Judul: A Comparative Study of GARCH, LSTM, and Hybrid GARCH-LSTM Models for Analyzing the Dynamical Pattern of Stock Price Volatility
Abstrak: Most of the statistical methods used in time series analytics assume that the data properties be stationary. In real cases, this assumption may be violated. The stock price is one of the highly volatile data or has a time-dependent variance. GARCH model is a model that overcomes the limitation of the stationary assumption on most statistical methods. In addition, artificial intelligence methods are widely used and have promising performance. This study aims to examine the performance of the GARCH, LSTM, and hybrid GARCH–LSTM models in analyzing the dynamical pattern of volatility data on simulation and empirical data. This study uses two kinds of data, simulation and empirical data. The simulation data are obtained from the simulation process by generating data from the GARCH model with ten scenarios. The scenarios are the combination of two factors: (1) variance with two levels, high and low; (2) dataset with five levels, GARCH (1,1), GARCH (1,3), GARCH (3,1), GARCH (3,3), and Contaminated GARCH. The design for the simulation study is the randomized complete block factorial design with three factors (i.e., variance, dataset, and model), and the response is the MAPE value. The effects of the factors on the MAPE values are analyzed using ANOVA and Tukey's multiple comparisons. Meanwhile, the stock closing prices of PT Bumi Resources Minerals Tbk. in 2021 are used as the empirical study. For the modeling process in empirical study, data are transformed into returns and then modeled using three proposed models. Seven days ahead, predictions are carried out after the model validation process. The ANOVA results show that there are different effects of variance on MAPE values, but these variance effects depend on the kind of dataset. For high variance, the MAPE values of Contaminated GARCH are low, while for the other datasets, the MAPE values are high. According to Tukey's multiple comparisons, the Contaminated GARCH dataset from high variance has different effects on the MAPE value than other datasets from low variance. In addition, the mean MAPE values of GARCH (3,1) and GARCH (3,3) datasets from high variance are higher than those of the GARCH (1,1) dataset from low variance. Another result shows that the GARCH (1,3) and GARCH (3,3) datasets from high variance have different effects on the MAPE value than the Contaminated GARCH dataset from low variance. Furthermore, all comparisons show no significant effect on the MAPE value for the same datasets but with different variances. Another significant factor that affects the MAPE value is the model. The effect of the model does not depend on the variance or the dataset type. Tukey's multiple comparisons show that the Hybrid GARCH–LSTM model outperforms all the other models, followed by the LSTM and GARCH models. For the empirical study, the results show that all models can capture the volatility pattern of the BRMS stock closing prices, but there are some different performances. The GARCH and LSTM models provide the MAPE values of 3.18% and 3.06%, respectively. Meanwhile, for the Hybrid GARCH–LSTM model, the MAPE value is 0.93%. The Hybrid GARCH–LSTM is the best model among others. Based on the three
Keyword: GARCH, Hybrid, LSTM, Stock price, Volatility