fjohansen (R)

R implementation of the Johansen cointegration test with Fourier-type smooth nonlinear deterministic trends restricted to cointegrating relations of

Kurita, T. & Shintani, M. (2025). Johansen test with Fourier-type smooth nonlinear trends in cointegrating relations. Econometric Reviews, 44(10), 1589–1616. DOI: 10.1080/07474938.2025.2530640

The package also bundles the FGLS Wald test of

Perron, P., Shintani, M. & Yabu, T. (2017, 2021). Testing for flexible nonlinear trends with an integrated or stationary noise component. OBES 79, 822–850.

used as a frequency-selection pre-step.

Author: Merwan Roudane — merwanroudane920@gmail.com Repository: https://github.com/merwanroudane/fjohansen

A sibling Python package with identical functionality is available on PyPI.

✨ Features

Six model variants — CNR, LNR, CNU, LNU, constant, linear.
Bundled Table B1 critical values + pre-computed moments for all common cells (no Monte-Carlo cost on cold start).
Sequential cointegrating-rank selection.
Perron-Shintani-Yabu (2021) FGLS Wald test with general-to-specific frequency selection (univariate and multivariate panels).
Publication-quality output: ASCII summary, LaTeX (booktabs), HTML, and ggplot2 figures matching the paper’s style.
All paper DGPs (NF-DGP-1..4, F-DGP-1, F-DGP-2) + a synthetic JGB surrogate.

📦 Installation

# Development version from GitHub
# install.packages("remotes")
remotes::install_github("merwanroudane/fjohansen", subdir = "fjohansenR")

Dependencies: ggplot2, scales, knitr (all available on CRAN). Suggested extras: testthat, kableExtra, patchwork.

🚀 Quick start

library(fjohansen)

# 1. Synthetic JGB-style dataset (Section 6 of the paper)
data <- sample_jgb_data(T = 108)

# 2. Pick the number of Fourier frequencies (PSY 2021)
sel <- select_frequencies(data, n_max = 5, p_d = 1, sig_level = 0.10)
print(sel)                          # n_selected, per_series, detail

# 3. Estimate the Johansen-Fourier (CNR) model
res <- johansen_fourier(data, k = 3, n = sel$n_selected, model = "CNR")

# 4. Pretty output
print(res)                           # Table-3 style ASCII
summary(res)                         # adds beta / alpha
cat(format_trace_latex(res))         # journal-ready LaTeX
cat(format_trace_html(res))          # styled HTML

# 5. ggplot2 figures
plot(res, which = "eigenvalues")
plot(res, which = "long_run")
plot(res, which = "risk_premium")
plot(res, which = "residuals")

🧩 Model variants

Code	\(Z_1\) (cointegrating space)	\(Z_2\) (unrestricted)
`CNR`	`(X[t-1]', F[t,T]', 1)'`	DX-lags only
`LNR`	`(X[t-1]', F[t,T]', t)'`	DX-lags + constant
`CNU`	`(X[t-1]', 1)'`	DX-lags + `F[t,T]`
`LNU`	`(X[t-1]', t)'`	DX-lags + constant + `F[t,T]`
`constant`	`(X[t-1]', 1)'`	DX-lags only (standard Johansen)
`linear`	`(X[t-1]', t)'`	DX-lags + constant (standard)

with F[t,T] = [sin(2*pi*t/T), cos(2*pi*t/T), ..., sin(2*pi*n*t/T), cos(2*pi*n*t/T)]'.

📚 Reference

Main public functions:

Function	Purpose
`johansen_fourier(data, k, n, model)`	Reduced-rank regression + trace test.
`select_frequencies(data, n_max, ...)`	PSY 2021 general-to-specific selection.
`psy_wald_test(y, k_freqs, p_d, ...)`	Univariate FGLS Wald test.
`jf_quantile(level, p_minus_r, n, model)`	Critical-value lookup / Gamma fallback.
`jf_p_value(stat, p_minus_r, n, model)`	Gamma-approximation p-value.
`simulate_limit_distribution(...)`	Limit-distribution sampler.
`format_trace_table / _latex / _html`	Table exports.
`plot.johansen_fourier`	`ggplot2` figures: eigenvalues, long-run, risk-premium, residuals.
`sample_jgb_data()`	JGB surrogate dataset.
`generate_f_dgp1 / _f_dgp2 / _nf_dgp1..4`	Paper DGPs.

📑 Citation

@article{kurita_shintani_2025,
  author  = {Takamitsu Kurita and Mototsugu Shintani},
  title   = {Johansen test with Fourier-type smooth nonlinear trends in cointegrating relations},
  journal = {Econometric Reviews},
  year    = {2025},
  volume  = {44},
  number  = {10},
  pages   = {1589--1616},
  doi     = {10.1080/07474938.2025.2530640}
}

@misc{roudane_fjohansenR,
  author = {Merwan Roudane},
  title  = {fjohansen: Johansen test with Fourier-type smooth nonlinear trends (R)},
  year   = {2025},
  url    = {https://github.com/merwanroudane/fjohansen}
}