sim_psy1 {exuber} | R Documentation |
Simulation of a single-bubble process
Description
The following function generates a time series which switches from a martingale to a mildly explosive process and then back to a martingale.
Usage
sim_psy1(
n,
te = 0.4 * n,
tf = 0.15 * n + te,
c = 1,
alpha = 0.6,
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. |
c |
A positive scalar determining the autoregressive coefficient in the explosive regime. |
alpha |
A positive scalar in (0, 1) determining the value of the expansion rate in the autoregressive coefficient. |
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
|
Details
The data generating process is described by the following equation:
where the autoregressive coefficient is given by:
with ,
,
and
with
,
dates the origination of the bubble,
and
dates the collapse of the bubble.
During the pre- and post- bubble periods,
,
is a pure random walk process. During the bubble expansion period
becomes a mildly explosive process with expansion rate
given by the autoregressive coefficient
; and, finally
during the post-bubble period,
reverts to a martingale.
For further details see Phillips et al. (2015) p. 1054.
Value
A numeric vector of length n.
References
Phillips, P. C. B., Shi, S., & Yu, J. (2015). Testing for Multiple Bubbles: Historical Episodes of Exuberance and Collapse in the S&P 500. International Economic Review, 5 6(4), 1043-1078.
See Also
Examples
# 100 periods with bubble origination date 40 and termination date 55
sim_psy1(n = 100, seed = 123) %>%
autoplot()
# 200 periods with bubble origination date 80 and termination date 110
sim_psy1(n = 200, seed = 123) %>%
autoplot()
# 200 periods with bubble origination date 100 and termination date 150
sim_psy1(n = 200, te = 100, tf = 150, seed = 123) %>%
autoplot()