loglikelihood_int {uGMAR} | R Documentation |
Compute the log-likelihood of GMAR, StMAR, or G-StMAR model
Description
loglikelihood_int
computes the log-likelihood of the specified GMAR, StMAR, or G-StMAR model.
Usage
loglikelihood_int(
data,
p,
M,
params,
model = c("GMAR", "StMAR", "G-StMAR"),
restricted = FALSE,
constraints = NULL,
conditional = TRUE,
parametrization = c("intercept", "mean"),
boundaries = TRUE,
checks = TRUE,
to_return = c("loglik", "mw", "mw_tplus1", "loglik_and_mw", "terms", "term_densities",
"regime_cmeans", "regime_cvars", "total_cmeans", "total_cvars", "qresiduals"),
minval
)
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 |
conditional |
a logical argument specifying whether the conditional or exact log-likelihood function should be used. |
parametrization |
is the model parametrized with the "intercepts" |
boundaries |
a logical argument. If
Argument |
checks |
|
to_return |
should the returned object be the log-likelihood value, mixing weights, mixing weights including
value for |
minval |
this will be returned when the parameter vector is outside the parameter space and |
Value
Note that the first p observations are taken as the initial values so the mixing weights and conditional moments start from the p+1:th observation (interpreted as t=1).
- By default:
log-likelihood value of the specified model,
- If
to_return=="mw"
: a size
((n_obs-p)\times M)
matrix containing the mixing weights: for m:th component in the m:th column.- If
to_return=="mw_tplus1"
: a size
((n_obs-p+1)\times M)
matrix containing the mixing weights: for m:th component in the m:th column. The last row is for\alpha_{m,T+1}
.- If
to_return=="loglik_and_mw"
: a list of two elements. The first element contains the log-likelihood value and the second element contains the mixing weights.
- If
to_return=="terms"
: a size
((n_obs-p)\times 1)
numeric vector containing the termsl_{t}
.- If
to_return=="term_densities"
: a size
((n_obs-p)\times M)
matrix containing the conditional densities that summed over in the termsl_{t}
, as[t, m]
.- If
to_return=="regime_cmeans"
: a size
((n_obs-p)\times M)
matrix containing the regime specific conditional means.- If
to_return=="regime_cvars"
: a size
((n_obs-p)\times M)
matrix containing the regime specific conditional variances.- If
to_return=="total_cmeans"
: a size
((n_obs-p)\times 1)
vector containing the total conditional means.- If
to_return=="total_cvars"
: a size
((n_obs-p)\times 1)
vector containing the total conditional variances.- If
to_return=="qresiduals"
: a size
((n_obs-p)\times 1)
vector containing the quantile residuals.
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.