uGMAR (version 3.2.4)

plot.qrtest: Quantile residual tests for GMAR, StMAR , and G-StMAR models

Description

quantileResidualTests performs quantile residual tests for GMAR, StMAR, and G-StMAR models, testing normality, autocorrelation, and conditional heteroscedasticity of the quantile residuals.

Usage

# S3 method for qrtest
plot(x, ...)
# S3 method for qrtest
print(x, ..., digits = 3)
quantileResidualTests(
  gsmar,
  lagsAC = c(1, 2, 5, 10),
  lagsCH = lagsAC,
  nsimu = 1,
  printRes = TRUE
)

Arguments

x

object of class 'qrtest' created with the function quantileResidualTests.

...

graphical parameters passed to segments in plot.qrtest. Currectly not used in print.qrtest

digits

the number of digits to be print

gsmar

object of class 'gsmar' created with the function fitGSMAR or GSMAR.

lagsAC

a numeric vector of positive integers specifying the lags for which autocorrelation is tested.

lagsCH

a numeric vector of positive integers specifying the lags for which conditional heteroscedasticity is tested.

nsimu

a positive integer specifying to how many simulated observations the covariance matrix Omega (see Kalliovirta (2012)) should be based on. If smaller than data size, then omega will be based on the given data and not on simulated data. Having the covariance matrix omega based on a large simulated sample might improve the tests size properties.

printRes

a logical argument defining whether the results should be printed or not.

Value

Returns an object of class 'qrtest' containing the test results in data frames. In the cases of autocorrelation and conditional heteroscedasticity tests, the returned object also contains the associated individual statistics and their standard errors, discussed in Kalliovirta (2012) at the pages 369-370.

Methods (by generic)

• plot: Plot p-values of the autocorrelation and conditional heteroskedasticity tests.

• print: Print method for class 'qrtest' objects

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 evaluations may take significantly long time without the package "gsl".

Details

For a correctly specified GSMAR model employing the maximum likelihood estimator, the quantile residuals are asymptotically independent with standard normal distribution. They can hence be used in a similar manner to conventional Pearson's residuals. For more details about quantile residual based diagnostics, and in particular, about the quantile residual tests, see the cited article by Kalliovirta (2012).

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.

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

• Virolainen S. 2020. A mixture autoregressive model based on Gaussian and Student's t-distribution. arXiv:2003.05221 [econ.EM].

See Also

profile_logliks, fitGSMAR, GSMAR, diagnosticPlot, predict.gsmar, getOmega,

Examples

# NOT RUN {
# GMAR model
fit12 <- fitGSMAR(data=logVIX, p=1, M=2, model="GMAR")
qrtest12 <- quantileResidualTests(fit12, nsimu=1)
plot(qrtest12)

# Restricted GMAR model
fit12r <- fitGSMAR(logVIX, 1, 2, model="GMAR", restricted=TRUE)
qrtest12r <- quantileResidualTests(fit12r, lagsAC=1:10, nsimu=1)
plot(qrtest12r)

# Non-mixture version of StMAR model
fit11t <- fitGSMAR(logVIX, 1, 1, model="StMAR", ncores=1, ncalls=1)
quantileResidualTests(fit11t, lagsAC=c(1, 2, 5), nsimu=1, printRes=FALSE)

# G-StMAR model
fit12gs <- fitGSMAR(logVIX, 1, M=c(1, 1), model="G-StMAR")
quantileResidualTests(fit12gs, lagsAC=c(1, 3), lagsCH=1:2,
 nsimu=1, printRes=FALSE)

# GMAR(p=2, M=2) model such that the second AR coefficient of the
# second regime is constrained to zero.
constraints <- list(diag(1, ncol=2, nrow=2), as.matrix(c(1, 0)))
fit22c <- fitGSMAR(logVIX, 2, 2, constraints=constraints)
quantileResidualTests(fit22c, lagsAC=c(1, 3), nsimu=1, printRes=FALSE)
# }