Testing for and dating periods of explosive dynamics (exuberance) in time series using the univariate and panel recursive unit root tests proposed by Phillips et al. (2015) and Pavlidis et al. (2016). The recursive least-squares algorithm utilizes the matrix inversion lemma to avoid matrix inversion which results in significant speed improvements. Simulation of a variety of periodically-collapsing bubble processes.
Testing for explosive dynamics is comprised of two distinct parts :
- Estimation
- Critical Values
Some Context: Conventional testing techniques compute critical values,and p-values from a standard distribution, where the user does not need to specify critical values explicitly. However, the recent literature in explosive dynamics require the use of non-standard distributions, which require the use of techniques that sample empirical distributions in order to calculate the critical values.
The cornerstone function of the package is:
radf(): Recursive Augmented Dickey-Fuller Test.
This function offers a vectorized estimation (i.e. single and/or multiple time-series) for individual and panel estimation. The estimation can parse data from multiple classes and handle dates as index.
There are several options for generating critical values:
radf_mc_cv(): Monte Carloradf_wb_cv(),radf_wb_ps_cv(): Wild Bootstrap (Harvey et al. 2016; Phillips & Shi 2020)radf_sb_cv(): Sieve Bootstrap (Panel)
When cv is omitted, exuber uses precomputed Monte Carlo critical
values: a shared store covering lag = 0 to 4 and every sample size
up to 4000, fetched once per (n, lag) and cached on disk.
radf_mc_cv() and the bootstrap functions are the offline route, and
the only route for other lags or larger samples.
For the analysis you should include both the output from estimation
(object) and critical values (cv). The below methods break the
process into small simple steps:
summary()summarizes the model.diagnostics()shows which series reject the null hypothesis .datestamp()computes the origination, termination and duration of episodes (if any).rootstamp()estimates how fast a detected episode is growing (the explosive root and its doubling time), run over everydatestamp()episode at once.
These combined provide a comprehensive analysis on the exuberant
behavior of the model. See vignette("exuber") for this workflow end to
end and vignette("plotting") for the autoplot() methods that go with
it.
The recursive ADF test is the core, but not the whole package. Each family below has its own vignette and its own section of the reference index:
- Volatility-robust tests (
radf_tt(),radf_sign(),radf_kp(),radf_sbz()): the same question asradf()under time-varying innovation variance –vignette("radf-tt"),vignette("volatility-robust-radf"). - Dating procedures (
dating_hls(),dating_knp(),dating_pdc(),dating_hlw(),radf_recovery()): regime-model estimates of when a bubble you already believe in starts and ends, no critical value needed –vignette("dating-methods"). - Real-time monitoring (
monitor(),monitor_cusum(),monitor_lbi(),monitor_quantile()): calibrate on a training window, then raise an alarm as new observations arrive –vignette("monitoring"). - Root inference (
rootstamp()): how fast a detected episode is growing –vignette("root-inference"). - Multivariate (
radf_common(),cobubble_test(),contagion_reg()): shared and transmitted bubbles across series –vignette("co-explosivity"). - Simulation (
sim_*()): the bubble processes and innovation generators every test above is validated on –vignette("simulation").
vignette("naming-and-analysis") explains the naming scheme (radf_,
_test, dating_, monitor_) and which results plug into
summary()/datestamp()/tidy()/autoplot().
# Install release version from CRAN
install.packages("exuber")You can install the development version of exuber from GitHub.
# install.packages("devtools")
devtools::install_github("kvasilopoulos/exuber")If you encounter a clear bug, please file a reproducible example on GitHub.
library(exuber)
rsim_data <- radf(sim_data)
summary(rsim_data)
#> Using precomputed critical values for `cv`.
#>
#> ── Summary (minw = 19, lag = 0) ────────────────── Monte Carlo (nboot = 2000) ──
#>
#> psy1 :
#> # A tibble: 3 × 5
#> stat tstat `90` `95` `99`
#> <fct> <dbl> <dbl> <dbl> <dbl>
#> 1 adf -2.46 -0.412 -0.0178 0.644
#> 2 sadf 1.95 0.965 1.25 1.77
#> 3 gsadf 5.19 1.65 1.93 2.60
#>
#> psy2 :
#> # A tibble: 3 × 5
#> stat tstat `90` `95` `99`
#> <fct> <dbl> <dbl> <dbl> <dbl>
#> 1 adf -2.86 -0.412 -0.0178 0.644
#> 2 sadf 7.88 0.965 1.25 1.77
#> 3 gsadf 7.88 1.65 1.93 2.60
#>
#> evans :
#> # A tibble: 3 × 5
#> stat tstat `90` `95` `99`
#> <fct> <dbl> <dbl> <dbl> <dbl>
#> 1 adf -5.83 -0.412 -0.0178 0.644
#> 2 sadf 5.28 0.965 1.25 1.77
#> 3 gsadf 5.99 1.65 1.93 2.60
#>
#> div :
#> # A tibble: 3 × 5
#> stat tstat `90` `95` `99`
#> <fct> <dbl> <dbl> <dbl> <dbl>
#> 1 adf -1.95 -0.412 -0.0178 0.644
#> 2 sadf 1.11 0.965 1.25 1.77
#> 3 gsadf 1.34 1.65 1.93 2.60
#>
#> blan :
#> # A tibble: 3 × 5
#> stat tstat `90` `95` `99`
#> <fct> <dbl> <dbl> <dbl> <dbl>
#> 1 adf -5.15 -0.412 -0.0178 0.644
#> 2 sadf 3.93 0.965 1.25 1.77
#> 3 gsadf 11.0 1.65 1.93 2.60
diagnostics(rsim_data)
#> Using precomputed critical values for `cv`.
#>
#> ── Diagnostics (option = gsadf) ───────────────────────────────── Monte Carlo ──
#>
#> psy1: Rejects H0 at the 1% significance level
#> psy2: Rejects H0 at the 1% significance level
#> evans: Rejects H0 at the 1% significance level
#> div: Cannot reject H0
#> blan: Rejects H0 at the 1% significance level
datestamp(rsim_data)
#> Using precomputed critical values for `cv`.
#>
#> ── Datestamp (min_duration = 0) ───────────────────────────────── Monte Carlo ──
#>
#> psy1 :
#> Start Peak End Duration Signal Ongoing
#> 1 44 48 56 12 positive FALSE
#>
#> psy2 :
#> Start Peak End Duration Signal Ongoing
#> 1 23 40 41 18 positive FALSE
#> 2 62 70 71 9 positive FALSE
#>
#> evans :
#> Start Peak End Duration Signal Ongoing
#> 1 20 20 21 1 positive FALSE
#> 2 44 44 45 1 positive FALSE
#> 3 66 67 68 2 positive FALSE
#>
#> blan :
#> Start Peak End Duration Signal Ongoing
#> 1 34 36 37 3 positive FALSE
#> 2 84 86 87 3 positive FALSE
autoplot(rsim_data)
#> Using precomputed critical values for `cv`.
radf()‘s recursive least-squares algorithm (matrix inversion lemma, no
per-window matrix inversion) is the reason exuber is fast. The chart
below reproduces the full software comparison from Section 4 of the JSS
paper – R’s
MultipleBubbles
and
psymonitor::PSY(),
EViews’ rtadf, MATLAB’s PSY.m, and Stata – alongside both exuber
as it was benchmarked at publication time and the current package
version. Same setup throughout: minw = 30, lag/adflag = 1, median
elapsed time over repeated runs on a random walk of length n.
All series except exuber 2.0.0 are the paper’s own archived benchmark
data rather than a re-run – MultipleBubbles/psymonitor are O(T^2)
pure-R loops that already cost minutes per run at n = 1000, and none
of these archived numbers depend on the current exuber implementation.
exuber 2.0.0 is faster than 0.4.1 at every sample size shown.
exuber is the product of ongoing research – if it’s useful in your own
work, please support it by citing the accompanying paper in the Journal
of Statistical Software:
Vasilopoulos, K., Pavlidis, E., & Martínez-García, E. (2022). exuber: Recursive Right-Tailed Unit Root Testing with R. Journal of Statistical Software, 103(10), 1-26. doi:10.18637/jss.v103.i10
citation("exuber")
#> To cite exuber in publications use:
#>
#> Vasilopoulos K, Pavlidis E, Martínez-García E (2022). "exuber:
#> Recursive Right-Tailed Unit Root Testing with R." _Journal of
#> Statistical Software_, *103*(10), 1-26. doi:10.18637/jss.v103.i10
#> <https://doi.org/10.18637/jss.v103.i10>.
#>
#> A BibTeX entry for LaTeX users is
#>
#> @Article{,
#> title = {{exuber}: Recursive Right-Tailed Unit Root Testing with {R}},
#> author = {Kostas Vasilopoulos and Efthymios Pavlidis and Enrique Mart{\'i}nez-Garc{\'i}a},
#> journal = {Journal of Statistical Software},
#> year = {2022},
#> volume = {103},
#> number = {10},
#> pages = {1--26},
#> doi = {10.18637/jss.v103.i10},
#> }Please note that the ‘exuber’ project is released with a Contributor Code of Conduct. By contributing to this project, you agree to abide by its terms.