This thesis examines the GARCH models. The purpose of the paper is to perform an analysis of different GARCH models, and to see how well they fit our dataset’slog-returns. The log-returns comefrom the closing price of the stock from Danske Bank. Firstly, we want to show that GARCH models are ideal to describe financial datasets, which we did. We used the statistical programming language Rstudio to implement the different GARCH models. Subsequently, we looked at the different distributions the White noise had, and wanted to compare them across different GARCH models. We saw that the t-distribution fitted our dataset best across several models.
Next we had to look how the different models estimated their parameters and how well they fitted the dataset. It was found that low orders of GARCH models were preferred over higher orders, since the Goodness-of-fit generally decrease as the order increases. We found two models, GARCH (1,1) and EGARCH (1,1), which were the best to describe our log-returns, where the EGARCH (1,1) was marginally better than the former. That was also the case when we used the models to forecast. We saw, that EGARCH could more accurately predict the confidence interval in which our datasets log-returns occurred. Although GARCH over a longer period of time was able to get a greater amount of data within the intervals of forecasts, we concluded that EGARCH is the better model for forecasting. We also used simulation to get an idea of how the return could look like inside the intervals of the forecasted models.
|Uddannelser||Cand.merc.mat Erhvervsøkonomi og Matematik, (Kandidatuddannelse) Afsluttende afhandling|