The constant challenge in the search for accurate forecasting has led researchers to improve existing techniques and invest in the search for alternative methodologies. However, the scientific literature has pointed out some limitations of specific forecasting methodologies. Particular characteristics present in time series, namely when historical data show changes outside the standards, can be an obstacle to the modelling and forecasting process. For example, some time series (TSD) show high variability with respect to its mean for a given period. Such data volatility makes predictions of future values very difficult when corresponding to long time horizons. These volatility issues entail two major problems: accuracy decreases, and trend does not hold. In this paper, we propose predict Tesla volatility using a hybrid model with a discrete wavelet transform ARIMA (W-ARIMA) and a generalized autoregressive model with conditional heteroskedasticity (GARCH). For the first case, in ARIMA models, which require stationarity of the time series, variances and regressions of statistical data are used to find patterns for approximating future values. When combined with a discrete wavelet transform, the time series is decomposed into an approximate series and one or more detail components, depending on the level of decomposition performed. Predictions are given by adding individual predictions for each term given by the ARIMA model. Alternatively, predictions by GARCH model are made considering variances and prior errors of the time series. Performance of the proposed models will be evaluated and compared through different error and goodness-of-fit metrics, to confirm the effectiveness of the discrete wavelet transform as a pre-filter for the ARIMA model and compare the results obtained with those delivered by the GARCH model. Based on these results, it is also proposed a novel hybridization technique for prediction error reduction. The results show that the hybrid w-ARIMA and GARCH model significantly improves predictions obtained when each model was used separately.

This work is partially financed by national funds through FCT – Fundação para a Ciência e a Tecnologia under the UIDB/00006/2020 project

Tesla,GARCH model,Wavelet transform,ARIMA model,Volatility.