## ARCH ModelsARCH (autoregressive conditional heteroskedasticity) models recognize the presence of successive periods of relative volatility and stability. The error variance, conditional on past information, evolves over time as a function of past errors. The model was introduced by Engle [1982]. Bollerslev [1986] proposed the GARCH (generalized ARCH) conditional variance specification that allows for a parsimonious parameterisation of the lag structure. Considerable interest has been in applications of ARCH/GARCH models to high frequency financial time series. The ## ExamplesThe examples in this section use a data set of daily exchange rate changes for the Deutschemark/British pound. The data set is from Bollerslev and Ghysels [1996] and has been adopted as a benchmark data set by McCullough and Renfro [1999] (also see the discussion in McCullough and Vinod [1999]). The model of interest is: Y where P - Testing for ARCH
- Estimation of a GARCH(1,1) model
- Benchmark comparisons of coefficients and standard errors
## ReferencesBaillie, R.T. and Bollerslev, T., "The Message in Daily Exchange
Rates: A Conditional-Variance Tale", Bollerslev, T., "Generalized Autoregressive Conditional
Heteroskedasticity", Bollerslev, T. and Ghysels, E., "Periodic Autoregressive
Conditional Heteroscedasticity", Bollerslev, T. and Wooldridge, J.M., "Quasi Maximum Likelihood
Estimation and Inference in Dynamic Models with Time Varying
Covariances", Engle, R.F., "Autoregressive Conditional Heteroscedasticity with
Estimates of the Variance of United Kingdom Inflation",
Judge, G.G., Griffiths, W.E., Hill, R.C., Lutkepohl, H. and
Lee, T., McCullough, B.D. and Renfro, C.G., "Benchmarks and Software Standards:
A Case Study of GARCH Procedures", McCullough, B.D. and Vinod, H.D., "The Numerical Reliability of
Econometric Software", Weiss, A.A., "Asymptotic Theory for ARCH Models: Estimation and
Testing",
[SHAZAM Guide home] |