Description Usage Arguments Details Value References See Also Examples
Simulation of an Evans (1991) rational periodically collapsing bubble process.
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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

delta
and alpha
are positive parameters which satisfy 0 < δ < (1+r)α.
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 B[t] ≤ α the bubble grows at an average rate of 1 + r:
B[t+1]= (1+r)*B[t]*u[t+1].
When B[t] > α the bubble expands at the increased rate of (1+r)π^{1}:
B[t+1] = δ*(1+r)/π* (B[t]δ/(1+r))) *u[t+1],
where θ theta is a binary variable that takes the value 0 with probability 1π and 1 with probability π.
In the second phase, there is a (1π) 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.
A numeric vector of length n
.
Evans, G. W. (1991). Pitfalls in testing for explosive bubbles in asset prices. The American Economic Review, 81(4), 922930.
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