Abstract
This chapter ties together most of the previous parts of this book. Macroprudential oversight and data alike not only motivate, but also provide guidelines for building tools with visual capabilities. Data and dimension reductions, as well as their combinations, provide means for creating visual displays for a wide range of tasks, whereas a qualitative comparison shows that the Self-Organizing Map (SOM) is suitable for the task we have at hand. This chapter unifies the above discussed topics by creating a SOM-based financial stability map, coined the Self-Organizing Financial Stability Map (SOFSM). The task involves five key building blocks: the SOM, crisis dates, vulnerability indicators, a model training framework and a model evaluation framework.
I would very much welcome inspiration from other disciplines: physics, engineering, psychology, biology. Bringing experts from these fields together with economists and central bankers is potentially very creative and valuable. Scientists have developed sophisticated tools for analysing complex dynamic systems in a rigorous way. These models have proved helpful in understanding many important but complex phenomena: epidemics, weather patterns, crowd psychology, magnetic fields.[...] I am hopeful that central banks can also benefit from these insights in developing tools to analyse financial markets and monetary policy transmission.
– Jean-Claude Trichet, President of the ECB, Frankfurt am Main,
18 November 2010
This chapter is partly based upon previous research. Please see the following works for further information: Sarlin and Peltonen (2013) and Sarlin (2013c)
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Notes
- 1.
When the 3-month government bill rate is not available, the spread between interbank and T-bill rates of the closest maturity is used. The equity returns are multiplied by minus one, so that negative returns increase stress, while positive returns are set to 0. When computing realized volatilities for components \(\text {Ind}_{3{-}5}\), average daily absolute changes over a quarter are used.
- 2.
The noise-to-signal ratio is a ratio of the probability of receiving a signal conditional on no crisis occurring to the probability of receiving a signal conditional on a crisis occurring. Demirgüç-Kunt and Detragiache (2000) and El-Shagi et al. (2012) showed that minimizing the noise-to-signal ratio could lead to a relatively high share of missed crisis episodes (i.e., only noise minimization) if crises are rare and the cost of missing a crisis is high. This type of a common corner solution to the optimization problem is mainly due to the fact that the marginal rate of substitution between type I and II errors is unrestricted. Lund-Jensen (2012) concludes the same, and chooses not to use the measure, while Drehmann et al. (2011) choose to minimize the noise-to-signal-ratio subject to at least two thirds of the crises being correctly called. Likewise, Sarlin (2013c) also illustrates such a corner solution.
- 3.
While the seminal loss function by Demirgüç-Kunt and Detragiache (2000) accounts for unconditional probabilities, they do not propose a Usefulness measure for the function. Given their complex definition of loss, deriving the Usefulness would not be an entirely straightforward exercise. Further, the version applied in Bussière and Fratzscher (2008) neither accounts for unconditional probabilities nor distinguishes between losses from correct and wrong calls of crisis.
- 4.
- 5.
The loss function used by Alessi and Detken (2011) differs from the one introduced here as it assumes equal class size. Their Usefulness measure does, similarly, not account for imbalanced classes, as the loss of disregarding a model depends solely on the preferences. Usefulness measures close to that in Alessi and Detken (2011) have been applied in a large number of works, such as Lo Duca and Peltonen (2013), Sarlin and Marghescu (2011a), El-Shagi et al. (2012), Bisias et al. (2012). Similar loss functions have been applied in Fuertes and Kalotychou (2007), Candelon et al. (2012), Lund-Jensen (2012), Knedlik and Schweinitz (2012).
- 6.
Recall positives \(= TP/(TP+FN)\), Recall negatives \(= TN/(TN+FP)\), Precision positives \(= TP/(TP+FP)\), Precision negatives \(= TN/(TN+FN)\), Accuracy \(= (TP+TN)/(TP+TN+FP+FN)\), TP rate \(= TP / (TP + FN)\), FP rate \(= FP/(FP+TN)\), FN rate \(= FN/(FN+TP)\) and TN rate \(= TN/(FP+TN)\).
- 7.
The BMU is the unit that has the shortest Euclidean distance to a data point. When evaluating an already trained SOM model, all data are projected onto the map using only the indicator vector \(x_{j(in)}\in \mathbb {R}^{14}\). For each data point, probabilities of a crisis in 6, 12, 18 and 24 months are obtained by retrieving the values of C6, C12, C18 and C24 of its BMU (\(m_{b(cl)}\)).
- 8.
The logistic regression proceeds as follows. First, it forms a predictor variable which is a linear combination of the explanatory variables. The values of this predictor variable are transformed into probabilities by a logistic function. This logistic function operates through \(f(z)=\frac{1}{1+e^{-z}}\), where \(z=\beta _{0}+\beta _{1}x_{1}+\beta _{2}x_{2}+\beta _{3}x_{3}+...+\beta _{k}x_{k}\), \(\upbeta _{o}\) is the intercept and \(\upbeta _{1}+\upbeta _{2}+\upbeta _{3}+...\upbeta _{k}\) are the regression coefficients of \(x_{1}+x_{2}+x_{3}+...+x_{k}\), respectively. The value of \(z\) measures the total contribution of all the predictor variables used in the model. It is worth to note that \(f(z)\rightarrow 0\) when \(z\rightarrow -\infty \), and \(f(z)\rightarrow 1\) when \(z\rightarrow \infty \). Moreover, when \(z=0\), then \(f(z)=0.5\). Thereby, a response curve for a logistic regression is S-shaped.
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Sarlin, P. (2014). Self-Organizing Financial Stability Map. In: Mapping Financial Stability. Computational Risk Management. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54956-4_7
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