This study investigates the volatility in daily stock returns for Total Nigeria Plc using nine variants of GARCH models: sGARCH, girGARCH, eGARCH, iGARCH, aGARCH, TGARCH, NGARCH, NAGARCH, and AVGARCH along with value at risk estimation and backtesting. We use daily data for Total Nigeria Plc returns for the period January 2, 2001 to May 8, 2017, and conclude that eGARCH and sGARCH perform better for normal innovations while NGARCH performs better for student t innovations. This investigation of the volatility, VaR, and backtesting of the daily stock price of Total Nigeria Plc is important as most previous studies covering the Nigerian stock market have not paid much attention to the application of backtesting as a primary approach. We found from the results of the estimations that the persistence of the GARCH models are stable except for few cases for which iGARCH and eGARCH were unstable. Additionally, for student t innovation, the sGARCH and girGARCH models failed to converge; the mean reverting number of days for returns differed from model to model. From the analysis of VaR and its backtesting, this study recommends shareholders and investors continue their business with Total Nigeria Plc because possible losses may be overcome in the future by improvements in stock prices. Furthermore, risk was reflected by significant up and down movement in the stock price at a 99% confidence level, suggesting that high risk brings a high return.

中文翻译：

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关于尼日利亚道达尔 Plc 每日股票收益的波动性：来自 GARCH 模型、风险价值和回溯测试的证据

本研究使用 GARCH 模型的九种变体：sGARCH、girGARCH、eGARCH、iGARCH、aGARCH、TGARCH、NGARCH、NAGARCH 和 AVGARCH，以及风险价值估计和回溯测试，调查了 Total Nigeria Plc 每日股票回报的波动性。我们使用 2001 年 1 月 2 日至 2017 年 5 月 8 日期间的 Total Nigeria Plc 回报的每日数据，并得出结论，eGARCH 和 sGARCH 在正常创新方面表现更好，而 NGARCH 在学生创新方面表现更好。对 Total Nigeria Plc 每日股票价格的波动性、VaR 和回溯测试的调查很重要，因为之前大多数涵盖尼日利亚股票市场的研究都没有过多关注回溯测试作为主要方法的应用。我们从估计的结果中发现，除了少数 iGARCH 和 eGARCH 不稳定的情况外，GARCH 模型的持久性是稳定的。此外，对于学生创新，sGARCH 和 girGARCH 模型未能收敛；回报的平均恢复天数因模型而异。根据对 VaR 及其回溯测试的分析，本研究建议股东和投资者继续与 Total Nigeria Plc 开展业务，因为未来可能会通过股价上涨来克服可能的损失。此外，在 99% 的置信水平下，股价的大幅上下波动反映了风险，这表明高风险带来高回报。回报的平均恢复天数因模型而异。根据对 VaR 的分析及其回溯测试，本研究建议股东和投资者继续与 Total Nigeria Plc 开展业务，因为未来可能会通过股价上涨来克服可能的损失。此外，在 99% 的置信水平下，股价的大幅上下波动反映了风险，这表明高风险带来高回报。回报的平均恢复天数因模型而异。根据对 VaR 及其回溯测试的分析，本研究建议股东和投资者继续与 Total Nigeria Plc 开展业务，因为未来可能会通过股价上涨来克服可能的损失。此外，在 99% 的置信水平下，股价的大幅上下波动反映了风险，这表明高风险带来高回报。