_iter: Maximum ALS iterations (default 100).
tol: Convergence tolerance on Frobenius norm of loading change (default 1e-6).
factor_mean: Character scalar specifying how the factor mean is modelled. One of "zero" (default, no mean adjustment), "constant" (time-series average), or "VAR1" (VAR(1) with intercept).

Value

An object of class "sdim_fit" with fields: factors (T x K), lambda (L x K characteristic loadings, i.e. Gamma in Kelly et al.), eigvals (factor variances), factor_mean (character scalar), call, method = "ipca", nfac. If factor_mean = "constant": also mu (length-K mean vector). If factor_mean = "VAR1": also var_coef (K x K), var_intercept (length-K), var_resid ((T-1) x K).

References

Kelly, B. T., Pruitt, S., and Su, Y. (2019). Characteristics are Covariances: A Unified Model of Risk and Return. Journal of Financial Economics, 134(3), 501–524. doi:10.1016/j.jfineco.2019.05.001

Examples

set.seed(1)
ret <- matrix(rnorm(50 * 10) / 100, 50, 10)
Z   <- array(rnorm(50 * 10 * 4), dim = c(50, 10, 4))
fit <- ipca_est(ret, Z, nfac = 2)
print(fit)
#> <sdim_fit [ipca]>
#>  Observations    : 50 
#>  Characteristics : 4 
#>  Factors         : 2 
#>  Factor mean     : zero