Get started with sdim • sdim

Overview

sdim implements five factor extraction methods for asset pricing and macroeconomic forecasting:

Function	Method	Reference
`pca_est()`	Principal Component Analysis (PCA)	He et al. (2023, MS)
`pls_est()`	Partial Least Squares (PLS)	He et al. (2023, MS)
`rra_est()`	Reduced-Rank Approach (RRA)	He et al. (2023, MS)
`spca_est()`	Scaled PCA (sPCA)	Huang et al. (2022, MS)
`ipca_est()`	Instrumented PCA (IPCA)	Kelly, Pruitt & Su (2019, JFE)

All estimators return S3 objects with print(), summary(), and predict() methods.

Quick start

library(sdim)

set.seed(42)
X   <- matrix(rnorm(200 * 20), 200, 20)
ret <- matrix(rnorm(200 * 30) / 100, 200, 30)

PCA, PLS, and RRA

These methods take a multivariate target (T × N returns) and a matrix of factor proxies (T × L):

fit_pca <- pca_est(target = ret, X = X, nfac = 3)
fit_pls <- pls_est(target = ret, X = X, nfac = 3)
fit_rra <- rra_est(target = ret, X = X, nfac = 3)

print(fit_rra)
#> <sdim_fit [rra]>
#>  Observations : 200 
#>  Predictors   : 20 
#>  Factors      : 3

Scaled PCA

sPCA takes a univariate target and scales each predictor by its OLS slope on the target before extracting principal components. When length(target) < nrow(X), the first length(target) rows are used for the scaling regression while all rows are used for factor extraction — this supports the predictive alignment needed in out-of-sample forecasting.

y <- rnorm(200)

fit_spca <- spca_est(target = y, X = X, nfac = 3)
print(fit_spca)
#> <sdim_spca>
#>  Observations : 200 
#>  Predictors   : 20 
#>  Factors      : 3

IPCA

IPCA extracts latent factors from panel data using time-varying characteristics as instruments:

TT <- 120 
K <- 50
n_chars <- 6
ret_panel <- matrix(rnorm(TT * K) / 100, TT, K)
Z <- array(rnorm(TT * K * n_chars), dim = c(TT, K, n_chars))

fit_ipca <- ipca_est(ret_panel, Z, nfac = 3)
#> Warning in ipca_als_cpp(ret_list, z_list, K = nfac, max_iter = max_iter, :
#> ipca_est: ALS did not converge in 100 iterations
print(fit_ipca)
#> <sdim_fit [ipca]>
#>  Observations    : 120 
#>  Characteristics : 6 
#>  Factors         : 3 
#>  Factor mean     : zero

Prediction

Use predict() to project new data onto the estimated factor loadings:

X_new <- matrix(rnorm(5 * 20), 5, 20)

# PCA projection
F_new <- predict(fit_pca, X_new)
dim(F_new)
#> [1] 5 3

# sPCA projection (standardizes newdata using training parameters)
F_spca_new <- predict(fit_spca, X_new)
dim(F_spca_new)
#> [1] 5 3

Factor evaluation

Evaluate extracted factors using the metrics from He et al. (2023, §2.4):

eval_factors(ret = ret, factors = fit_rra$factors)
#> Factor Evaluation
#> ---------------------------------------- 
#>  Portfolios       30
#>  Factors          3
#> 
#> Performance (He et al., 2023, §2.4)
#> ---------------------------------------- 
#>  RMSPE              0.9875  (%)
#>  Total adj-R²       2.9593  (%)
#>  SR                 0.0522
#>  A2R                0.9443

Bundled datasets

The package ships with datasets for replication:

grunfeld: Grunfeld (1958) investment panel (11 firms, 20 years) — used for IPCA validation.
he2023_*: Seven datasets from He et al. (2023) — factor proxies and portfolio returns.
huang2022_macro: 720 × 123 matrix of transformed FRED-MD predictors from Huang et al. (2022).
huang2022_ip: IP growth target for the Huang et al. (2022) out-of-sample exercise.

See vignette("ipca-grunfeld"), vignette("he2023-table3"), and vignette("huang2022-table4") for full examples.