Abstract
In this paper, we provide a mathematical and statistical methodology using heteroscedastic estimation to achieve the aim of building a more precise mathematical model for complex financial data. Considering a general regression model with explanatory variables (the expected value model form) and the error term (including heteroscedasticity), the optimal expected value and heteroscedastic model forms are investigated by linear, nonlinear, curvilinear, and composition function forms, using the minimum mean-squared error criterion to show the precision of the methodology. After combining the two optimal models, the fitted values of the financial data are more precise than the linear regression model in the literature and also show the fitted model forms in the example of Taiwan stock price index futures that has three cases: (1) before COVID-19, (2) during COVID-19, and (3) the entire observation time period. The fitted mathematical models can apparently show how COVID-19 affects the return rates of Taiwan stock price index futures. Furthermore, the fitted heteroscedastic models also show how COVID-19 influences the fluctuations of the return rates of Taiwan stock price index futures. This methodology will contribute to the probability of building algorithms for computing and predicting financial data based on mathematical model form outcomes and assist model comparisons after adding new data to a database.
Highlights
Complex financial time-series data are difficult to fit using a simple model for the core model in artificial intelligence
If we seek to build a more precise model, a simple model form cannot achieve this aim; at the same time, imprecise errors can lead to uncontrollable situations
If the reason for obtaining the precise model is to predict and to reduce the errors of the model, should we still follow the trend model up to power-to-three and avoid the overfitting problem? We propose that the complex data pattern should be modeled by using a mathematical model form
Summary
Complex financial time-series data are difficult to fit using a simple model for the core model in artificial intelligence. The third misspecification is heteroscedasticity and serial correlation The latter is not discussed in this paper, the lagged period mainly determines the data prediction and the reasonableness of the linear model assumption. The above series of AR models depend on the linear regression model form and normal distribution assumption, without considering whether or not the data characteristics satisfy those assumptions. The empirical results of the example show that the COVID-19 pandemic affects the expected value model and heteroscedastic model forms of Taiwan stock price index futures.
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