Investigating Ways to Construct Empirical Analysis of Financial Time Series

Abstract

Volatility refers to the extent to which a time series’s value varies over time. It is critical in finance since it reflects the likelihood of a stock or financial indicator deviating significantly from its current value. Mandelbrot (1963) recognised the tendency for periods of high and low volatility to cluster together. This concept resulted in the key findings of Engle (1982), who demonstrated that a model allowing for modifying conditional variance was capable of capturing the clustering characteristic found in financial data. The purpose of this research is to identify some of the essential properties of financial time series, investigate how successfully ARCH and GARCH models can capture them, and compare various GARCH models. In addition, the methods for implementing the notions in practice are examined, along with their advantages over more fundamental models. We have begun with fundamental time series ideas are reviewed and the technique for developing and assessing linear time series models, emphasising the ‘ARMA’ model. It is discovered that after using ARMA models to fit the best ARMA model to FMCC closing price data, which contains data on returns squared, there are significant problems in terms of the inability to explain the existing correlations in the data thoroughly. A discussion is given for the basic GARCH and ARCH classes, and how to tell which type of distribution the model has and how it can exhibit both heavy-tailed and fat-tailed distributions is illustrated. The ARCH model has strengths in that it considerably enhances the ARMA model’s limitations but has its downsides, such as requiring lots of additional parameters. However, when used with the same data set, the GARCH model overcomes these drawbacks. Several variations to these models are discussed and possible approaches for developing and evaluating forecasts of conditional variance. It utilised univariate time series data on (FMCC), which can be incredibly valuable for multivariate GARCH modelling and evaluation. Additionally, we compared the GARCH-X model to six other models: IGARCH, eGARCH, apGARCH, GJR-GARCH, csGARCH, and GARCHX. AIC and BIC were used to compare the models. Residual studies are conducted using the Ljung-Box test, which also detects white noise. We found that the GARCH-X model performs better than others when used for FMCC closing price stock returns. The closing prices of the Standard and Poor 500 stock index during the Coronavirus pandemic are analysed using summary statistics to demonstrate the financial time series’ characteristics further. We used the GARCH-X model for volatility modelling, with the covariates introduced in the model are Bank discount, Death Count (Number of people who died due to COVID19 in the New York only), the Death count in 7 days average, Case count (Number of positive COVID19 cases), Case count 7 days average and Oil Price. This research discovered that conditional variance models are beneficial when dealing with data sets. It is anticipated that this study will serve as a guide for future applications and evaluations of these models on various data sets.