Prediction intervals in conditionally heteroscedastic time series with stochastic components

By Santiago Pellegrini, Esther Ruiz, Antoni Espasa. 2011

24 citations recorded by the source corpus.

Differencing is a very popular stationary transformation for series with stochastic trends. Moreover, when the differenced series is heteroscedastic, authors commonly model it using an ARMA-GARCH model. The corresponding ARIMA-GARCH model is then used to forecast future values of the original series. However, the heteroscedasticity observed in the stationary transformation should be generated by the transitory and/or the long-run component of the original data. In the former case, the shocks to the variance are transitory and the prediction intervals should converge to homoscedastic intervals with the prediction horizon. We show that, in this case, the prediction intervals constructed from the ARIMA-GARCH models could be inadequate because they never converge to homoscedastic intervals. All of the results are illustrated using simulated and real time series with stochastic levels.

Subfields: Economics and Econometrics, Finance, Management Science and Operations Research

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Citations in the corpus

Stock Market Prediction on High-Frequency Data Using Generative Adversarial Nets (2018, methodology): “values of stock time series and the GARCH model forecasts future volatilities [20].”
Optimal predictions of powers of conditionally heteroscedastic processes (2013, background): “Pellegrini et al. (2012) analyse the effects of differencing GARCH with stochastic trend on the prediction intervals.”