Can basic statistics save your economy? A case on Turkish lira.

Change in Turkish Lira (₺) compared to US Dollar ($) from October 2018 to October 2021.

Living in Turkey has been a financial roller coaster for the last three years. For example, in the above chart, you can see the performance of Turkish Lira (₺) versus US Dollar ($) where the currency depreciated nearly by 50%.

But where does this roller coaster go? A rising parity casts heavy burden on the people of the country and to the businesses within. Determining how the parity would behave is therefore exteremely important. As a Data Scientist, I wanted to see where the USDTRY parity will most likely be in three months of time and below I will show you how far you can get by using statistical tools like bootstrapping.

Histogram of daily percent change in Turkish Lira (₺) versus US Dollar ($) indicated by blue bars. Black line denotes best fit Cauchy distribution to the data with an average of 0.06 and scale of 0.4.

So I went online and downloaded daily USDTRY parity rate from October 2018 to October 2021. Then calculated daily percent change. For example, let’s say on day one parity is 1 and on the second day parity is 1.5, then daily percent change is 100x(1.5–1)/1 = 50%. Finally I plotted the percent changes in a histogram to see the regularity in these fluctuations. You can see the histogram above in color blue.

Histogram shows us that almost all of the time, daily percent change is within +-2%. But once in a blue moon hell breaks loose and the parity can change by up to 8% in a day!

We can explain this kind of behavior with a Cauchy distribution. If you are not familiar with this distribution you might think that it is simply a normal distribution. Though, it certainly is not. Cauchy distribution is a fat-tailed distribution. Meaning that it is far more likely to host extreme events compared to the normal distribution.

With normal distribution, it is very unlikely to see extreme events such as a -4% daily change in the parity. But with the Cauchy distribution it simply is part of the game.

So by looking at the Cauchy distribution we can forecast that Turkish Lira will resume with small fluctuations and then BOOM an upward or downward kick (more likely to be upward) and then it resumes until the other kick, and so on…

Quantifying Booms and Kicks

In order to have a more scientific outcome compared to a narrative with booms and kicks, we will make use of the histogram we calculated.

Now we write each day’s daily percent change on a ball and we put the ball in a sack. Then we draw 90 balls out of this sack. These balls will represent percent change in the parity 90 days onward. We will call this a simulation.

For example, say we drew two balls: +10% and -5%, and our parity value at day zero is 100. Then on day one our parity is 100*(1+0.1) = 110 and on day two the parity is 110*(1–0.05) = 104.5.

Then thanks to a computer, we repeat this simulation a million times and finally get the figure below.

Three month long projections of $/₺ parity obtained from the bootstrapped samples. Red curves denote the 95% confidence levels. Orange line indicates the average value per day.

Each hair like trajectory is a forecast of USDTRY parity 90 days onward. Darker colors mean overlapping simulations (likely outcomes). We see that some of the simulations goes down to 1$=8₺ and some goes up to 11₺. Yet on average (orange line) we can see that the parity has an upward trend.

The area within the red curve is where 95% of the simulations lie. So we can say that with 95% confidence the parity will be somewhere in between those red curves.

Let’s see how the actual trajectory has evolved.

Actual trajectory compared to the forecasts.

Although it seems like a child’s joyful drawing on a wall with a purple crayon, the purple trajectory is the actual the movement of the USDTRY parity. In the first 30 days, trajectory and our forecast was in-line but then things go wild. But how couldn’t we see this coming? We had the data and the distribution and the math. Well I could find three reasons:

1. We visualize the first 1000 simulations among a million. There could be a simulation close to this trajectory that we do not visualize.
2. We are bootstrapping on the actual daily change rates. If we sampled the daily change rates from the Cauchy distribution we just fitted, we could have obtained daily change rates beyond our data (e.g. greater than 8%).
3. This could be an extremely rare event and we have found a black swan.

I’ll go with the third one. Throughout the experiment, we were assuming that the parity was drawn from a static behavior (distribution, sack). However, as of late-September, The Turkish Central Bank started lowering its one-week auction repo rate consistently over the course of three months, in the midst of high inflation and a global pandemic. This action resulted in extreme devaluation of the country’s currency.

I wanted to share this as a humbling exercise for the data savvy. Because, as we are utilizing our mathematical tools to predict, classify or forecast an entity, we are trying to utilize the information we already have upon the unknown. And the unknown is full of surprises. So it is best to approach our model predictions with a grain of salt.

Thank you for your time!