In this study, we examine the fluctuation in the value of the Great Britain
Pound (GBP). We focus particularly on its relationship with the United States
Dollar (USD) and the Euro (EUR) currency pairs. Utilizing data from June 15,
2018, to June 15, 2023, we apply various mathematical models to assess their
effectiveness in predicting the 20-day variation in the pairs' daily returns.
Our analysis involves the implementation of Exponentially Weighted Moving
Average (EWMA), Generalized Autoregressive Conditional Heteroskedasticity
(GARCH) models, and Implied Volatility (IV) models. To evaluate their
performance, we compare the accuracy of their predictions using Root Mean
Square Error (RMSE) and Mean Absolute Error (MAE) metrics. We delve into the
intricacies of GARCH models, examining their statistical characteristics when
applied to the provided dataset. Our findings suggest the existence of
asymmetric returns in the EUR/GBP pair, while such evidence is inconclusive for
the GBP/USD pair. Additionally, we observe that GARCH-type models better fit
the data when assuming residuals follow a standard t-distribution rather than a
standard normal distribution. Furthermore, we investigate the efficacy of
different forecasting techniques within GARCH-type models. Comparing rolling
window forecasts to expanding window forecasts, we find no definitive
superiority in either approach across the tested scenarios. Our experiments
reveal that for the GBP/USD pair, the most accurate volatility forecasts stem
from the utilization of GARCH models employing a rolling window methodology.
Conversely, for the EUR/GBP pair, optimal forecasts are derived from GARCH
models and Ordinary Least Squares (OLS) models incorporating the annualized
implied volatility of the exchange rate as an independent variable.

通过应用数学模型和评估预测准确率，研究了英镑与美元和欧元货币对的波动性。发现 EUR/GBP 货币对存在不对称的回报，而 GBP/USD 货币对的证据不确定。使用 GARCH 模型时，假设残差遵循标准 t 分布而不是标准正态分布，效果更好。对于 GBP/USD 货币对，使用滚动窗口方法得到的 GARCH 模型产生最准确的波动率预测，而对于 EUR/GBP 货币对，最佳预测来自 GARCH 模型和 OLS 模型，其中 OLS 模型中的独立变量是年化的隐含波动率。

分析货币波动：GARCH、EWMA 和 IV 模型对 GBP/USD 和 EUR/GBP 货币对的比较研究

Analyzing Currency Fluctuations: A Comparative Study of GARCH, EWMA, and  IV Models for GBP/USD and EUR/GBP Pairs

In this paper, we develop a hybrid approach to forecasting the volatility and
risk of financial instruments by combining common econometric GARCH time series
models with deep learning neural networks. For the latter, we employ Gated
Recurrent Unit (GRU) networks, whereas four different specifications are used
as the GARCH component: standard GARCH, EGARCH, GJR-GARCH and APARCH. Models
are tested using daily logarithmic returns on the S&P 500 index as well as gold
price Bitcoin prices, with the three assets representing quite distinct
volatility dynamics. As the main volatility estimator, also underlying the
target function of our hybrid models, we use the price-range-based Garman-Klass
estimator, modified to incorporate the opening and closing prices. Volatility
forecasts resulting from the hybrid models are employed to evaluate the assets'
risk using the Value-at-Risk (VaR) and Expected Shortfall (ES) at two different
tolerance levels of 5% and 1%. Gains from combining the GARCH and GRU
approaches are discussed in the contexts of both the volatility and risk
forecasts. In general, it can be concluded that the hybrid solutions produce
more accurate point volatility forecasts, although it does not necessarily
translate into superior VaR and ES forecasts.

采用深度学习神经网络和 GARCH 时间序列模型的混合方法来预测金融工具的波动性和风险，研究发现混合模型能够提供更准确的点波动率预测，但不一定能转化为优越的风险预测。

深度学习和 GARCH 模型结合的金融波动率和风险预测

Combining Deep Learning and GARCH Models for Financial Volatility and  Risk Forecasting

This study aims at comparing several deep learning-based forecasters in the
task of volatility prediction using multivariate data, proceeding from simpler
or shallower to deeper and more complex models and compare them to the naive
prediction and variations of classical GARCH models. Specifically, the
volatility of five assets (i.e., S\&P500, NASDAQ100, gold, silver, and oil) was
predicted with the GARCH models, Multi-Layer Perceptrons, recurrent neural
networks, Temporal Convolutional Networks, and the Temporal Fusion Transformer.
In most cases the Temporal Fusion Transformer followed by variants of Temporal
Convolutional Network outperformed classical approaches and shallow networks.
These experiments were repeated, and the difference between competing models
was shown to be statistically significant, therefore encouraging their use in
practice.

该研究旨在比较基于深度学习的多变量数据预测模型在波动率预测方面的表现，结果表明 Temporal Fusion Transformer 优于传统方法和浅层网络，因此鼓励将其应用到实践中。