A Subset SARIMA Model For Daily Euro-Dollar Exchange Rates

This write-up is on the seasonal autoregressive integrated moving average (SARIMA) modelling of daily exchange rates of the Euro and the US Dollar. The realization analyzed is from June 21 to December 17 in the year 2014. Its time-plot has a downward secular trend which depicts the fact that the dollar is relatively appreciating within the 180-day period. An inspection reveals that the series is seasonal of weekly periodicity. Therefore a seven-day differencing of the series yields a series adjudged stationary by the Augmented Dickey Fuller (ADF) Test. However its time-plot shows a generally slightly positive secular trend and its correlogram does not support the stationarity hypothesis as it reveals a sinusoidal pattern of period 7 days. A further non-seasonal differencing yields a series which has a generally horizontal trend and is adjudged as stationary by the ADF Test. Its correlogram not only supports the stationarity hypothesis but also confirms the 7-day seasonality assumption. By application of a new subset SARIMA modelling algorithm an adequate subset SARIMA (1,1,0)x(1,1,0)7 model is fitted to the data. Forecasting of the series may therefore be based on the model.