Description Usage Arguments Details Value References
View source: R/quantileResiduals.R
quantile_residuals_int
computes the quantile residuals of the specified GMAR, StMAR, or G-StMAR model.
1 2 3 4 5 6 7 8 9 10 |
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 φ denotes an AR coefficient, σ^2 a variance, α a mixing weight, and ν a degrees of
freedom parameter. If |
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 φ_{m,1},...,φ_{m,p} are restricted to be the same for all regimes. |
constraints |
specifies linear constraints imposed to each regime's autoregressive parameters separately.
The symbol φ denotes an AR coefficient. Note that regardless of any constraints, the autoregressive order
is always |
parametrization |
is the model parametrized with the "intercepts" φ_{m,0} or "means" μ_{m} = φ_{m,0}/(1-∑φ_{i,m})? |
Numerical integration is employed if the quantile residuals cannot be obtained analytically with the hypergeometric function using the package 'gsl'.
Returns a (Tx1) numeric vector containing the quantile residuals of the specified GMAR, StMAR or G-StMAR model.
Note that there are no quantile residuals for the first p
observations as they are the initial values.
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, 247-266.
Meitz M., Preve D., Saikkonen P. 2021. A mixture autoregressive model based on Student's t-distribution. Communications in Statistics - Theory and Methods, doi: 10.1080/03610926.2021.1916531
Virolainen S. 2021. A mixture autoregressive model based on Gaussian and Student's t-distributions. Studies in Nonlinear Dynamics & Econometrics, doi: 10.1515/snde-2020-0060
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