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FCUSUM 1.1.0

Critical corrections — results from 1.0.0 should be recomputed

• Critical values were the wrong tail. The table in 1.0.0 contained the 1%, 5% and 10% lower quantiles of the null distribution. Because the test rejects for large values, fcum() rejected a true null of cointegration in roughly 90% of samples at the nominal 5% level.
• Estimation. The cointegrating regression is now estimated by dynamic OLS (leads and lags of the differenced regressors; number chosen by BIC unless q is given), as Xiao and Phillips (2002) require for a nuisance-parameter-free limit distribution. 1.0.0 used plain OLS.
• Scaling. The CUSUM is now scaled by a Bartlett long-run variance (bw = "nw" default, "kurozumi", "andrews") instead of the residual standard deviation, so the test is robust to serially correlated errors.
• Multiple regressors. x given as a matrix or data frame was flattened into a single column in 1.0.0, so p > 1 failed. Fixed.

New testing procedure

With fractional frequencies the null distribution of the Fourier CUSUM depends on the true frequency, and the frequency search shrinks the statistic, so no single table indexed by kstar can be valid. fcum() now proceeds in three steps:

1. DOLS estimation and search for the frequency that minimises the RSS.
2. A sup-F pre-test for the Fourier terms (tabulated critical values for p = 1..4, kstar = 1..5, fractional and integer grids).
3. If the Fourier terms are significant, the Fourier CUSUM with bootstrap critical values that replicate the frequency search around the estimated break (boot = "iid", default, or "sieve"); otherwise the Xiao-Phillips CUSUM without Fourier terms (tabulated critical values).

fourier = "always" / "never" override the pre-test; cv = "table" uses fast asymptotic critical values at the selected frequency instead of the bootstrap (conservative in finite samples). Configurations outside the tables are simulated automatically.

Other changes

• kstar must be a positive integer (non-integer values silently fell back to the p = 1, k = 1 critical values in 1.0.0).
• Frequency selection is by minimum RSS. All candidate models have the same number of parameters, so this is identical to the AICc rule of 1.0.0; the internal aicc() helper was removed.
• New exported function fcum_cv_sim() simulates the null distribution of the plain CUSUM, the sup-F statistic or the fixed-frequency Fourier CUSUM for any n, p and settings.
• fcum objects now carry p-values, the pre-test, both CUSUM statistics, and gain plot(), coef() and residuals() methods.
• data-raw/critical_values.R reproduces all tables and data-raw/size_power.R reproduces the size and power experiments.

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
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