sim_ps1 {exuber} | R Documentation |
Simulation of a single-bubble process with multiple forms of collapse regime
Description
The new generating process considered here differs from the sim_psy1
model in
three respects - Phillips and Shi (2018):
First, it includes an asymptotically negligible drift in the martingale path during normal periods. Second, the collapse process is modeled directly as a transient mildly integrated process that covers an explicit period of market collapse. Third, a market recovery date is introduced to capture the return to normal market behavior.
-
sudden:
withbeta = 0.1
andtr = tf + 0.01*n
-
disturbing:
withbeta = 0.5
andtr = tf + 0.1*n
-
smooth:
withbeta = 0.9
andtr = tf + 0.2*n
In order to provide the duration of the collapse period tr
as tr = tf + 0.2n
,
you have to provide tf
as well.
Usage
sim_ps1(
n,
te = 0.4 * n,
tf = te + 0.2 * n,
tr = tf + 0.1 * n,
c = 1,
c1 = 1,
c2 = 1,
eta = 0.6,
alpha = 0.6,
beta = 0.5,
sigma = 6.79,
seed = NULL
)
Arguments
n |
A positive integer specifying the length of the simulated output series. |
te |
A scalar in (0, tf) specifying the observation in which the bubble originates. |
tf |
A scalar in (te, n) specifying the observation in which the bubble collapses. |
tr |
A scalar in (tf, n) specifying the observation in which market recovers |
c |
A positive scalar determining the drift in the normal market periods. |
c1 |
A positive scalar determining the autoregressive coefficient in the explosive regime. |
c2 |
A positive scalar determining the autoregressive coefficient in the collapse regime. |
eta |
A positive scalar (>0.5) determining the drift in the normal market periods. |
alpha |
A positive scalar in (0, 1) determining the autoregressive coefficient in the bubble period. |
beta |
A positive scalar in (0, 1) determining the autoregressive coefficient in the collapse period. |
sigma |
A positive scalar indicating the standard deviation of the innovations. |
seed |
An object specifying if and how the random number generator (rng)
should be initialized. Either NULL or an integer will be used in a call to
|
Value
A numeric vector of length n
.
References
Phillips, Peter CB, and Shu-Ping Shi. "Financial bubble implosion and reverse regression." Econometric Theory 34.4 (2018): 705-753.
See Also
Examples
# Disturbing collapse (default)
disturbing <- sim_ps1(100)
autoplot(disturbing)
# Sudden collapse
sudden <- sim_ps1(100, te = 40, tf= 60, tr = 61, beta = 0.1)
autoplot(sudden)