Forecasting High-Frequency Currency Data Using GARCH-Models

The aim of this research is to build GARCH models, which are able to forecast different exchange rates rather accurate. The following stages can be distinguished as tasks – analyze previously written literature about forecasting different financial assets with GARCH models, find the data and process it correctly for research, then build, teach and test GARCH models on collected data and compare them with each other using information criteria, build confidence intervals of forecasts for GARCH models, make conclusions. As a data 6 exchange rates were collected from the web-site “Investing.com” in the period from the 5th of February 2004 to 5th of February 2024, for each dataset 3 statistic tests were conducted – Diki-Fuller stationarity test(unit-root test), Ljung-Box test for autocorrelation in residuals and Shapiro-Wilk test on the normality of the residuals. During the research different models were introduced and built – basic GARCH model, GARCH model with asymmetric distribution, GJR-GARCH and EGARCH. In addition, for assessing the quality of forecasts and building confidence intervals were used models of realized volatility(HAR-RV). All stages of the study were performed using the Python software. Before building the model, all time series were brought to stationary ones by calculating profitability of exchange rates. Turning to results it is worth emphasizing that in four of six models EGARCH turned to be the most optimal, however in case of the Euro-Dollar and Dollar-Yuan time series, the GJR-GARCH model turned out to be more adequate. For an experiment different EGARCH and GJR-GARCH models with the selection of hyperparameters were built, in most cases standard models with parameters (1,1) turned to be the most optimal, but in other cases it was necessary to take into account more distant values of squares of residuals and variances. Also at the end of the main part, confidence interval forecasts were built based on the realized volatility model and GARCH models on both train and test samples in order to analyze the quality of volatility forecasts, judging by the results of building confidence intervals, they turned out to be quite good.