Exchange rates play a pivotal role in global trade and finance, influencing investment decisions, economic policies, and cross-border transactions. Understanding how exchange rates move relative to each other is crucial for policymakers, traders, and multinational corporations. This project focuses on analyzing the co-movement of the British Pound (GBP) and the Euro (EUR)—two of the most influential currencies in the global economy.

This study achieves four essential things. First, it analyses the time-series idea of stationarity in two exchange rates, the pounds sterling and the euro. Secondly, ask if a long-run equilibrium relationship exists between the pounds and euro and uses the cointegration concept to answer. Thirdly, apply the principle of the GARCH (1,1) model to the specified exchange rate to forecast volatility and consider volatility accuracy.

The motivation for this study stems from the intertwined economic relationship between the UK and the Eurozone. Despite the UK’s withdrawal from the European Union, trade, investment, and financial markets remain closely linked. Investigating whether and how their exchange rates move together provides valuable insights into market dynamics, shared economic risks, and the potential for diversification in currency portfolios.

Findings. 

The statistical outcome of the co-integration of the two rates agrees with Granger’s representation theorem of long-run equilibrium relationship and the four parts (random walk, stationary process, a deterministic trend, a term that relies upon the underlying values).  of a cointegrated VAR process.  Engaging the GARCH model, we arrived at statistically significant outcomes for the correlation between the exchange rates implying there is a strong relationship, and it varies over time. This agrees with (Engle and Yoo, 1987) who suggested the VAR model as an appropriate forecast model for time series that move together or trend together.

Read More here.