sim_evans {exuber} | R Documentation |
Simulation of an Evans (1991) bubble process
Description
Simulation of an Evans (1991) rational periodically collapsing bubble process.
Usage
sim_evans(
n,
alpha = 1,
delta = 0.5,
tau = 0.05,
pi = 0.7,
r = 0.05,
b1 = delta,
seed = NULL
)
Arguments
n |
A positive integer specifying the length of the simulated output series. |
alpha |
A positive scalar, with restrictions (see details). |
delta |
A positive scalar, with restrictions (see details). |
tau |
The standard deviation of the innovations. |
pi |
A positive value in (0, 1) which governs the probability of the bubble continuing to grow. |
r |
A positive scalar that determines the growth rate of the bubble process. |
b1 |
A positive scalar, the initial value of the series. Defaults to |
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
delta
and alpha
are positive parameters which satisfy .
delta
represents the size of the bubble after collapse.
The default value of r
is 0.05.
The function checks whether alpha
and delta
satisfy this condition and will return an error if not.
The Evans bubble has two regimes. If the bubble grows at an average rate of
:
When the bubble expands at the increased rate of
:
where theta is a binary variable that takes the value 0 with probability
and 1 with probability
.
In the second phase, there is a (
) probability of the bubble process collapsing to
delta
.
By modifying the values of delta
, alpha
and pi
the user can change the frequency at which bubbles appear, the mean duration of a bubble before collapse and the scale of the bubble.
Value
A numeric vector of length n
.
References
Evans, G. W. (1991). Pitfalls in testing for explosive bubbles in asset prices. The American Economic Review, 81(4), 922-930.
See Also
Examples
sim_evans(100, seed = 123) %>%
autoplot()