In our discussion, we’ve taken a deep dive into the world of foreign exchange (FX) data. We’ve crunched the numbers to understand the characteristics of these financial variables. Let’s break it down step by step in a more straightforward manner.
Getting to Know the Data
Firstly, you would have to lay out some essential statistics for independent and identically distributed normal variates. This table gives us insights into the data’s central tendencies, spread, and more. Then look at mean, median, maximum, minimum, standard deviation, skewness, kurtosis, the Jarque-Bera statistic, its probability, sum, sum squared deviation, and the number of observations.
The Jarque-Bera test helps us assess whether the data’s skewness and kurtosis are in line with a normal distribution. If not, that implies that we need to explore alternative distributions that might fit better, like the Student’s t distribution and GED, which have fatter tails.
Preparing the Numbers
Once the initial descriptive statistics are understood and shows the possible transformations you can make on the data then you can obtain the mean daily return for FX and its standard deviation. Using the Jarque-Bera statistic to determine whether that data doesn’t follow a normal distribution. Regardless of the Jarque-Bera being unable to pinpoint whether skewness or kurtosis is the culprit, as long as it shows that the magnitude of kurtosis seems to play a more significant role then we can proceed to prep the numbers for forecasting.
Patterns in the Data
Once the data is prepped and ready, we then observe the Ljung-Box Q statistic for the residuals and squared residuals. To check if there’s no serial correlation in the residuals (suggesting they aren’t correlated) or that there is a presence of volatility clustering in US FX data.
Alternative GARCH Models
The key component in this exercise is to explore the alternative GARCH models (as mentioned in the last article) to find the best fit for our data, so we go back to them and test which variant of the model (Standard GARCH, Extended GARCH, GARCH-M (in-mean), etc.) works best for the data at hand. The differences between the alternative GARCH models vary but generally the differences lie between how each alternative will treat the GARCH model would treat the data such as allowing for asymmetric volatility like the Extended GARCH. Of course, there is the possibility that some models won’t converge when that happens; it may require a revisiting of the input data to determine the root cause or move on to a better fitting alternative GARCH model. Once the models are done estimating you can proceed to choose the model that best fits that data according to the AIC levels for the distribution types you tested.
Evaluating Forecasts
Once your initial forecasting is done you can then proceed to back test the results. When it comes to forecasting FX, the most often used tests are the RMSE and MAE formulas mentioned in the previous article. Once you’ve determined the proper out-of-time sample to test (e.g., 2 months forecast or less), then you can set out to find the best choice for forecasting among the models you’ve examined and maybe start writing about it in an article published weekly.