uGMAR (version 3.0.1)

diagnosticPlot: Quantile residual based diagnostic plots for GMAR, StMAR and G-StMAR models

Description

diagnosticPlot plots quantile residual time series, normal QQ-plot, autocorrelation function and squared quantile residual autocorrelation function. There is an option to also plot the individual statistics associated with the quantile residual tests (for autocorrelation and conditional heteroskedasticity) divided by their approximate standard errors with their approximate 95% critical bounds.

Usage

diagnosticPlot(gsmar, nlags = 20, nsimu = 2000, plot_indstats = FALSE)

Arguments

gsmar

object of class 'gsmar', generated by function fitGSMAR() or GSMAR().

nlags

a positive integer specifying how many lags should be calculated for the autocorrelation and conditional heteroscedasticity statistics.

nsimu

a positive integer specifying to how many simulated values from the process the covariance matrix "Omega" (used to compute the tests) should be based on. Larger number of simulations may result more reliable tests. If smaller than data size, then it will be based on the given data. Ignored if plot_indstats==FALSE.

plot_indstats

set TRUE if the individual statistics discussed in Kalliovirta (2012) should be plotted with their approximate 95% critical bounds (this may take some time).

Value

diagnosticPlot only plots to a graphical device and doesn't return anything. Use the function quantileResidualTests in order to obtain the individual statistics.

Suggested packages

Install the suggested package "gsl" for faster evaluations in the cases of StMAR and G-StMAR models. For large StMAR and G-StMAR models with large data the calculations to obtain the individual statistics may take a significantly long time without the package "gsl".

Details

Sometimes the individual statistics are not plotted because it's not (numerically) possible for to calculate all the necessary estimates required. This may suggest that the model is misspecified.

The dashed lines plotted with autocorrelation functions (for quantile residuals and their squares) are plus-minus \(1.96*T^{-1/2}\).

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, 247-266.

• Lutkepohl H. 2005. New Introduction to Multiple Time Series Analysis. Springer.

• Meitz M., Preve D., Saikkonen P. 2018. A mixture autoregressive model based on Student's t-distribution. arXiv:1805.04010 [econ.EM].

• There are currently no published references for G-StMAR model, but it's a straight forward generalization with theoretical properties similar to GMAR and StMAR models.

See Also

fitGSMAR, GSMAR, quantileResidualTests, predict.gsmar

Examples

# NOT RUN {
# GMAR model
params13 <- c(1.4, 0.88, 0.26, 2.46, 0.82, 0.74, 5.0, 0.68, 5.2, 0.72, 0.2)
gmar13 <- GSMAR(data=VIX, p=1, M=3, params=params13, model="GMAR")
diagnosticPlot(gmar13)

# Restricted GMAR model: plot also the individual statistics with
# their approximate critical bounds using the given data
params12r <- c(1.4, 1.8, 0.88, 0.29, 3.18, 0.84)
gmar12r <- GSMAR(data=VIX, p=1, M=2, params=params12r, model="GMAR",
 restricted=TRUE)
diagnosticPlot(gmar12r, nlags=10, nsimu=1, plot_indstats=TRUE)

# StMAR model
params12t <- c(1.38, 0.88, 0.27, 3.8, 0.74, 3.15, 0.8, 100, 3.6)
stmar12 <- GSMAR(data=VIX, p=1, M=2, params=params12t, model="StMAR")
diagnosticPlot(stmar12)

# G-StMAR model (similar to the StMAR model above)
params12gs <- c(1.38, 0.88, 0.27, 3.8, 0.74, 3.15, 0.8, 3.6)
gstmar12 <- GSMAR(data=VIX, p=1, M=c(1, 1), params=params12gs,
 model="G-StMAR")
diagnosticPlot(gstmar12)

# Restricted G-StMAR-model
params13gsr <- c(1.3, 1, 1.4, 0.8, 0.4, 2, 0.2, 0.25, 0.15, 20)
gstmar13r <- GSMAR(data=VIX, p=1, M=c(2, 1), params=params13gsr,
 model="G-StMAR", restricted=TRUE)
diagnosticPlot(gstmar13r)

# GMAR model as a mixture of AR(2) and AR(1) models
constraints <- list(diag(1, ncol=2, nrow=2), as.matrix(c(1, 0)))
params22c <- c(1.2, 0.85, 0.04, 0.3, 3.3, 0.77, 2.8, 0.77)
gmar22c <- GSMAR(data=VIX, p=2, M=2, params=params22c,
 model="GMAR", constraints=constraints)
diagnosticPlot(gmar22c)

# 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(2.2, 1.8, 0.88, -0.03, 2.4, 0.27, 0.40, 3.9, 1000)
stmar32rc <- GSMAR(data=VIX, p=3, M=2, params=params32trc, model="StMAR",
 restricted=TRUE, constraints=matrix(c(1, 0, 0, 0, 0, 1), ncol=2))
diagnosticPlot(stmar32rc)
# }