mixing_weights {uGMAR} | R Documentation |
Calculate mixing weights of GMAR, StMAR or G-StMAR model
Description
mixing_weights
calculates the mixing weights of the specified GMAR, StMAR or G-StMAR model and returns them as a matrix.
Usage
mixing_weights(
data,
p,
M,
params,
model = c("GMAR", "StMAR", "G-StMAR"),
restricted = FALSE,
constraints = NULL,
parametrization = c("intercept", "mean")
)
Arguments
data |
a numeric vector or class |
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 |
parametrization |
is the model parametrized with the "intercepts" |
Details
The first p observations are taken to be the initial values.
Value
- If
to_return=="mw"
: a size ((n_obs-p)xM) matrix containing the mixing weights: for m:th component in m:th column.
- If
to_return=="mw_tplus1"
: a size ((n_obs-p+1)xM) matrix containing the mixing weights: for m:th component in m:th column. The last row is for
\alpha_{m,T+1}
.
References
Galbraith, R., Galbraith, J. 1974. On the inverses of some patterned matrices arising in the theory of stationary time series. Journal of Applied Probability 11, 63-71.
Kalliovirta L. (2012) Misspecification tests based on quantile residuals. The Econometrics Journal, 15, 358-393.
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
params12 <- c(1.70, 0.85, 0.30, 4.12, 0.73, 1.98, 0.63)
mixing_weights(simudata, p=1, M=2, params=params12, model="GMAR")
# G-StMAR-model
params42gs <- c(0.04, 1.34, -0.59, 0.54, -0.36, 0.01, 0.06, 1.28, -0.36,
0.2, -0.15, 0.04, 0.19, 9.75)
mixing_weights(M10Y1Y, p=4, M=c(1, 1), params=params42gs, model="G-StMAR")