Tuning-free inference on fixed-dimensional parameters of
dependent time series using affine-equivariant adjusted-range
self-normalization. The centered partial-sum path of estimated
influence contributions is normalized by its increment hull, the
convex hull of all path increments. The gauge of the hull provides
an asymptotically pivotal test statistic and an affine-equivariant
confidence region without estimating the long-run covariance matrix,
and its support function gives simultaneous confidence intervals for
linear contrasts. For a single parameter the construction reduces
exactly to adjusted-range self-normalization, whose limiting
distribution is available in closed form. The Brownian reference law
is simulated on a grid matched to the sample size or a supplied
common variance-accumulation profile; inference for dependent
observations remains asymptotic. Five further methods are provided
for comparison on the same estimate and influence contributions:
componentwise adjusted ranges after lag-zero partial prewhitening,
quadratic self-normalization following Shao (2010)
Version 0.2.3
aersn provides tests, confidence intervals and joint confidence regions
for parameters estimated from dependent time series. Start with a sample
mean, a fitted regression, or your own estimate and influence contributions.
Use the same fitted object to compare adjusted-range inference with LDL
partial prewhitening, Shao self-normalization, heteroskedasticity and
autocorrelation consistent (HAC) covariance estimation, Bartlett fixed-b,
and equal-weighted cosine (EWC) inference.
The main method, affine-equivariant adjusted-range self-normalization, constructs one joint region from the ranges of the centered influence path in all directions. Changing the units or applying a nonsingular linear transformation changes the region in the corresponding way. It needs no kernel or bandwidth and reduces to scalar adjusted-range inference when there is one parameter. The construction uses the convex hull of path increments; tests and simultaneous intervals use its gauge and support function. See Hong, Lin, Linton, Newey and Sun (2026), Cambridge Working Papers in Economics No. 2678 and Hong, Linton, McCabe, Sun and Wang (2024, Journal of Econometrics).
A supplied or consistently estimated common variance-accumulation profile
can be used with the hull, LDL and Shao methods. For Shao, the profile option also
changes the integration weights; the adjusted-range construction uses path
ranges. These options require the common-profile conditions described in
help("aersn_profile").
For a CRAN release, install with install.packages("aersn").
For a source archive supplied by the authors, use the following commands.
Only lpSolve and sandwich are needed beyond the packages that ship with R.
install.packages(c("lpSolve", "sandwich"))
install.packages("/path/to/aersn_0.2.3.tar.gz", repos = NULL, type = "source")
The source tarball includes built tutorials. After installation, open them
with vignette(package = "aersn"); no vignette-building step is needed.
Only developers rebuilding tutorials from the repository need knitr and
rmarkdown.
library(aersn)
set.seed(1)
n <- 300
e <- matrix(rnorm(2 * n), n, 2)
Y <- e
for (t in 2:n) Y[t, ] <- 0.5 * Y[t - 1, ] + e[t, ] # bivariate AR(1)
fit <- aersn_mean(Y, names = c("m1", "m2")) # psi_t = Y_t - Ybar
aersn_test(fit, null = c(0, 0)) # increment-hull test
confint(fit) # simultaneous intervals
aersn_contrast(fit, c(1, -1)) # a linear contrast
plot(aersn_region(fit)) # joint region
method |
Normalizer | Tuning | Reference law |
|---|---|---|---|
"hull" (default) |
increment hull of the centered path | none | simulated Brownian gauge law |
"ldl" |
componentwise adjusted ranges after lag-zero prewhitening | coordinate order | simulated independent-component law |
"shao" |
integrated outer product of the path | integration rule | simulated Brownian quadratic law |
"hac" |
kernel long-run covariance estimate | kernel, bandwidth | chi-squared |
"fixedb" |
Bartlett estimate with bandwidth fraction b | b | simulated fixed-b law |
"ewc" |
equal-weighted cosine estimate | number of terms | scaled F |
aersn_compare(fit, null = c(0, 0))
aersn_test(fit, method = "shao")
aersn_test(fit, method = "hac", kernel = "Parzen", bandwidth = "andrews")
aersn_test(fit, method = "fixedb", b = 0.5)
aersn_test(fit, method = "ewc", nu = 20)
confint(fit, method = "ldl")
Each result records the tuning values actually used, including bandwidths selected from the data and fixed-b fractions rounded to an integer lag bandwidth. Statistics and critical values are on different scales across methods and are not comparable as numbers; p-values, decisions and interval widths are. The vignette Comparing inference methods on one estimate works through this.
Supply an estimate and its observation-level influence contributions to
aersn(), or use a model interface that computes them: aersn_lm() for
least squares, aersn_gmm() for smooth generalized method of moments
including instrumental variables, and aersn_mle() for conditional
likelihood scores. For a parameter that is a function of a larger estimated
vector, aersn_target() applies the Jacobian, so that jointly estimated
nuisance coefficients keep their first-order effect. All interfaces feed the
same core construction.
Seven vignettes: scalar mean inference; multivariate mean inference and
linear contrasts; supplied influence contributions; linear regression and
smooth generalized method of moments; conditional likelihood scores and
variance-accumulation profiles; reference distributions and reproducibility;
and comparing inference methods. Use help(package = "aersn") for the
function index and vignette(package = "aersn") for the installed tutorials.
All six need the influence contributions to satisfy a functional central limit theorem with a nonsingular long-run covariance matrix, and the estimator to be asymptotically linear in them. The package cannot verify those conditions; each method's help page states what else it needs. The componentwise method's reference law requires the transformed long-run covariance to be diagonal in the limit, which diagonalizing the sample lag-zero covariance does not deliver, and its statistic is not affine equivariant. HAC inference relies on the conditions under which the estimate is consistent. Fixed-b and EWC reference laws are fixed-smoothing asymptotic laws, not exact finite-sample distributions. Strong persistence can cause finite-sample size distortion; a matched reference grid does not remove it.
Not included: the Kolmogorov-Smirnov type structural-break test of Hong et al. (2024) and the autocorrelation tests of Sun, Zhu and Linton (2025). The comparator methods here are not adjusted-range versions of those procedures.
MIT, held by the five authors. Maintainer: Jiajing Sun ([email protected]).