Fall to avoid macroeconomic variables in forecasts (part II) |FIC advice (2023)

By Michael Sureace andRobert Chang

Despite the prevalence of forecasting tools based on macroeconomic basis, the correlation of the results with macroeconomic time series is a statistically complex process full of challenges (challenges (challengesSee part I) The organizations must be ready to understand parking, time trends, unit roots, structural editions, co -fertilization and models of correction of vectorholish.The naive linear regression with a number of macroeconomic times often leads to false regressions and meaningless results^[1]The creation of forecast models based on macroeconomic conditions, which could add hundreds of thousands.

Fi Consulting has created an automated instrument to withdraw an interest variable (e.g. violation rate, prepaid rate) against macroeconomic factors, based on our deep experience with the construction of prognostic models that are based on macroeconomic environments in several environments of the public sector.Our tool is looking for.Via a long list of macroeconomic candidates based on the preferences of the business lines and automatically prepares the regression variables, parking, co -fertration and structural fractures.The tool then proves candidate models and classify them after the adaptation quality.Model for the commercial purpose, make sure that the model is statistically solid and that the model exists statistical tests.

In the following sections, we show how our instrument exceeds the statistical challenges of the structure of forecast models based on macroeconomic language.Different economic environments.If we use the mortgage crime rates and the charge rates of loans to consumers as examples, we design our tool for forecast for forecast every variable that depends on the selection, depending on any number of potential macroeconomic variables as predictors.

1 repair solution

As described in Part I, the inclusion of macroeconomic variables in the forecast processes of a company is statistically challenging and requires considerable resources to implement correctly.In order to reduce the effort for institutions, FI has developed a tool that developed the construction of forecast models based on the basis of efforts, macroeconomic of the automated FI tool, the value that it offers the financial institutions, and analyzing the performance of the toolOverview of the automated process for the construction of models.

In order to show a macroeconomic forecast instance with non -stationary time series, we apply the tool to predict a crime rate of the mortgage portfolio and the credit loads on the consumer by returning in several macroeconomic factors.If we use the interest rates, we use the interest rates of mortgage crime crime and loan fees to the consumer In this example, we design the tool in order to predict variable depending on the selection of any number of potential macroeconomic variables such as predictors.In this section, the model is initially analyzed statistically solid.

Data preparation

We design the instrument for prediction of any selected variable variables and develop forecast models with relevant macroeconomic variables as independent variables.The tool houses a number of historical macroeconomic data from raw and publicly available to build a forecast models^[2]The data cover a wide range of macroeconomic variables, including interest rates, real estate market variables, consumer debt, emotional feeling and money data.

First we import macroeconomic data and place it in a panel format (every column that represents a temporary series of another variable).We create transformations, including delays, differences and growth rates.[3]The following diagram shows the types of transformations that are carried out in macroeconomic data.

The transformations of each macroeconomic variables expand the number of possible predictors for the estimate and can be an expensive exercise of resources.A modeler must carry out a number of tests in each variable to determine which transformation does the best work to predict the dependent variables.The automation of this step is of crucial importance, since a manual approach would severely limit the number of macroeconomic variables available for consideration.

Uniform root test

As soon as the data has been imported and created, we have to analyze it to determine whether they can be used in the regression analysis.One of the main problems with the temporary series data is the presence of a uniform root.This means that the data series is not inpatient and has changes on average over time, variations and covariance.The non -stationary data used in regression analysis can lead to biased predictions.The tool carries out three different statistical tests to check whether there are parking spaces in every temporary series:

1. Dickey-Fuller (ADF) Test: Null hypothesis that there is a unit root in the temporal series.The non -compliance with the null hypothesis comes to the conclusion that the temporal series is not inpatient.
2. Prueba de Kwiatkowski-Phillips-Schmidt-Shin (KPSS): Null hypothesis that a unit root is not available in the temporal series.The non -compliance with the null hypothesis comes to the conclusion that the temporal series is inpatient.
3. Phillips-Perron (PP) Test: Null hypothesis that there is a unit root in the temporal series.The non -compliance with the null hypothesis comes to the conclusion that the temporal series is not inpatient.

For every macroeconomic variable we follow the following process:

1. Perform the three root tests of the device to check -Stationer.
2. Discard all variables that are classified as not inpatient.

The result of this process is a number of macroeconomic variables and transformations that are inpatient.These variables are used as predictors in the forecast models.

Selection of variables

As soon as the model has identified the sentence of candidate variables that can be used in the regression models, we must determine which combination of variables the "best" models generates[4]The algorithm proves all possible combinations of variables and select the groups of variables based on a defined criterion, which work better, it is advantageous because it proves all possible variable groups.As soon as all possible combinations of "n" predictors have been specified, the model reduces the number of candidate models with the following approach:

1. It eliminates models that do not consider different macroeconomic data.For example, a model is removed that uses three different GDP transformations.This is intended to ensure that the final model takes into account different types of macroeconomic indicators.
2. Eliminated models in which waste are not stationary.This ensures that we do not violate linear regression assumptions and use OLs for estimate.

As soon as the model has eliminated the candidate models that contain redundant predictors, and those who have no stationary waste, the tool selects the best candidate based on a certain test criterion, e.g.B. Candidate models with the highest adapted R.²Or the lowest amount of squares (RSS).This approach is advantageous because every possible combination of variables is tested.When working with a large number of predictors, however, the number of possible combinations can be immense.There are 2^kPossible combinations.This approach can be a very intensive resource and time.The following diagram shows the resulting data record that was created according to the best partial scarf gorithm, and the filter process has been completed.

Prognosemodell

As soon as we have identified the optimal predictors of the dependent variables, the tool carries out a final regression in the dependent variables.In this model we use the predictor variables observed in the time (X X_{t, 1}, X_{t, 2}, … X_{t, k}) Forecast and_TIn a classic linear regression environment[5]The model can be summarized in the equation as follows:

We appreciate the coefficients (β) according to OLS. The model estimation window is specified.Suppose we have 100 observations in our time series.We use the first 70 observations to estimate the coefficients.According to the estimation procedure, we use the coefficient of the same estimated to predict the values of the dependent variables for the remaining observations.This corresponds to the distribution of our data into training and test data sets.[6].

2 forecast results

In order to evaluate the model output, we carry out the algorithm in two sets of dependent variables;1) mortgage crime sentences and 2) Specification interest to the consumer.The results of the model are shown in the following sections.

Mortgage crime interest

Quarterly Mortgage Crime (MDR) for the period 1991 to 2021.ThatTool It formed the regression of the data from 1991 to 2013.We choose theFinal specifications below:

wo,

Diffcpi= First IPC difference
Growing= 5 quarters of the feeling of the American consumer
Growth= 4 quarters VIX index growth rate

The following figure shows the prediction of the model compared to real installments for the retention period.

Figure 1. mortgages crime rates outside the sample performance

Consumer loan Last interest rate

Fred Consumption Loan Last Sentences (COR) from Fred for the period 1987 to 2021. The model Schulte Schulte the regression of the data from 1987 to 2013. We choose the final specification shown below:

wo,

Growth finds= 8 quarters of growth rate of federal funds
Growth= 8 quarters of growth rate of the crime rate of credit cards
Vix= 8 quarters of the VIX index delay

The following figure shows the prediction of the model compared to real installments for the retention period.

Figure 2. Credit rates outside the sample performance

conclusion

The inclusion of macroeconomic variables in the forecast processes of a company is statistically challenging and requires considerable resources to [Macrooeronicomia - Telel I.] In order to reduce the effort to which institutions are confronted, FI has developed a tool that automatically automatically automatically the construction of forecast models based on macroeconomically.Any intent to learn more or check whether the models of your institutions are implemented correctly?Send an e -mail to Robert Chang to Robert Chang and Michael Sureaceinfo@ficoning.com.

References:

[1]Granger, C.W.J.and Newbold, P. (1974) Espurias reciptions in the Economics.jour of Econometrics, 2, 111-120

[2]Historical macroeconomic data are extracted from Fred (https://fred.stlouisfed.org/).

[3]Although it is possible to generate an infinite number of transformations, we conduct delays of up to 8 periods and the first differential and growth rates of up to 8 periods.

[4]Furnival, G. M. and Wilson, R. W. (1974)."Regression to jump and borders". Technometrics 16: 499–511.

[5]The model enables contemporary relationships between dependent and independent variables.Based on this design, we assume that macroeconomic forecasts are perfect.This is a joint assumption that is used by institutions in the forecast.

[6]Note that the model currently uses 70% of the observations to train regression and the remaining 30% as a retention test.However, this can be configured by the user.