The null is a constant mean with independent Gaussian noise. This release uses the supplied empirical calibration only for 100 observations and w1=22. The finite-sample probabilities are approximate; they are not Gumbel p-values.
set.seed(12)
y <- rnorm(100) + rep(c(0, 3), each=50)
fit <- i1_test(y)
fit
#> pvalue i1 etahat cpmag
#> 1 0 47.1701 51 3.799967
diagnostics <- attr(fit, "diagnostics")
diagnostics
#> $sigma
#> [1] 0.8434712
#>
#> $rho
#> [1] 0
#>
#> $calibration
#> [1] "reference"
#>
#> $calibration_key
#> [1] "0"
#>
#> $w1
#> [1] 22
#>
#> $statistic
#> [1] 47.17013
#>
#> $calibration_n
#> [1] 100
#>
#> $calibration_length_matches
#> [1] TRUE
#>
#> $calibration_provenance
#> [1] "supplied Gaussian reference density; n=100, w1=22"
#>
#> $inference_scope
#> [1] "iid Gaussian, n=100, w1=22"
fit$cpmag * diagnostics$sigma
#> [1] 3.205162etahat is the last observation before a candidate boundary, whether or not the test rejects. The signed cpmag is in standardized units. Multiplication by sigma expresses that local contrast in data units.
Adaptive future-minus-past contrasts are summed symmetrically. The maximum absolute aggregate is taken over w,…,n-w, following the research script. The standard deviation estimate is IQR(diff(y))/[-2 sqrt(2) Phi_inverse(.25)]. WD mode divides that scale by (1-rho), exactly as in Appendix B.1, and estimates rho using 1+2 cor(diff(y)[-last],diff(y)[-first]). The radical covers 2 only.
i1_test(y, archeck=1, calibration="none")
#> pvalue i1 etahat cpmag
#> 1 NA 50.5476 51 4.072048
i1_test(y, w1=16, calibration="none")
#> pvalue i1 etahat cpmag
#> 1 NA 33.1022 51 3.566918
set.seed(13)
long_series <- rnorm(300)
i1_stt(long_series)
#> [1] 13.41701
i1_test(long_series, calibration="none")
#> pvalue i1 etahat cpmag
#> 1 NA 13.417 160 0.6909279Statistic-only results have pvalue=NA. Reference mode rejects other lengths, windows and WD mode. Input checks do not establish Gaussian independence. Zero IQR and inadmissible dependence estimates error explicitly.
In 10000 independent Gaussian null series (seed 26102403), rejection rates were .0086, .0415 and .0857 at nominal .01, .05 and .10. The same fixed density was used throughout. These conservative rates do not prove exact size or validity under other distributions. A reported zero is a finite-grid tail approximation. Rounded p-values limit significance resolution.
There is no adjustment for repeated testing. The package targets mean shifts; a linear trend is not the constant-mean null. For multiple descriptive candidates, see the DCI vignette.
Waychal, N., Laha, A. K. and Sinha, A. (2026). Closely spaced change-point detection with an application to geopolitical shocks in oil and gas markets. https://doi.org/10.48550/arXiv.2610.23476.