Econometric Analysis of Explosive Time Series

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 utilizes the matrix inversion lemma from the recursive least squares algorithm, which results in a significant speed improvement.

Description

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) <:10.1111/iere.12132>. 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.

Overview

radf() : Recursive Augmented Dickey-Fuller test
mc_cv() : Monte Carlo Critical Values
wb_cv() : Wild Bootstrap Critical values

Installation

The package is still under development, to install the development version from GitHub:

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.

Usage

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

library(exuber)
# Simulate data witn n = 100 observations
set.seed(123)
a1 <- sim_dgp1(n = 100) # one bubble
a2 <- sim_dgp2(n = 100) # two bubbles
a3 <- sim_blan(n = 100) # blanchard model
a4 <- sim_evans(n = 100) # evans model
 
dta <- data.frame("oneb" = a1, "twob" = a2, "blan" = a3, "evans" = a4)
 
ts <- radf(dfrm, lag = 1)
 
# Critical Values mc = Monte Carlo, wb= Wild Bootstrapped
## Use 500 repetions(boostraps) for faster computation
mc <- mc_cv(n = NROW(dta), nrep = 500, parallel = T)
wb <- wb_cv(dta, nboot = 500, parallel = T)

Report

Report summary statistics, diagnostics and date stamping periods of mildly explosive behaviour.

report(ts, mc)
diagnostics(ts, mc)
datestamp(ts, mc)

Plotting

The output of plot will be a list,

# All together
plot(ts, mc, plot_type = "single", breaks_x = 20)
 
# Individually
plot(ts, mc, plot_type = "multiple", breaks_x = 20)
 
library(gridExtra)
p1 <- plot(ts, mc, plot_type = "multiple", breaks_x = 20, breaks_y = 3)
do.call("grid.arrange", c(p1, ncol = 2))