is_stationary {uGMAR} | R Documentation |
Check the stationary condition of specified GMAR, StMAR, or G-StMAR model.
Description
is_stationary
checks the stationarity condition of the specified GMAR, StMAR, or G-StMAR model.
Usage
is_stationary(
p,
M,
params,
model = c("GMAR", "StMAR", "G-StMAR"),
restricted = FALSE,
constraints = NULL
)
Arguments
p |
a positive integer specifying the autoregressive order of the model. |
M |
|
params |
a real valued parameter vector specifying the model.
Symbol |
model |
is "GMAR", "StMAR", or "G-StMAR" model considered? In the G-StMAR model, the first |
restricted |
a logical argument stating whether the AR coefficients |
constraints |
specifies linear constraints imposed to each regime's autoregressive parameters separately.
The symbol |
Details
This function falsely returns FALSE
for stationary models when the parameter is extremely close
to the boundary of the stationarity region.
Value
Returns TRUE
or FALSE
accordingly.
References
Kalliovirta L., Meitz M. and Saikkonen P. 2015. Gaussian Mixture Autoregressive model for univariate time series. Journal of Time Series Analysis, 36(2), 247-266.
Meitz M., Preve D., Saikkonen P. 2023. A mixture autoregressive model based on Student's t-distribution. Communications in Statistics - Theory and Methods, 52(2), 499-515.
Virolainen S. 2022. A mixture autoregressive model based on Gaussian and Student's t-distributions. Studies in Nonlinear Dynamics & Econometrics, 26(4) 559-580.
Examples
# GMAR model
params22 <- c(0.4, 0.39, 0.6, 0.3, 0.4, 0.1, 0.6, 0.3, 0.8)
is_stationary(p=2, M=2, params=params22)
# StMAR model
params12t <- c(-0.3, 1, 0.9, 0.1, 0.8, 0.6, 0.7, 10, 12)
is_stationary(p=1, M=2, params=params12t, model="StMAR")
# G-StMAR model
params12gs <- c(1, 0.1, 1, 2, 0.2, 2, 0.8, 20)
is_stationary(p=1, M=c(1, 1), params=params12gs, model="G-StMAR")
# Restricted GMAR model
params13r <- c(0.1, 0.2, 0.3, -0.99, 0.1, 0.2, 0.3, 0.5, 0.3)
is_stationary(p=1, M=3, params=params13r, restricted=TRUE)
# Such StMAR(3, 2) that the AR coefficients are restricted to be the
# same for both regimes and that the second AR coefficients are
# constrained to zero.
params32trc <- c(1, 2, 0.8, -0.3, 1, 2, 0.7, 11, 12)
is_stationary(p=3, M=2, params=params32trc, model="StMAR", restricted=TRUE,
constraints=matrix(c(1, 0, 0, 0, 0, 1), ncol=2))