Contents<\/h3>\n\n- Application type<\/a>.<\/li>\n
- Data set<\/a>.<\/li>\n
- Neural network<\/a>.<\/li>\n
- Training strategy<\/a>.<\/li>\n
- Model selection<\/a>.<\/li>\n
- Testing analysis<\/a>.<\/li>\n
- Model deployment<\/a>.<\/li>\n<\/ol>\n
We solve this example with the data science and machine learning platform Neural Designer<\/a>.<\/p>\nTo follow this example step by step, you can use the free trial<\/a>.<\/p>\n<\/section>\n\n1. Application type<\/h2>\n
This is a forecasting<\/a> project since the variable to predict is the future inflation.<\/p>\nThe goal is to model the inflation rate for the next month based on various macroeconomic features from the past three months.<\/p>\n<\/section>\n\n2. Data set<\/h2>\n
The data set contains information to create our model. We need to configure three things:<\/p>\n
\n- Data source.<\/li>\n
- Variables.<\/li>\n
- Instances.<\/li>\n<\/ul>\n
Data source<\/h3>\n
The data file used for this example is macroeconomics.csv<\/a>, which contains monthly information about 16 features for 19 years.<\/p>\nVariables<\/h3>\n
The data set includes the following variables<\/a>:<\/p>\n<\/section>\nTime<\/strong><\/h4>\n\n- \n
Date<\/strong>: Monthly data from January 2001 to November 2019.<\/p>\n<\/li>\n<\/ul>\nMonetary Policy & Inflation<\/strong><\/h4>\n\n- Reference rate (NBP)<\/strong>: Central Bank of Poland\u2019s reference interest rate.<\/li>\n
- Core inflation<\/strong>: Inflation rate excluding food and energy prices.<\/li>\n
- Consumer Price Index (CPI)<\/strong>: Measure of average changes in consumer prices.<\/li>\n
- WIBOR 3M<\/strong>: Three-month Warsaw Interbank Offered Rate.<\/li>\n<\/ul>\n
Labor Market<\/strong><\/h4>\n\n- Average monthly salary (enterprise sector)<\/strong>: Growth rate of gross nominal wages in enterprises.<\/li>\n
- Average employment (enterprise sector)<\/strong>: Growth rate of employment in enterprises.<\/li>\n
- Unemployment rate<\/strong>: Registered unemployment rate at the end of each month.<\/li>\n<\/ul>\n
Industry & Production<\/strong><\/h4>\n\n- Sold production of industry<\/strong>: Growth rate of total industrial production sold.<\/li>\n
- Price index of industry<\/strong>: Growth rate of the industrial production price index.<\/li>\n<\/ul>\n
External Balance<\/strong><\/h4>\n\n- \n
Account balance<\/strong>: Poland\u2019s current account balance (in million euros).<\/p>\n<\/li>\n<\/ul>\nExchange Rates<\/strong><\/h4>\n\n- EUR\/PLN<\/strong>: Monthly average of daily closing exchange rates (euro to zloty).<\/li>\n
- USD\/PLN<\/strong>: Monthly average of daily closing exchange rates (US dollar to zloty).<\/li>\n
- CHF\/PLN<\/strong>: Monthly average of daily closing exchange rates (Swiss franc to zloty).<\/li>\n<\/ul>\n
Stock Market<\/strong><\/h4>\n\n- WIG20<\/strong>: Monthly average of the Warsaw Stock Exchange index for the 20 largest companies.<\/li>\n
- WIG<\/strong>: Monthly average of the Warsaw Stock Exchange main index.<\/li>\n<\/ul>\n
\nInstances<\/h3>\n
On the other hand, the instances<\/a> are divided sequentially into training, selection, and testing subsets, containing 60%, 20%, and 20% of the cases, respectively.<\/p>\nInputs-targets correlations<\/h3>\n
We can calculate the input-target correlations. These indicate which macroeconomic factors have the most significant influence on inflation.<\/p>\n
![](\"https:\/\/www.neuraldesigner.com\/images\/core_inflation_correlations.webp\")
<\/p>\n
In this example, there are a few variables that correlate highly with the target variable. They are WIBOR_3M<\/i>, consumer_price_index<\/i>, and reference_rate_NBP<\/i>.<\/p>\nTime series charts<\/h3>\n
We can also check the time series charts<\/a> for these variables.<\/p>\n![](\"https:\/\/www.neuraldesigner.com\/images\/core_inflation_time_series.webp\")
<\/p>\n
Looking at the time series plot for the target variable, we can see that core inflation has been in the same range for the past 15 years.<\/p>\n
![](\"https:\/\/www.neuraldesigner.com\/images\/core_inflation_WIBOR_3M_time_series.webp\")
<\/p>\n
We can also look at the WIBOR_3M<\/i> chart. If we compare the two previous plots, we see the correlation between the two variables.<\/p>\n<\/section>\n\n3. Neural network<\/h2>\n
The next step is to set the neural network<\/a> parameters. In our case, it is composed of:<\/p>\n\n- Scaling layer.<\/li>\n
- Perceptron layer.<\/li>\n
- Probabilistic layer.<\/li>\n<\/ul>\n
We could have also used an LSTM layer<\/a>.<\/p>\nThe mean and standard deviation scaling method<\/a> has been set for the scaling layer.<\/p>\nNext, we set one perceptron layer<\/a> with 3 neurons that have the hyperbolic tangent activation function<\/a>. This layer has 45 inputs, which are the 15 variables of the dataset for three months. The output is one, the core inflation<\/i>\u00a0for the next month.<\/p>\nNeural network graph<\/h3>\n
The neural network for this example can be represented with the following diagram:<\/p>\n
![](\"https:\/\/www.neuraldesigner.com\/images\/core_inflation_nn.webp\")
<\/p>\n<\/section>\n\n4. Training strategy<\/h2>\n
The fourth step is to set the training strategy<\/a>, defining\u00a0what the neural network will learn.<\/p>\nA general training strategy for classification is composed of two terms:<\/p>\n
\n- A loss index.<\/li>\n
- An optimization algorithm.<\/li>\n<\/ul>\n
Loss index<\/h3>\n
The loss index<\/a> chosen for this problem is the normalized squared error<\/a>\u00a0between the outputs from the neural network and the targets in the data set with L1 regularization.<\/p>\nOptimization algorithm<\/h3>\n
The selected optimization algorithm<\/a> is the Quasi-Newton method<\/a>.<\/p>\nTraining<\/h3>\n
The following chart shows how the training error develops with the epochs during the training process.<\/p>\n
![](\"https:\/\/www.neuraldesigner.com\/images\/core_inflation_training.webp\")
<\/p>\n
The final value is training error = 0.006 NSE<\/b> and selection error = 0.289 NSE<\/b>.<\/p>\n<\/section>\n\n5. Model selection<\/h2>\n
The objective of model selection<\/a> is to improve the neural network’s generalization capabilities or, in other words, to reduce the selection error.<\/p>\nFirst, we perform the neuron selection<\/a>. We want a model whose complexity is the most appropriate to produce an adequate fit of the data. The optimal value for this example is one neuron.<\/p>\nNext, we will apply an input selection<\/a> algorithm. This reduces our inputs to six: the consumer_price_index<\/i> and the core_inflation<\/i> for the past three months.<\/p>\nThe resulting neural network is as follows.<\/p>\n
![](\"https:\/\/www.neuraldesigner.com\/images\/core_inflation_growing_inputs.webp\")
<\/p>\n
With it, the selection error decreases to 0.057 NSE<\/b>. It is a significant improvement compared to the previous value.<\/p>\n<\/section>\n\n6. Testing analysis<\/h2>\n
The objective of the testing analysis<\/a> is to validate the generalization performance of the trained neural network.<\/p>\nTo validate a forecasting technique, we need to compare the values provided by this technique to the observed values.<\/p>\n
Goodnes-of-fit<\/h3>\n
We can use linear regression analysis<\/a> as the standard testing method for these projects.<\/p>\n![](\"https:\/\/www.neuraldesigner.com\/images\/core_inflation_linear_regression.webp\")
<\/p>\n
The correlation value for this example is R2 = 0.977<\/b>, which is close to 1.<\/p>\n
This means that we have a good predictive model.<\/p>\n
Error statistics<\/h3>\n
We solve this example with the data science and machine learning platform Neural Designer<\/a>.<\/p>\n To follow this example step by step, you can use the free trial<\/a>.<\/p>\n<\/section>\n This is a forecasting<\/a> project since the variable to predict is the future inflation.<\/p>\n The goal is to model the inflation rate for the next month based on various macroeconomic features from the past three months.<\/p>\n<\/section>\n The data set contains information to create our model. We need to configure three things:<\/p>\n The data file used for this example is macroeconomics.csv<\/a>, which contains monthly information about 16 features for 19 years.<\/p>\n The data set includes the following variables<\/a>:<\/p>\n<\/section>\n Date<\/strong>: Monthly data from January 2001 to November 2019.<\/p>\n<\/li>\n<\/ul>\n Account balance<\/strong>: Poland\u2019s current account balance (in million euros).<\/p>\n<\/li>\n<\/ul>\n On the other hand, the instances<\/a> are divided sequentially into training, selection, and testing subsets, containing 60%, 20%, and 20% of the cases, respectively.<\/p>\n We can calculate the input-target correlations. These indicate which macroeconomic factors have the most significant influence on inflation.<\/p>\n In this example, there are a few variables that correlate highly with the target variable. They are WIBOR_3M<\/i>, consumer_price_index<\/i>, and reference_rate_NBP<\/i>.<\/p>\n We can also check the time series charts<\/a> for these variables.<\/p>\n Looking at the time series plot for the target variable, we can see that core inflation has been in the same range for the past 15 years.<\/p>\n We can also look at the WIBOR_3M<\/i> chart. If we compare the two previous plots, we see the correlation between the two variables.<\/p>\n<\/section>\n The next step is to set the neural network<\/a> parameters. In our case, it is composed of:<\/p>\n We could have also used an LSTM layer<\/a>.<\/p>\n The mean and standard deviation scaling method<\/a> has been set for the scaling layer.<\/p>\n Next, we set one perceptron layer<\/a> with 3 neurons that have the hyperbolic tangent activation function<\/a>. This layer has 45 inputs, which are the 15 variables of the dataset for three months. The output is one, the core inflation<\/i>\u00a0for the next month.<\/p>\n The neural network for this example can be represented with the following diagram:<\/p>\n The fourth step is to set the training strategy<\/a>, defining\u00a0what the neural network will learn.<\/p>\n A general training strategy for classification is composed of two terms:<\/p>\n The loss index<\/a> chosen for this problem is the normalized squared error<\/a>\u00a0between the outputs from the neural network and the targets in the data set with L1 regularization.<\/p>\n The selected optimization algorithm<\/a> is the Quasi-Newton method<\/a>.<\/p>\n The following chart shows how the training error develops with the epochs during the training process.<\/p>\n The final value is training error = 0.006 NSE<\/b> and selection error = 0.289 NSE<\/b>.<\/p>\n<\/section>\n The objective of model selection<\/a> is to improve the neural network’s generalization capabilities or, in other words, to reduce the selection error.<\/p>\n First, we perform the neuron selection<\/a>. We want a model whose complexity is the most appropriate to produce an adequate fit of the data. The optimal value for this example is one neuron.<\/p>\n Next, we will apply an input selection<\/a> algorithm. This reduces our inputs to six: the consumer_price_index<\/i> and the core_inflation<\/i> for the past three months.<\/p>\n The resulting neural network is as follows.<\/p>\n With it, the selection error decreases to 0.057 NSE<\/b>. It is a significant improvement compared to the previous value.<\/p>\n<\/section>\n The objective of the testing analysis<\/a> is to validate the generalization performance of the trained neural network.<\/p>\n To validate a forecasting technique, we need to compare the values provided by this technique to the observed values.<\/p>\n We can use linear regression analysis<\/a> as the standard testing method for these projects.<\/p>\n The correlation value for this example is R2 = 0.977<\/b>, which is close to 1.<\/p>\n This means that we have a good predictive model.<\/p>\n1. Application type<\/h2>\n
2. Data set<\/h2>\n
\n
Data source<\/h3>\n
Variables<\/h3>\n
Time<\/strong><\/h4>\n
\n
Monetary Policy & Inflation<\/strong><\/h4>\n
\n
Labor Market<\/strong><\/h4>\n
\n
Industry & Production<\/strong><\/h4>\n
\n
External Balance<\/strong><\/h4>\n
\n
Exchange Rates<\/strong><\/h4>\n
\n
Stock Market<\/strong><\/h4>\n
\n
Instances<\/h3>\n
Inputs-targets correlations<\/h3>\n
<\/p>\nTime series charts<\/h3>\n
<\/p>\n<\/p>\n3. Neural network<\/h2>\n
\n
Neural network graph<\/h3>\n
<\/p>\n<\/section>\n4. Training strategy<\/h2>\n
\n
Loss index<\/h3>\n
Optimization algorithm<\/h3>\n
Training<\/h3>\n
<\/p>\n5. Model selection<\/h2>\n
<\/p>\n6. Testing analysis<\/h2>\n
Goodnes-of-fit<\/h3>\n
<\/p>\nError statistics<\/h3>\n
![](\"https:\/\/www.neuraldesigner.com\/images\/core_inflation_output_plot.webp\")
<\/p>\n<\/section>\n