# Money Neutrality, Monetary Aggregates and Machine Learning
## 2 Methodology and Data
### The Data  
The dataset consists of the Eurocoin index and the Simple Sum and Divisia monetary aggregates in three levels of aggregation: M1, M2, and M3. M1 is the sum of currency in circulation and overnight deposits, M2 is the sum of M1, deposits with an agreed maturity of up to two years and deposits redeemable at notice of up to three months and M3 is the sum of M2, repurchase agreements, money market fund shares/units and debt securities with a maturity of up to two years.  
The data are monthly covering the period from 2001:1 to 2018:6. The data for the Eurocoin index was obtained from the Centre for Economic Policy Research (CEPR) and the monetary aggregates from Bruegel. Bruegel is a leading independent and non-doctrinal international economics think-tank, contributing to European and global economic policy-making.  
The Eurocoin is an index coincident with the euro area business cycle, and among other properties, it is published monthly and includes information on the underlying growth rate of the euro area GDP. It is computed by the Bank of Italy and the CEPR [21] (the data is available at: [[https://eurocoin.cepr.org/](https://eurocoin.cepr.org/)]([https://eurocoin.cepr.org/](https://eurocoin.cepr.org/))). The monetary aggregates used by most central banks are simple-sum indices in which all monetary components are assigned the same weight. The Divisia indices, originated from [4], apply different weights to different assets in accordance with the degree of their contribution to the flow of monetary services in an economy. The computation of the Divisia monetary aggregates for the Eurozone was conducted by [22] (the data is available at: [[http://bruegel.org/publications/datasets/divisia-monetary-aggregates-for-the-euro-area/](http://bruegel.org/publications/datasets/divisia-monetary-aggregates-for-the-euro-area/)]([http://bruegel.org/publications/datasets/divisia-monetary-aggregates-for-the-euro-area/](http://bruegel.org/publications/datasets/divisia-monetary-aggregates-for-the-euro-area/))).  
In what follows, we use the levels of the Eurocoin index, since seasonality and time trend are well removed by the Bank of Italy and CEPR [21], and log-levels for all the monetary aggregates.  
Figure 3: Overview of a three-fold cross validation for a given set of values of the model’s parameters. Each fold is used as a testing sample, while the rest are used for training the model. The model is evaluated by the average forecasting accuracy for each set of parameters over the k-folds.  
We do not use log returns for the monetary aggregates because we would be testing for money super neutrality. According to the money neutrality theory, changes in the money supply only affect nominal variables (exchange rates, wages and prices) and not real variables (GDP, unemployment, etc.), while the super-neutrality theory assumes that changes in the rate of money supply growth do not affect real variables. Moreover, since the SVM methodology is robust in the existence of unit root processes in the data [23], we did not test for stationarity and proceeded with the levels of all variables. The data are normalized to the [-1,1] range.  
We split our 195-samples dataset into two parts: The first 156 observations form the training sample, and the rest 39 observations were used to evaluate the out-of-sample forecasting accuracy (80-20 split). In order to avoid overfitting, we used a 10-fold cross validation and the out-of sample subset that was kept aside during training and which did not participate in the cross validation procedure, was used to evaluate the generalization ability of the model (out-of-sample forecasting). We implemented the linear and the RBF kernels (the parameter c was scanned from 1 to 50.001 with step 100 and g from 1 to 101 with step 10.).