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inst/plans/2026-04-18-ipca.md
In sdim: An R Package for Supervised Dimension Reduction
IPCA Implementation Plan
For agentic workers: REQUIRED SUB-SKILL: Use superpowers:subagent-driven-development (recommended) or superpowers:executing-plans to implement this plan task-by-task. Steps use checkbox (- [ ]) syntax for tracking.
Goal: Add ipca_est() to the sdim R package as a native R + RcppArmadillo implementation of Instrumented PCA (Kelly, Pruitt & Su 2019).
Architecture: Input validation in R builds per-period observation lists; a single Rcpp function runs the full ALS loop using RcppArmadillo; the R wrapper wraps the result into an sdim_fit object with the standard lambda/eigvals/factors fields so all existing display/evaluation functions work unchanged.
Tech Stack: R (≥ 4.1.0), Rcpp, RcppArmadillo, testthat 3
File Map
| File | Action | Responsibility |
|---|---|---|
| DESCRIPTION | Modify | Add Rcpp to Imports, Rcpp + RcppArmadillo to LinkingTo |
| NAMESPACE | Modify | Add useDynLib + importFrom(Rcpp, sourceRcpp) |
| src/ipca_als.cpp | Create | Full ALS loop: factor step, loading step, normalization |
| R/ipca_est.R | Create | Input validation, data prep, calls Rcpp, builds sdim_fit |
| R/sdim_fit.R | Modify | Add "ipca" branch in print.sdim_fit; label fix in print.summary.sdim_fit |
| tests/testthat/test-ipca_est.R | Create | All tests for ipca_est |
Task 1: Package infrastructure (DESCRIPTION, NAMESPACE, src/)
Files:
- Modify: DESCRIPTION
- Modify: NAMESPACE
- Create: src/ directory (empty placeholder)
- [ ] Step 1.1: Add Rcpp dependencies to DESCRIPTION
Open DESCRIPTION. Change the Imports line from:
Imports: stats, graphics
to:
Imports: stats, graphics, Rcpp
Add a new line after Imports:
LinkingTo: Rcpp, RcppArmadillo
Note: RcppArmadillo goes in LinkingTo only, not Imports.
- [ ] Step 1.2: Update NAMESPACE
Open NAMESPACE. Add these three lines (anywhere in the file):
useDynLib(sdim, .registration = TRUE)
importFrom(Rcpp, sourceRcpp)
export(ipca_est)
Note: useDynLib requires a compiled shared library to exist. Step 1.3 creates a minimal stub so load_all() can compile it before ipca_als.cpp is written.
- [ ] Step 1.3: Create src/ directory with a compilation stub
bash
mkdir -p src
Create src/stub.cpp with the following content (required so devtools::load_all() has something to compile against useDynLib):
cpp
// placeholder — will be superseded by ipca_als.cpp in Task 2
#include <Rcpp.h>
- [ ] Step 1.4: Verify package compiles and loads
r
devtools::load_all()
Expected: package compiles stub.cpp and loads without errors.
- [ ] Step 1.5: Commit
bash
git add DESCRIPTION NAMESPACE src/stub.cpp
git commit -m "feat: add Rcpp/RcppArmadillo package infrastructure"
Task 2: Rcpp ALS core
Files:
- Create: src/ipca_als.cpp
This is the performance-critical inner loop. It receives two R lists (one vector per time period, one matrix per time period), runs ALS, and returns Gamma, F, and singular values.
- [ ] Step 2.1: Create
src/ipca_als.cpp
```cpp
// [[Rcpp::depends(RcppArmadillo)]]
#include
using namespace Rcpp;
// [[Rcpp::export]]
List ipca_als_cpp(List ret_list, List Z_list,
int K, int max_iter, double tol) {
int T = ret_list.size();
// --- Determine L from first non-empty Z_t ---
int L = 0;
for (int t = 0; t < T; t++) {
arma::mat Zt = as<arma::mat>(Z_list[t]);
if (Zt.n_rows > 0) { L = Zt.n_cols; break; }
}
// --- Initialization: build M (L x T), column t = Z_t' r_t ---
arma::mat M(L, T, arma::fill::zeros);
for (int t = 0; t < T; t++) {
arma::vec rt = as<arma::vec>(ret_list[t]);
arma::mat Zt = as<arma::mat>(Z_list[t]);
if (rt.n_elem > 0) M.col(t) = Zt.t() * rt;
}
arma::mat U; arma::vec s_init; arma::mat V_init;
arma::svd_econ(U, s_init, V_init, M);
arma::mat Gamma = U.cols(0, K - 1); // L x K
arma::mat F_mat(T, K, arma::fill::zeros);
arma::mat Gamma_old = Gamma;
arma::vec sv(K);
bool converged = false;
for (int iter = 0; iter < max_iter; iter++) {
// --- Factor step: solve K x K system for each t ---
for (int t = 0; t < T; t++) {
arma::vec rt = as<arma::vec>(ret_list[t]);
arma::mat Zt = as<arma::mat>(Z_list[t]);
if (rt.n_elem == 0) continue;
arma::mat A = Gamma.t() * Zt.t() * Zt * Gamma; // K x K
arma::vec b = Gamma.t() * Zt.t() * rt; // K x 1
arma::vec ft;
// arma::solve returns false (does not throw) when no_approx is absent
bool ok = arma::solve(ft, A, b, arma::solve_opts::likely_sympd);
if (!ok) {
// Ridge fallback for near-singular A
A.diag() += 1e-8;
ft = arma::solve(A, b);
}
F_mat.row(t) = ft.t();
}
// --- Loading step: Kronecker-vectorized pooled OLS (Kelly et al. eq. 12) ---
// vec(Gamma) = LHS^{-1} RHS
// LHS = sum_t kron(f_t f_t', Z_t' Z_t) [KL x KL]
// RHS = vec( sum_t Z_t' r_t f_t' ) [KL x 1]
// Armadillo is column-major: vec stacks columns of L x K Gamma.
// kron order: kron(K x K, L x L) = KL x KL — consistent with vec(Gamma).
arma::mat LHS(K * L, K * L, arma::fill::zeros);
arma::mat RHS_mat(L, K, arma::fill::zeros);
for (int t = 0; t < T; t++) {
arma::vec rt = as<arma::vec>(ret_list[t]);
arma::mat Zt = as<arma::mat>(Z_list[t]);
if (rt.n_elem == 0) continue;
arma::vec ft = F_mat.row(t).t();
LHS += arma::kron(ft * ft.t(), Zt.t() * Zt);
RHS_mat += Zt.t() * rt * ft.t();
}
arma::vec rhs_vec = arma::vectorise(RHS_mat); // stacks columns
arma::vec g_vec = arma::solve(LHS, rhs_vec);
Gamma = arma::reshape(g_vec, L, K); // fills columns
// --- Normalize: thin SVD of Gamma ---
arma::mat Usvd, Vsvd;
arma::svd_econ(Usvd, sv, Vsvd, Gamma);
Gamma = Usvd.cols(0, K - 1); // L x K, Gamma'Gamma = I_K
// Rotate F to preserve fitted values: F_new = F * V * diag(sv)
F_mat = F_mat * Vsvd * arma::diagmat(sv);
// Sign convention: flip so largest-abs element of each Gamma column is positive
for (int k = 0; k < K; k++) {
arma::uword idx;
arma::abs(Gamma.col(k)).max(idx);
if (Gamma(idx, k) < 0.0) {
Gamma.col(k) *= -1.0;
F_mat.col(k) *= -1.0;
}
}
// --- Convergence ---
double diff = arma::norm(Gamma - Gamma_old, "fro");
Gamma_old = Gamma;
if (diff < tol) { converged = true; break; }
}
if (!converged) {
Rcpp::warning("ipca_est: ALS did not converge in %d iterations", max_iter);
}
return List::create(Named("Gamma") = Gamma,
Named("F") = F_mat,
Named("sv") = sv);
}
```
- [ ] Step 2.2: Compile and verify no build errors
r
devtools::load_all()
Expected: package loads, ipca_als_cpp is available.
Fix any compiler errors before proceeding.
- [ ] Step 2.3: Smoke-test the Rcpp function directly
r
set.seed(1)
T <- 50; N <- 20; L <- 5; K <- 2
ret <- matrix(rnorm(T * N), T, N)
Z <- array(rnorm(T * N * L), dim = c(T, N, L))
ret_list <- lapply(seq_len(T), function(t) ret[t, ])
Z_list <- lapply(seq_len(T), function(t) matrix(Z[t, , ], N, L))
res <- ipca_als_cpp(ret_list, Z_list, K = K, max_iter = 100, tol = 1e-6)
stopifnot(dim(res$Gamma) == c(L, K))
stopifnot(dim(res$F) == c(T, K))
stopifnot(length(res$sv) == K)
cat("Smoke test passed\n")
Expected: Smoke test passed.
- [ ] Step 2.4: Commit
bash
git rm src/stub.cpp
git add src/ipca_als.cpp
git commit -m "feat: add Rcpp ALS core for IPCA"
Task 3: R wrapper ipca_est()
Files:
- Create: R/ipca_est.R
The R wrapper validates inputs, builds ret_list/Z_list, calls ipca_als_cpp, and returns an sdim_fit.
- [ ] Step 3.1: Write failing tests first
Create tests/testthat/test-ipca_est.R with only the structural tests for now (full test suite comes in Task 5):
r
test_that("ipca_est returns sdim_fit with correct dimensions", {
set.seed(42)
T <- 50; N <- 15; L <- 5; K <- 2
ret <- matrix(rnorm(T * N) / 100, T, N)
Z <- array(rnorm(T * N * L), dim = c(T, N, L))
fit <- ipca_est(ret, Z, nfac = K)
expect_s3_class(fit, "sdim_fit")
expect_equal(fit$method, "ipca")
expect_equal(dim(fit$factors), c(T, K))
expect_equal(dim(fit$lambda), c(L, K))
expect_length(fit$eigvals, K)
expect_false(is.null(fit$call))
})
- [ ] Step 3.2: Run test to verify it fails
r
devtools::load_all()
devtools::test(filter = "ipca_est")
Expected: FAIL — could not find function "ipca_est".
- [ ] Step 3.3: Create
R/ipca_est.R
```r
#' IPCA factor extraction
#'
#' @param ret Numeric matrix (T x N) of asset returns. Use \code{NA} for
#' missing observations (unbalanced panel).
#' @param Z Numeric array (T x N x L) of asset characteristics. \code{NA}s
#' must mirror \code{ret} exactly.
#' @param nfac Positive integer; number of latent factors K to extract.
#' @param max_iter Maximum ALS iterations (default 100).
#' @param tol Convergence tolerance on Frobenius norm of loading change
#' (default 1e-6).
#'
#' @return An object of class \code{"sdim_fit"} with fields:
#' \code{factors} (T x K), \code{lambda} (L x K characteristic loadings,
#' i.e. Gamma in Kelly et al.), \code{eigvals} (singular values of Gamma),
#' \code{call}, \code{method = "ipca"}, \code{nfac}.
#' @references Kelly, Pruitt, Su (2019) \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)
#' @export
ipca_est <- function(ret, Z, nfac, max_iter = 100, tol = 1e-6) {
cl <- match.call()
# --- Input validation ---
if (!is.matrix(ret) || !is.numeric(ret))
stop("`ret` must be a numeric matrix.", call. = FALSE)
if (!is.array(Z) || length(dim(Z)) != 3L || !is.numeric(Z))
stop("`Z` must be a 3-dimensional numeric array.", call. = FALSE)
T_obs <- nrow(ret)
N <- ncol(ret)
L <- dim(Z)[3L]
if (dim(Z)[1L] != T_obs || dim(Z)[2L] != N)
stop("`Z` dimensions [T, N, L] must match `ret` dimensions [T, N].", call. = FALSE)
if (!is.numeric(nfac) || length(nfac) != 1L || is.na(nfac) || nfac < 1L)
stop("`nfac` must be a positive integer.", call. = FALSE)
nfac <- as.integer(nfac)
if (nfac > L)
stop("`nfac` cannot exceed the number of characteristics L.", call. = FALSE)
# Check NAs mirror between ret and Z
na_ret <- is.na(ret)
for (l in seq_len(L)) {
if (!identical(na_ret, is.na(Z[, , l])))
stop("NAs in `Z` must mirror NAs in `ret` (same positions).", call. = FALSE)
}
# Build per-period lists; validate N_t >= K
ret_list <- vector("list", T_obs)
Z_list <- vector("list", T_obs)
for (t in seq_len(T_obs)) {
obs <- which(!is.na(ret[t, ]))
if (length(obs) < nfac)
stop(sprintf(
"Time period %d has %d observed assets, fewer than nfac = %d.",
t, length(obs), nfac), call. = FALSE)
ret_list[[t]] <- ret[t, obs]
Z_list[[t]] <- matrix(Z[t, obs, ], nrow = length(obs), ncol = L)
}
# --- Call Rcpp ALS ---
res <- ipca_als_cpp(ret_list, Z_list, K = nfac,
max_iter = max_iter, tol = tol)
structure(
list(method = "ipca",
call = cl,
factors = res[["F"]],
lambda = res[["Gamma"]],
eigvals = as.numeric(res[["sv"]]),
nfac = nfac),
class = "sdim_fit"
)
}
```
- [ ] Step 3.4: Run the test to verify it passes
r
devtools::load_all()
devtools::test(filter = "ipca_est")
Expected: PASS.
- [ ] Step 3.5: Commit
bash
git add R/ipca_est.R tests/testthat/test-ipca_est.R
git commit -m "feat: add ipca_est R wrapper"
Task 4: Display methods in sdim_fit.R
Files:
- Modify: R/sdim_fit.R
Two targeted edits: add an "ipca" branch to print.sdim_fit, and fix the "Predictors" label in print.summary.sdim_fit.
- [ ] Step 4.1: Write failing display tests
Add to tests/testthat/test-ipca_est.R:
```r
test_that("print.sdim_fit shows Characteristics for ipca", {
set.seed(1)
ret <- matrix(rnorm(40 * 8) / 100, 40, 8)
Z <- array(rnorm(40 * 8 * 4), dim = c(40, 8, 4))
fit <- ipca_est(ret, Z, nfac = 2)
out <- capture.output(print(fit))
expect_true(any(grepl("Characteristics", out)))
expect_false(any(grepl("Predictors", out)))
})
test_that("summary.sdim_fit shows Characteristics for ipca", {
set.seed(1)
ret <- matrix(rnorm(40 * 8) / 100, 40, 8)
Z <- array(rnorm(40 * 8 * 4), dim = c(40, 8, 4))
fit <- ipca_est(ret, Z, nfac = 2)
out <- capture.output(summary(fit))
expect_true(any(grepl("Characteristics", out)))
expect_true(any(grepl("IPCA", out)))
})
```
- [ ] Step 4.2: Run to verify they fail
r
devtools::load_all()
devtools::test(filter = "ipca_est")
Expected: the two new display tests FAIL (output says "Predictors", not "Characteristics").
- [ ] Step 4.3: Add
"ipca" branch to print.sdim_fit
In R/sdim_fit.R, replace the body of print.sdim_fit (lines 2–10):
```r
#' @export
print.sdim_fit <- function(x, ...) {
if (x$method == "ipca") {
cat(sprintf("<sdim_fit [%s]>\n", x$method))
cat(" Observations :", nrow(x$factors), "\n")
cat(" Characteristics :", nrow(x$lambda), "\n")
cat(" Factors :", ncol(x$factors), "\n")
return(invisible(x))
}
cat(sprintf("<sdim_fit [%s]>\n", x$method))
cat(" Observations :", nrow(x$factors), "\n")
cat(" Predictors :", nrow(x$lambda), "\n")
cat(" Factors :", ncol(x$factors), "\n")
invisible(x)
}
```
- [ ] Step 4.4: Add
"ipca" to method_label switch and fix Dimensions label
In print.summary.sdim_fit (around line 43–48), add ipca to the switch:
r
method_label <- switch(x$method,
pca = "Principal Component Analysis (PCA)",
pls = "Partial Least Squares (PLS)",
rra = "Reduced-Rank Approach (RRA)",
ipca = "Instrumented Principal Components Analysis (IPCA)",
toupper(x$method)
)
Then find the Dimensions block line that prints "Predictors" (around line 57–58):
r
cat(sprintf(" %-16s %d\n", "Predictors", x$n_pred))
Replace it with:
r
pred_label <- if (x$method == "ipca") "Characteristics" else "Predictors"
cat(sprintf(" %-16s %d\n", pred_label, x$n_pred))
- [ ] Step 4.5: Run tests to verify they pass
r
devtools::load_all()
devtools::test(filter = "ipca_est")
Expected: all tests PASS.
- [ ] Step 4.6: Run full test suite to confirm no regressions
r
devtools::test()
Expected: all tests PASS (no existing test broken).
- [ ] Step 4.7: Commit
bash
git add R/sdim_fit.R tests/testthat/test-ipca_est.R
git commit -m "feat: add ipca display methods to sdim_fit"
Task 5: Full test suite
Files:
- Modify: tests/testthat/test-ipca_est.R
Add the remaining tests: input validation, algorithm correctness, edge cases.
- [ ] Step 5.1: Add input validation tests
Append to tests/testthat/test-ipca_est.R:
``r
test_that("ipca_est errors on non-matrix ret", {
Z <- array(rnorm(50 * 10 * 4), dim = c(50, 10, 4))
expect_error(ipca_est(as.data.frame(matrix(1, 50, 10)), Z, nfac = 2),
"ret` must be a numeric matrix")
})
test_that("ipca_est errors on non-array Z", {
ret <- matrix(rnorm(50 * 10), 50, 10)
expect_error(ipca_est(ret, matrix(1, 50, 10), nfac = 2),
"Z must be a 3-dimensional numeric array")
})
test_that("ipca_est errors on dimension mismatch", {
ret <- matrix(rnorm(50 * 10), 50, 10)
Z_bad <- array(rnorm(50 * 9 * 4), dim = c(50, 9, 4)) # N mismatch
expect_error(ipca_est(ret, Z_bad, nfac = 2),
"dimensions")
})
test_that("ipca_est errors when nfac > L", {
ret <- matrix(rnorm(50 * 10), 50, 10)
Z <- array(rnorm(50 * 10 * 3), dim = c(50, 10, 3))
expect_error(ipca_est(ret, Z, nfac = 5),
"nfac cannot exceed")
})
test_that("ipca_est errors when N_t < nfac", {
set.seed(1)
T <- 50; N <- 10; L <- 4; K <- 3
ret <- matrix(rnorm(T * N) / 100, T, N)
Z <- array(rnorm(T * N * L), dim = c(T, N, L))
# Force period 1 to have only 2 observed assets (< K=3)
ret[1, 3:N] <- NA
Z[1, 3:N, ] <- NA
expect_error(ipca_est(ret, Z, nfac = K),
"fewer than nfac")
})
test_that("ipca_est errors when Z NAs don't mirror ret", {
set.seed(1)
ret <- matrix(rnorm(50 * 10) / 100, 50, 10)
Z <- array(rnorm(50 * 10 * 4), dim = c(50, 10, 4))
ret[1, 1] <- NA # NA in ret
# Z[1,1,] left as non-NA — mismatch
expect_error(ipca_est(ret, Z, nfac = 2),
"NAs in Z must mirror")
})
```
- [ ] Step 5.2: Run validation tests
r
devtools::load_all()
devtools::test(filter = "ipca_est")
Expected: all validation tests PASS.
- [ ] Step 5.3: Add algorithm correctness tests
```r
test_that("ipca_est recovers true factor structure up to rotation", {
set.seed(123)
T <- 200; N <- 50; L <- 6; K <- 2
# True Gamma (L x K) and F (T x K)
Gamma_true <- matrix(rnorm(L * K), L, K)
F_true <- matrix(rnorm(T * K), T, K)
# Characteristics: random
Z <- array(rnorm(T * N * L), dim = c(T, N, L))
# Returns: r_{i,t} = z_{i,t}' Gamma_true f_t + noise
ret <- matrix(0, T, N)
for (t in seq_len(T)) {
Zt <- matrix(Z[t, , ], N, L)
ret[t, ] <- Zt %*% Gamma_true %*% F_true[t, ] + rnorm(N, sd = 0.1)
}
fit <- ipca_est(ret, Z, nfac = K, max_iter = 200)
# Rotation-invariant check: Gamma Gamma' should be close to Gamma_true Gamma_true'
# (up to scale since normalization sets Gamma'Gamma = I)
GG_fit <- fit$lambda %*% t(fit$lambda)
GG_true <- Gamma_true %*% solve(t(Gamma_true) %*% Gamma_true) %*% t(Gamma_true)
expect_lt(norm(GG_fit - GG_true, "F") / norm(GG_true, "F"), 0.3)
})
test_that("eval_factors works unchanged on ipca output", {
set.seed(42)
ret <- matrix(rnorm(60 * 12) / 100, 60, 12)
Z <- array(rnorm(60 * 12 * 4), dim = c(60, 12, 4))
fit <- ipca_est(ret, Z, nfac = 2)
expect_no_error(eval_factors(ret = ret, factors = fit$factors))
})
test_that("non-convergence triggers a warning", {
set.seed(1)
ret <- matrix(rnorm(40 * 10) / 100, 40, 10)
Z <- array(rnorm(40 * 10 * 4), dim = c(40, 10, 4))
expect_warning(ipca_est(ret, Z, nfac = 2, max_iter = 1),
"did not converge")
})
```
- [ ] Step 5.4: Add edge case tests
```r
test_that("ipca_est works with nfac = 1", {
set.seed(7)
ret <- matrix(rnorm(50 * 10) / 100, 50, 10)
Z <- array(rnorm(50 * 10 * 4), dim = c(50, 10, 4))
fit <- ipca_est(ret, Z, nfac = 1)
expect_equal(dim(fit$factors), c(50L, 1L))
expect_equal(dim(fit$lambda), c(4L, 1L))
})
test_that("ipca_est works with nfac = L (square Gamma)", {
set.seed(8)
L <- 4
ret <- matrix(rnorm(50 * 10) / 100, 50, 10)
Z <- array(rnorm(50 * 10 * L), dim = c(50, 10, L))
fit <- ipca_est(ret, Z, nfac = L)
expect_equal(dim(fit$lambda), c(L, L))
})
test_that("ipca_est handles unbalanced panel (10% NAs)", {
set.seed(99)
T <- 60; N <- 20; L <- 4; K <- 2
ret <- matrix(rnorm(T * N) / 100, T, N)
Z <- array(rnorm(T * N * L), dim = c(T, N, L))
# Introduce 10% missing — ensure each period keeps at least K observed assets
n_missing <- floor(0.10 * T * N)
# Pick (t, n) pairs where period t will still have >= K+1 obs after removal
candidates <- which(rowSums(!is.na(ret)) > K + 1, arr.ind = FALSE)
# Randomly pick cells from rows with enough obs
set.seed(99)
for (i in seq_len(n_missing)) {
t_idx <- sample(which(rowSums(!is.na(ret)) > K + 1), 1)
n_idx <- sample(which(!is.na(ret[t_idx, ])), 1)
ret[t_idx, n_idx] <- NA
Z[t_idx, n_idx, ] <- NA
}
fit <- ipca_est(ret, Z, nfac = K)
expect_equal(dim(fit$factors), c(T, K))
})
test_that("print.sdim_list works with mixed rra and ipca fits", {
set.seed(5)
X <- matrix(rnorm(60 * 6), 60, 6)
ret <- matrix(rnorm(60 * 10) / 100, 60, 10)
Z <- array(rnorm(60 * 10 * 6), dim = c(60, 10, 6))
fit_rra <- rra_est(target = ret, X = X, nfac = 2)
fit_ipca <- ipca_est(ret, Z, nfac = 2)
sdl <- structure(list(rra = fit_rra, ipca = fit_ipca), class = "sdim_list")
expect_no_error(print(sdl))
})
```
- [ ] Step 5.5: Run full test suite
r
devtools::load_all()
devtools::test()
Expected: all tests PASS, including all pre-existing tests.
- [ ] Step 5.6: Commit
bash
git add tests/testthat/test-ipca_est.R
git commit -m "test: add full test suite for ipca_est"
Task 6: Package polish
- [ ] Step 6.1: Update DESCRIPTION description field
In DESCRIPTION, update the Description: field to mention IPCA:
Description: Implements five factor extraction methods for asset pricing and
macroeconomic forecasting: principal component analysis (PCA), partial
least squares (PLS), scaled PCA (sPCA) of Huang, Jiang, Li, Tong, and
Zhou (2022) <doi:10.1287/mnsc.2021.4020>, the reduced-rank approach
(RRA) of He, Huang, Li, and Zhou (2023) <doi:10.1287/mnsc.2022.4563>,
and Instrumented PCA (IPCA) of Kelly, Pruitt, and Su (2019)
<doi:10.1016/j.jfineco.2019.05.001>.
- [ ] Step 6.2: Run
R CMD check
bash
Rscript -e "devtools::check()"
Expected: 0 errors, 0 warnings. Notes about useDynLib registration are acceptable.
- [ ] Step 6.3: Final commit
bash
git add DESCRIPTION
git commit -m "docs: update DESCRIPTION to include IPCA"
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IPCA Implementation Plan
For agentic workers: REQUIRED SUB-SKILL: Use superpowers:subagent-driven-development (recommended) or superpowers:executing-plans to implement this plan task-by-task. Steps use checkbox (
- [ ]) syntax for tracking.
Goal: Add ipca_est() to the sdim R package as a native R + RcppArmadillo implementation of Instrumented PCA (Kelly, Pruitt & Su 2019).
Architecture: Input validation in R builds per-period observation lists; a single Rcpp function runs the full ALS loop using RcppArmadillo; the R wrapper wraps the result into an sdim_fit object with the standard lambda/eigvals/factors fields so all existing display/evaluation functions work unchanged.
Tech Stack: R (≥ 4.1.0), Rcpp, RcppArmadillo, testthat 3
File Map
| File | Action | Responsibility |
|---|---|---|
| DESCRIPTION | Modify | Add Rcpp to Imports, Rcpp + RcppArmadillo to LinkingTo |
| NAMESPACE | Modify | Add useDynLib + importFrom(Rcpp, sourceRcpp) |
| src/ipca_als.cpp | Create | Full ALS loop: factor step, loading step, normalization |
| R/ipca_est.R | Create | Input validation, data prep, calls Rcpp, builds sdim_fit |
| R/sdim_fit.R | Modify | Add "ipca" branch in print.sdim_fit; label fix in print.summary.sdim_fit |
| tests/testthat/test-ipca_est.R | Create | All tests for ipca_est |
Task 1: Package infrastructure (DESCRIPTION, NAMESPACE, src/)
Files:
- Modify: DESCRIPTION
- Modify: NAMESPACE
- Create: src/ directory (empty placeholder)
- [ ] Step 1.1: Add Rcpp dependencies to DESCRIPTION
Open DESCRIPTION. Change the Imports line from:
Imports: stats, graphics
to:
Imports: stats, graphics, Rcpp
Add a new line after Imports:
LinkingTo: Rcpp, RcppArmadillo
Note: RcppArmadillo goes in LinkingTo only, not Imports.
- [ ] Step 1.2: Update NAMESPACE
Open NAMESPACE. Add these three lines (anywhere in the file):
useDynLib(sdim, .registration = TRUE)
importFrom(Rcpp, sourceRcpp)
export(ipca_est)
Note: useDynLib requires a compiled shared library to exist. Step 1.3 creates a minimal stub so load_all() can compile it before ipca_als.cpp is written.
- [ ] Step 1.3: Create src/ directory with a compilation stub
bash
mkdir -p src
Create src/stub.cpp with the following content (required so devtools::load_all() has something to compile against useDynLib):
cpp
// placeholder — will be superseded by ipca_als.cpp in Task 2
#include <Rcpp.h>
- [ ] Step 1.4: Verify package compiles and loads
r
devtools::load_all()
Expected: package compiles stub.cpp and loads without errors.
- [ ] Step 1.5: Commit
bash
git add DESCRIPTION NAMESPACE src/stub.cpp
git commit -m "feat: add Rcpp/RcppArmadillo package infrastructure"
Task 2: Rcpp ALS core
Files:
- Create: src/ipca_als.cpp
This is the performance-critical inner loop. It receives two R lists (one vector per time period, one matrix per time period), runs ALS, and returns Gamma, F, and singular values.
- [ ] Step 2.1: Create
src/ipca_als.cpp
```cpp // [[Rcpp::depends(RcppArmadillo)]] #include using namespace Rcpp;
// [[Rcpp::export]] List ipca_als_cpp(List ret_list, List Z_list, int K, int max_iter, double tol) {
int T = ret_list.size();
// --- Determine L from first non-empty Z_t ---
int L = 0;
for (int t = 0; t < T; t++) {
arma::mat Zt = as<arma::mat>(Z_list[t]);
if (Zt.n_rows > 0) { L = Zt.n_cols; break; }
}
// --- Initialization: build M (L x T), column t = Z_t' r_t ---
arma::mat M(L, T, arma::fill::zeros);
for (int t = 0; t < T; t++) {
arma::vec rt = as<arma::vec>(ret_list[t]);
arma::mat Zt = as<arma::mat>(Z_list[t]);
if (rt.n_elem > 0) M.col(t) = Zt.t() * rt;
}
arma::mat U; arma::vec s_init; arma::mat V_init;
arma::svd_econ(U, s_init, V_init, M);
arma::mat Gamma = U.cols(0, K - 1); // L x K
arma::mat F_mat(T, K, arma::fill::zeros);
arma::mat Gamma_old = Gamma;
arma::vec sv(K);
bool converged = false;
for (int iter = 0; iter < max_iter; iter++) {
// --- Factor step: solve K x K system for each t ---
for (int t = 0; t < T; t++) {
arma::vec rt = as<arma::vec>(ret_list[t]);
arma::mat Zt = as<arma::mat>(Z_list[t]);
if (rt.n_elem == 0) continue;
arma::mat A = Gamma.t() * Zt.t() * Zt * Gamma; // K x K
arma::vec b = Gamma.t() * Zt.t() * rt; // K x 1
arma::vec ft;
// arma::solve returns false (does not throw) when no_approx is absent
bool ok = arma::solve(ft, A, b, arma::solve_opts::likely_sympd);
if (!ok) {
// Ridge fallback for near-singular A
A.diag() += 1e-8;
ft = arma::solve(A, b);
}
F_mat.row(t) = ft.t();
}
// --- Loading step: Kronecker-vectorized pooled OLS (Kelly et al. eq. 12) ---
// vec(Gamma) = LHS^{-1} RHS
// LHS = sum_t kron(f_t f_t', Z_t' Z_t) [KL x KL]
// RHS = vec( sum_t Z_t' r_t f_t' ) [KL x 1]
// Armadillo is column-major: vec stacks columns of L x K Gamma.
// kron order: kron(K x K, L x L) = KL x KL — consistent with vec(Gamma).
arma::mat LHS(K * L, K * L, arma::fill::zeros);
arma::mat RHS_mat(L, K, arma::fill::zeros);
for (int t = 0; t < T; t++) {
arma::vec rt = as<arma::vec>(ret_list[t]);
arma::mat Zt = as<arma::mat>(Z_list[t]);
if (rt.n_elem == 0) continue;
arma::vec ft = F_mat.row(t).t();
LHS += arma::kron(ft * ft.t(), Zt.t() * Zt);
RHS_mat += Zt.t() * rt * ft.t();
}
arma::vec rhs_vec = arma::vectorise(RHS_mat); // stacks columns
arma::vec g_vec = arma::solve(LHS, rhs_vec);
Gamma = arma::reshape(g_vec, L, K); // fills columns
// --- Normalize: thin SVD of Gamma ---
arma::mat Usvd, Vsvd;
arma::svd_econ(Usvd, sv, Vsvd, Gamma);
Gamma = Usvd.cols(0, K - 1); // L x K, Gamma'Gamma = I_K
// Rotate F to preserve fitted values: F_new = F * V * diag(sv)
F_mat = F_mat * Vsvd * arma::diagmat(sv);
// Sign convention: flip so largest-abs element of each Gamma column is positive
for (int k = 0; k < K; k++) {
arma::uword idx;
arma::abs(Gamma.col(k)).max(idx);
if (Gamma(idx, k) < 0.0) {
Gamma.col(k) *= -1.0;
F_mat.col(k) *= -1.0;
}
}
// --- Convergence ---
double diff = arma::norm(Gamma - Gamma_old, "fro");
Gamma_old = Gamma;
if (diff < tol) { converged = true; break; }
}
if (!converged) {
Rcpp::warning("ipca_est: ALS did not converge in %d iterations", max_iter);
}
return List::create(Named("Gamma") = Gamma,
Named("F") = F_mat,
Named("sv") = sv);
} ```
- [ ] Step 2.2: Compile and verify no build errors
r
devtools::load_all()
Expected: package loads, ipca_als_cpp is available.
Fix any compiler errors before proceeding.
- [ ] Step 2.3: Smoke-test the Rcpp function directly
r
set.seed(1)
T <- 50; N <- 20; L <- 5; K <- 2
ret <- matrix(rnorm(T * N), T, N)
Z <- array(rnorm(T * N * L), dim = c(T, N, L))
ret_list <- lapply(seq_len(T), function(t) ret[t, ])
Z_list <- lapply(seq_len(T), function(t) matrix(Z[t, , ], N, L))
res <- ipca_als_cpp(ret_list, Z_list, K = K, max_iter = 100, tol = 1e-6)
stopifnot(dim(res$Gamma) == c(L, K))
stopifnot(dim(res$F) == c(T, K))
stopifnot(length(res$sv) == K)
cat("Smoke test passed\n")
Expected: Smoke test passed.
- [ ] Step 2.4: Commit
bash
git rm src/stub.cpp
git add src/ipca_als.cpp
git commit -m "feat: add Rcpp ALS core for IPCA"
Task 3: R wrapper ipca_est()
Files:
- Create: R/ipca_est.R
The R wrapper validates inputs, builds ret_list/Z_list, calls ipca_als_cpp, and returns an sdim_fit.
- [ ] Step 3.1: Write failing tests first
Create tests/testthat/test-ipca_est.R with only the structural tests for now (full test suite comes in Task 5):
r
test_that("ipca_est returns sdim_fit with correct dimensions", {
set.seed(42)
T <- 50; N <- 15; L <- 5; K <- 2
ret <- matrix(rnorm(T * N) / 100, T, N)
Z <- array(rnorm(T * N * L), dim = c(T, N, L))
fit <- ipca_est(ret, Z, nfac = K)
expect_s3_class(fit, "sdim_fit")
expect_equal(fit$method, "ipca")
expect_equal(dim(fit$factors), c(T, K))
expect_equal(dim(fit$lambda), c(L, K))
expect_length(fit$eigvals, K)
expect_false(is.null(fit$call))
})
- [ ] Step 3.2: Run test to verify it fails
r
devtools::load_all()
devtools::test(filter = "ipca_est")
Expected: FAIL — could not find function "ipca_est".
- [ ] Step 3.3: Create
R/ipca_est.R
```r #' IPCA factor extraction #' #' @param ret Numeric matrix (T x N) of asset returns. Use \code{NA} for #' missing observations (unbalanced panel). #' @param Z Numeric array (T x N x L) of asset characteristics. \code{NA}s #' must mirror \code{ret} exactly. #' @param nfac Positive integer; number of latent factors K to extract. #' @param max_iter Maximum ALS iterations (default 100). #' @param tol Convergence tolerance on Frobenius norm of loading change #' (default 1e-6). #' #' @return An object of class \code{"sdim_fit"} with fields: #' \code{factors} (T x K), \code{lambda} (L x K characteristic loadings, #' i.e. Gamma in Kelly et al.), \code{eigvals} (singular values of Gamma), #' \code{call}, \code{method = "ipca"}, \code{nfac}. #' @references Kelly, Pruitt, Su (2019) \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) #' @export ipca_est <- function(ret, Z, nfac, max_iter = 100, tol = 1e-6) {
cl <- match.call()
# --- Input validation ---
if (!is.matrix(ret) || !is.numeric(ret))
stop("`ret` must be a numeric matrix.", call. = FALSE)
if (!is.array(Z) || length(dim(Z)) != 3L || !is.numeric(Z))
stop("`Z` must be a 3-dimensional numeric array.", call. = FALSE)
T_obs <- nrow(ret)
N <- ncol(ret)
L <- dim(Z)[3L]
if (dim(Z)[1L] != T_obs || dim(Z)[2L] != N)
stop("`Z` dimensions [T, N, L] must match `ret` dimensions [T, N].", call. = FALSE)
if (!is.numeric(nfac) || length(nfac) != 1L || is.na(nfac) || nfac < 1L)
stop("`nfac` must be a positive integer.", call. = FALSE)
nfac <- as.integer(nfac)
if (nfac > L)
stop("`nfac` cannot exceed the number of characteristics L.", call. = FALSE)
# Check NAs mirror between ret and Z
na_ret <- is.na(ret)
for (l in seq_len(L)) {
if (!identical(na_ret, is.na(Z[, , l])))
stop("NAs in `Z` must mirror NAs in `ret` (same positions).", call. = FALSE)
}
# Build per-period lists; validate N_t >= K
ret_list <- vector("list", T_obs)
Z_list <- vector("list", T_obs)
for (t in seq_len(T_obs)) {
obs <- which(!is.na(ret[t, ]))
if (length(obs) < nfac)
stop(sprintf(
"Time period %d has %d observed assets, fewer than nfac = %d.",
t, length(obs), nfac), call. = FALSE)
ret_list[[t]] <- ret[t, obs]
Z_list[[t]] <- matrix(Z[t, obs, ], nrow = length(obs), ncol = L)
}
# --- Call Rcpp ALS ---
res <- ipca_als_cpp(ret_list, Z_list, K = nfac,
max_iter = max_iter, tol = tol)
structure(
list(method = "ipca",
call = cl,
factors = res[["F"]],
lambda = res[["Gamma"]],
eigvals = as.numeric(res[["sv"]]),
nfac = nfac),
class = "sdim_fit"
)
} ```
- [ ] Step 3.4: Run the test to verify it passes
r
devtools::load_all()
devtools::test(filter = "ipca_est")
Expected: PASS.
- [ ] Step 3.5: Commit
bash
git add R/ipca_est.R tests/testthat/test-ipca_est.R
git commit -m "feat: add ipca_est R wrapper"
Task 4: Display methods in sdim_fit.R
Files:
- Modify: R/sdim_fit.R
Two targeted edits: add an "ipca" branch to print.sdim_fit, and fix the "Predictors" label in print.summary.sdim_fit.
- [ ] Step 4.1: Write failing display tests
Add to tests/testthat/test-ipca_est.R:
```r test_that("print.sdim_fit shows Characteristics for ipca", { set.seed(1) ret <- matrix(rnorm(40 * 8) / 100, 40, 8) Z <- array(rnorm(40 * 8 * 4), dim = c(40, 8, 4)) fit <- ipca_est(ret, Z, nfac = 2) out <- capture.output(print(fit)) expect_true(any(grepl("Characteristics", out))) expect_false(any(grepl("Predictors", out))) })
test_that("summary.sdim_fit shows Characteristics for ipca", { set.seed(1) ret <- matrix(rnorm(40 * 8) / 100, 40, 8) Z <- array(rnorm(40 * 8 * 4), dim = c(40, 8, 4)) fit <- ipca_est(ret, Z, nfac = 2) out <- capture.output(summary(fit)) expect_true(any(grepl("Characteristics", out))) expect_true(any(grepl("IPCA", out))) }) ```
- [ ] Step 4.2: Run to verify they fail
r
devtools::load_all()
devtools::test(filter = "ipca_est")
Expected: the two new display tests FAIL (output says "Predictors", not "Characteristics").
- [ ] Step 4.3: Add
"ipca"branch toprint.sdim_fit
In R/sdim_fit.R, replace the body of print.sdim_fit (lines 2–10):
```r #' @export print.sdim_fit <- function(x, ...) {
if (x$method == "ipca") {
cat(sprintf("<sdim_fit [%s]>\n", x$method))
cat(" Observations :", nrow(x$factors), "\n")
cat(" Characteristics :", nrow(x$lambda), "\n")
cat(" Factors :", ncol(x$factors), "\n")
return(invisible(x))
}
cat(sprintf("<sdim_fit [%s]>\n", x$method))
cat(" Observations :", nrow(x$factors), "\n")
cat(" Predictors :", nrow(x$lambda), "\n")
cat(" Factors :", ncol(x$factors), "\n")
invisible(x)
} ```
- [ ] Step 4.4: Add
"ipca"tomethod_labelswitch and fix Dimensions label
In print.summary.sdim_fit (around line 43–48), add ipca to the switch:
r
method_label <- switch(x$method,
pca = "Principal Component Analysis (PCA)",
pls = "Partial Least Squares (PLS)",
rra = "Reduced-Rank Approach (RRA)",
ipca = "Instrumented Principal Components Analysis (IPCA)",
toupper(x$method)
)
Then find the Dimensions block line that prints "Predictors" (around line 57–58):
r
cat(sprintf(" %-16s %d\n", "Predictors", x$n_pred))
Replace it with:
r
pred_label <- if (x$method == "ipca") "Characteristics" else "Predictors"
cat(sprintf(" %-16s %d\n", pred_label, x$n_pred))
- [ ] Step 4.5: Run tests to verify they pass
r
devtools::load_all()
devtools::test(filter = "ipca_est")
Expected: all tests PASS.
- [ ] Step 4.6: Run full test suite to confirm no regressions
r
devtools::test()
Expected: all tests PASS (no existing test broken).
- [ ] Step 4.7: Commit
bash
git add R/sdim_fit.R tests/testthat/test-ipca_est.R
git commit -m "feat: add ipca display methods to sdim_fit"
Task 5: Full test suite
Files:
- Modify: tests/testthat/test-ipca_est.R
Add the remaining tests: input validation, algorithm correctness, edge cases.
- [ ] Step 5.1: Add input validation tests
Append to tests/testthat/test-ipca_est.R:
``r
test_that("ipca_est errors on non-matrix ret", {
Z <- array(rnorm(50 * 10 * 4), dim = c(50, 10, 4))
expect_error(ipca_est(as.data.frame(matrix(1, 50, 10)), Z, nfac = 2),
"ret` must be a numeric matrix")
})
test_that("ipca_est errors on non-array Z", {
ret <- matrix(rnorm(50 * 10), 50, 10)
expect_error(ipca_est(ret, matrix(1, 50, 10), nfac = 2),
"Z must be a 3-dimensional numeric array")
})
test_that("ipca_est errors on dimension mismatch", { ret <- matrix(rnorm(50 * 10), 50, 10) Z_bad <- array(rnorm(50 * 9 * 4), dim = c(50, 9, 4)) # N mismatch expect_error(ipca_est(ret, Z_bad, nfac = 2), "dimensions") })
test_that("ipca_est errors when nfac > L", {
ret <- matrix(rnorm(50 * 10), 50, 10)
Z <- array(rnorm(50 * 10 * 3), dim = c(50, 10, 3))
expect_error(ipca_est(ret, Z, nfac = 5),
"nfac cannot exceed")
})
test_that("ipca_est errors when N_t < nfac", { set.seed(1) T <- 50; N <- 10; L <- 4; K <- 3 ret <- matrix(rnorm(T * N) / 100, T, N) Z <- array(rnorm(T * N * L), dim = c(T, N, L)) # Force period 1 to have only 2 observed assets (< K=3) ret[1, 3:N] <- NA Z[1, 3:N, ] <- NA expect_error(ipca_est(ret, Z, nfac = K), "fewer than nfac") })
test_that("ipca_est errors when Z NAs don't mirror ret", {
set.seed(1)
ret <- matrix(rnorm(50 * 10) / 100, 50, 10)
Z <- array(rnorm(50 * 10 * 4), dim = c(50, 10, 4))
ret[1, 1] <- NA # NA in ret
# Z[1,1,] left as non-NA — mismatch
expect_error(ipca_est(ret, Z, nfac = 2),
"NAs in Z must mirror")
})
```
- [ ] Step 5.2: Run validation tests
r
devtools::load_all()
devtools::test(filter = "ipca_est")
Expected: all validation tests PASS.
- [ ] Step 5.3: Add algorithm correctness tests
```r test_that("ipca_est recovers true factor structure up to rotation", { set.seed(123) T <- 200; N <- 50; L <- 6; K <- 2
# True Gamma (L x K) and F (T x K)
Gamma_true <- matrix(rnorm(L * K), L, K)
F_true <- matrix(rnorm(T * K), T, K)
# Characteristics: random
Z <- array(rnorm(T * N * L), dim = c(T, N, L))
# Returns: r_{i,t} = z_{i,t}' Gamma_true f_t + noise
ret <- matrix(0, T, N)
for (t in seq_len(T)) {
Zt <- matrix(Z[t, , ], N, L)
ret[t, ] <- Zt %*% Gamma_true %*% F_true[t, ] + rnorm(N, sd = 0.1)
}
fit <- ipca_est(ret, Z, nfac = K, max_iter = 200)
# Rotation-invariant check: Gamma Gamma' should be close to Gamma_true Gamma_true'
# (up to scale since normalization sets Gamma'Gamma = I)
GG_fit <- fit$lambda %*% t(fit$lambda)
GG_true <- Gamma_true %*% solve(t(Gamma_true) %*% Gamma_true) %*% t(Gamma_true)
expect_lt(norm(GG_fit - GG_true, "F") / norm(GG_true, "F"), 0.3)
})
test_that("eval_factors works unchanged on ipca output", { set.seed(42) ret <- matrix(rnorm(60 * 12) / 100, 60, 12) Z <- array(rnorm(60 * 12 * 4), dim = c(60, 12, 4)) fit <- ipca_est(ret, Z, nfac = 2) expect_no_error(eval_factors(ret = ret, factors = fit$factors)) })
test_that("non-convergence triggers a warning", { set.seed(1) ret <- matrix(rnorm(40 * 10) / 100, 40, 10) Z <- array(rnorm(40 * 10 * 4), dim = c(40, 10, 4)) expect_warning(ipca_est(ret, Z, nfac = 2, max_iter = 1), "did not converge") }) ```
- [ ] Step 5.4: Add edge case tests
```r test_that("ipca_est works with nfac = 1", { set.seed(7) 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 = 1) expect_equal(dim(fit$factors), c(50L, 1L)) expect_equal(dim(fit$lambda), c(4L, 1L)) })
test_that("ipca_est works with nfac = L (square Gamma)", { set.seed(8) L <- 4 ret <- matrix(rnorm(50 * 10) / 100, 50, 10) Z <- array(rnorm(50 * 10 * L), dim = c(50, 10, L)) fit <- ipca_est(ret, Z, nfac = L) expect_equal(dim(fit$lambda), c(L, L)) })
test_that("ipca_est handles unbalanced panel (10% NAs)", { set.seed(99) T <- 60; N <- 20; L <- 4; K <- 2 ret <- matrix(rnorm(T * N) / 100, T, N) Z <- array(rnorm(T * N * L), dim = c(T, N, L))
# Introduce 10% missing — ensure each period keeps at least K observed assets
n_missing <- floor(0.10 * T * N)
# Pick (t, n) pairs where period t will still have >= K+1 obs after removal
candidates <- which(rowSums(!is.na(ret)) > K + 1, arr.ind = FALSE)
# Randomly pick cells from rows with enough obs
set.seed(99)
for (i in seq_len(n_missing)) {
t_idx <- sample(which(rowSums(!is.na(ret)) > K + 1), 1)
n_idx <- sample(which(!is.na(ret[t_idx, ])), 1)
ret[t_idx, n_idx] <- NA
Z[t_idx, n_idx, ] <- NA
}
fit <- ipca_est(ret, Z, nfac = K)
expect_equal(dim(fit$factors), c(T, K))
})
test_that("print.sdim_list works with mixed rra and ipca fits", { set.seed(5) X <- matrix(rnorm(60 * 6), 60, 6) ret <- matrix(rnorm(60 * 10) / 100, 60, 10) Z <- array(rnorm(60 * 10 * 6), dim = c(60, 10, 6))
fit_rra <- rra_est(target = ret, X = X, nfac = 2)
fit_ipca <- ipca_est(ret, Z, nfac = 2)
sdl <- structure(list(rra = fit_rra, ipca = fit_ipca), class = "sdim_list")
expect_no_error(print(sdl))
}) ```
- [ ] Step 5.5: Run full test suite
r
devtools::load_all()
devtools::test()
Expected: all tests PASS, including all pre-existing tests.
- [ ] Step 5.6: Commit
bash
git add tests/testthat/test-ipca_est.R
git commit -m "test: add full test suite for ipca_est"
Task 6: Package polish
- [ ] Step 6.1: Update DESCRIPTION description field
In DESCRIPTION, update the Description: field to mention IPCA:
Description: Implements five factor extraction methods for asset pricing and
macroeconomic forecasting: principal component analysis (PCA), partial
least squares (PLS), scaled PCA (sPCA) of Huang, Jiang, Li, Tong, and
Zhou (2022) <doi:10.1287/mnsc.2021.4020>, the reduced-rank approach
(RRA) of He, Huang, Li, and Zhou (2023) <doi:10.1287/mnsc.2022.4563>,
and Instrumented PCA (IPCA) of Kelly, Pruitt, and Su (2019)
<doi:10.1016/j.jfineco.2019.05.001>.
- [ ] Step 6.2: Run
R CMD check
bash
Rscript -e "devtools::check()"
Expected: 0 errors, 0 warnings. Notes about useDynLib registration are acceptable.
- [ ] Step 6.3: Final commit
bash
git add DESCRIPTION
git commit -m "docs: update DESCRIPTION to include IPCA"
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