Testing for and dating periods of explosive dynamics (exuberance) in time series using recursive unit root tests as proposed by Phillips, P. C., Shi, S. and Yu, J. (2015a). Simulate a variety of periodically-collapsing bubble models. The estimation and simulation utilize the matrix inversion lemma from the recursive least squares algorithm, which results in a significant speed improvement.

• radf() : Recursive Augmented Dickey-Fuller test

• mc_cv() : Monte Carlo critical values
• wb_cv() : Wild Bootstrap critical values
• sb_cv() : Sieve Bootstrap (panel) critical values

• sim_dgp1() : Simulation of a single-bubble process
• sim_dgp2() : Simulation of a two-bubble process
• sim_blan() : Simulation of a Blanchard (1979) bubble process
• sim_evans() : Simulation of a Evans (1991) bubble process
• sim_div() : Simulation of dividends

You can install the released version of exuber from CRAN with:

install.packages("exuber")

And the development version from GitHub with:

if(!require(devtools)) install.packages("devtools")
devtools::install_github("kvasilopoulos/exuber")

Note that development version requires compilation, so to install you will need the appropriate development tools.

• Window Users should install Rtools
• Mac User should install Clang or GNU Fortran.

If you encounter a clear bug, please file a reproducible example on GitHub.

This is a basic example which shows you how to use exuber:

library(exuber)
# Simulate data witn n = 100 observations
set.seed(112)
sim1 <- sim_dgp1(n = 100) # one bubble
sim2 <- sim_dgp2(n = 100) # two bubbles

dta <- data.frame("onebubble" = sim1, 
                  "twobbubbles" = sim2)

ts <- radf(dta, lag = 1)

Report t-stats with the assiged critical values

summary(ts)
#> 
#>  Recursive Unit Root
#>  ----------------------------------
#>  H0: Unit root
#>  H1: Explosive root
#>  ----------------------------------
#>  Critical values: Monte Carlo 
#>  Minimum window: 19 
#>  Iterations: 2000 
#>  Lag: 1 
#>  ----------------------------------
#>  onebubble 
#>         tstat      90%      95%     99%
#> ADF    -2.304  -0.4035  -0.0762  0.5104
#> SADF    4.522   1.0074   1.3484  1.9454
#> GSADF   4.718   1.6942   1.9259  2.6191
#> 
#>  twobbubbles 
#>         tstat      90%      95%     99%
#> ADF    -2.411  -0.4035  -0.0762  0.5104
#> SADF    4.057   1.0074   1.3484  1.9454
#> GSADF   5.571   1.6942   1.9259  2.6191

Date stamp periods of explosive behaviour

datestamp(ts)
#> 
#> Datestamp: Individual
#>  -----------------------------------
#> onebubble :
#>   Start End Duration
#> 1    40  55       16
#> 
#> twobbubbles :
#>   Start End Duration
#> 1    24  40       17
#> 2    62  70        9

The output of autoplot is a list of ggplots

ts %>% 
  autoplot() %>% 
  ggarrange()

This package is free and open source software, licensed under GPL-3.

Please note that this project is released with a Contributor Code of Conduct. By participating in this project you agree to abide by its terms.