Exploratory Data Analysis - Madrid

Data¶

For this first experiment, we are looking at Madrid

In this figure, we are showing different representations for the time series of Madrid. In Figure 1, there is a daily time series for the 2m max temperature. In Figure 2, there is a histogram for all of the values. Of course, the distribution does not look like any of the traditional distributions from the GEVD (Figure 1). Unless we decide to condition on the seasonal cycle and/or other covariates, then we need to use some extreme value parser, e.g., block maximum or peak over threshold.

Block Maxima¶

In these examples, we are applying the Block Maxima (BM) method on a yearly basis. So, our block size is of one year which leaves us 62 years in total for our time series. While this is not a lot of data, we see in Figure 5 that the distribution does match one of the classical GEVD distributions. In particular, the Fréchet distribution where the shape parameter, κ, is less than 0 (Figure 1).

In this figure, we have different representations for the block maximum method. We already see a trend line and perhaps a hint of cyclic behaviour. In our first experiments, we see will assume a unconditional distribution however we can see that this assumption is incorrect as we can clearly see from Figure 4.

Peak-Over-Threshold¶

In these examples, we are applying the Peak-Over-Threshold (POT) method with a decluster So, our block size is of 3 days, aka the declustering frequency. In other words, we discretize the time domain to 3 days where we take the maximum value of said 3 days. We see that there is a lot more data available Figure 8 compared to Figure 5. We also see that the distribution does match one of the staple GPD distributions as it has a longer tail.

In this figure, we have different representations for the block maximum method. We already see a trend line and perhaps a hint of cyclic behaviour. In our first experiments, we see will assume a unconditional distribution however we can see that this assumption is incorrect as we can clearly see from Figure 4.

Point Process¶

In these examples, we are applying the Point-Process (PP) method. Similar to the POT example, our block size is of 3 days, aka the declustering frequency. Again, in other words, we discretize the time domain to 3 days and count any event over the threshold as 1 event. The counts represent the number of events that have surpassed the threshold within a year. We see that there is a lot more data available Figure 8 compared to Figure 5. We also see that the distribution does match one of the staple GPD distributions as it has a longer tail.