A stock market risk forecasting model through integration of switching regime, ANFIS and GARCH techniques
Graphical abstract
Introduction
Forecasting market risk is a widely studied subject that has captured the interest of scholars due to its highly non-linearity and volatility. Thus, several approaches use these data for model testing. Generalized auto regressive conditional heteroscedasticity (GARCH) models [1] are one of the most commonly used models to study volatility. Although response to these models is generally good, they are unable to successfully capture extreme changes in the complete time series. Due to this shortcoming, one of the focuses of research has been to work on alternatives that can better approximate the non-linear part of the series, mainly using Artificial Intelligence, such as artificial neural networks (ANN) [2]. This algorithm has been used extensively in stock markets and for market risk, because it is able to theoretically approximate any non-linear function with minimal error. In practice, the use of an ANN allows us to improve forecasting systems [3] as well as forecasts from econometric models [4] with excellent results.
Nonetheless, from an economic point of view, the volatility behavior of an asset depends on several other variables that may have impacts on the particular asset. Therefore, it is key to understand how these new variables (external to the asset) affect it. These variables are not necessarily the same as the explanatory variables of an econometric model. As their influence could be non-linear, the inclusion of these variables may result in a worse forecast. Thus, a variable that could be important in a linear model is not necessarily a good input for an ANN model, and an irrelevant variable in a linear model could be a good input for the ANN. The variables used in this paper were particularly selected because of their importance in the region [5]. We considered 11 factors that may influence the behavior of the stock index return volatility of three different countries, 6 exchange rates, 4 commodity prices, and one interest rate. The exchange rates are Euro to Dollar, Chilean Peso to Dollar, Mexican Peso to Dollar, Brazilian Real to Dollar, Yen to Dollar, and Peruvian Sol to Dollar. We chose to include the interest rate of United States Federal Reserve, and the four commodities are prices of WTI, gold, silver, and copper.
It is not straightforward to apply an auto-regressive (AR) model since these variables, and specifically their impact, may be seasonal or depend on time. Regime switching models are often used for such a task, because they dynamically model a variable depending on the probability that in that time, it could be affected by the selected explanatory variables. The Markov Switching (MS) model can be used for this problem. According to the above, we propose the use of MS in this paper in order to determine the states of each external factor in terms of high and low volatility.
These states can be used to explain different changes in asset volatility in a linear model. However, metaheuristics that can explain non-linear relationships provide better results. To observe the actual relationship between the variable states and the studied asset, several techniques are mentioned in the literature, such as genetic algorithm (GA) [6], support vector machine (SV) [7], artificial neural fuzzy inference system (ANFIS) [8], among others. The ANFIS approach has exhibited solid results when the task involves integrating external variables in the forecast [9], due to its ability to relate different inputs in a “non-crisp” way. In this paper, the use of ANFIS is proposed to study this relationship, acting as a practical link between the external variables that may influence asset behavior and the asset itself.
Some recent papers have addressed the goal to predict financial asset volatility with fuzzy systems. Regarding Hung [34], a fuzzy system is used in which the GARCH model is integrated inside the architecture and optimized using a GA. The contribution that makes our study different is that we use the Markov switching technique to integrate the effects of external factors and with this, enhance the forecast of the best GARCH in each case. We then use this effect and outperform the GARCH forecast with the use of an ANN. Regarding Dash and Dash [35], they use a novel methodology in which the neural network of the fuzzy system is changed for a functional link neural network and combined with the EGARCH model to perform the volatility forecast. The difference between their approach and the presented paper is that we integrated the Markov Switching to capture the effects of external factors in the prediction of GARCH. Then, these effects are combined into a neural network and thus outperform the best GARCH prediction.
The remainder of this paper is ordered as follows: In Section (2), we perform a full review of studies related to the presented problem. Section (3) explains the methodologies used in detail. In Section (4), we present the model results and analyses, and Section (5) discusses the different sensitivity results for the crucial parameters. Finally, Section (6) presents the discussion and conclusions.
Section snippets
Literature review
There is a great amount of research related to the study of stock market volatility, mainly because of its importance in both economic approaches and modeling. In terms of economics, there is a clear relationship between external variables and stock market assets. In a study conducted by Engel, Ghysels & Sohn [10], these authors analyze how macroeconomic variables, such as growth and inflation, can have a strong influence on long-term stock market volatility. Moreover, they found that, in the
Methodology
As mentioned in the literature review, economic variables improve forecasting. For this reason, we considered 11 factors in this study that may influence the behavior of stock index return volatility in three different countries. Specifically, we chose 6 exchange rates, 4 commodities, and a global market interest rate as a reference. Exchange rates, commodities, and global macroeconomic variables are widely considered to be influential in the stock market, especially in emerging economies [[69]
Factor identification and data collection
For the following study, the data used for the ANN methodology were GARCH-type model predictions for the IPC, IPSA, and IBOV, the main stock market indexes of Mexico, Chile, and Brazil, respectively. Specifically, we use 21 inputs related to the previous predictions (t-a, whit a = 1… 21). The data source is the Economatica database. For the MS-FNN-GARCH methodology, apart from the basic data, eleven volatility factors were used as additional data, which were selected according to relevance in
Sensitivity analysis
Even though the previously proposed methodology provided good results for different markets, it is still interesting to study whether these results are affected as well as if the magnitude of the arbitrary parameters, such as neurons and layers, are modified. Therefore, we change several parameters of the base model (3 hidden layers and 15 neurons). The Model Confidence Set (MCS) test is also applied to determine the best forecasting model(s) in each market and for each loss function.
Conclusions
This study focuses on improving the forecasting power of the well-known GARCH model, combining forecasts and additional external variables (macroeconomics) in a fuzzy intelligent system that allows us to analyze new relationships and obtain more precise results.
The methodology allows us to conclude that an important improvement is obtained by using fuzzy system inference in combination with analytic models in comparison with the results delivered individually. This makes the use of hybrid
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