# Stationarity & Macroeconomic Forecasting

I'm working with a time series of macroeconomic data (independent variables) and bank loss rates (dependent variable) to show how bank losses vary based on the state of the economy. What I'm doing is two-fold: I need to identify the most predictive economic indicators for my model and then I need to regress those variables against bank losses using OLS. The ultimate application of this is to forecast loss rates in varying economic climates.

One topic that has been coming up over and over again in terms of my model structure is regarding the stationarity of the data. As most on this board know, time series of economic data rarely pass stationarity tests. My question to everyone is how I should proceed in the event that my model does not satisfy stationarity test results.

Let's assume for the example below that I have a simply univariate model where Loss = a + B*UnemploymentRate + e. Please note that the univariate model is only for example - when I'm constructing the actual model, I use multiple economic variables in my regression.

Below is an example of my model construction process, and was hoping for feedback on what's wrong with my process

### 1: Cleaning the dependent data using decompose() in R

Because I'm using quarterly data, I want to remove seasonality as well as remove noise. I use the decompose() function to do this. My final dependent variable is the trend series shown in the plot below:

I don't clean the economic variable because I'm using the seasonally adjusted unemployment rate that's provided by Bureau of Labor Statistics.

### 2: Regress the variables

When I regress unemployment rate against bank losses, I get the following regression output:

                     Estimate Std. Error t value Pr(>|t|)
(Intercept)       -1.236e-03  2.077e-04  -5.954 4.96e-08 ***
Unemployment Rate  3.762e-04  3.077e-05  12.225  < 2e-16 ***
Multiple R-squared:  0.6242,    Adjusted R-squared:   0.62


The fitted results (red) vs. dependent variable (black) is plotted below. For a single factor model, the fitted results mostly capture the trend in my data:

### 3: Validate the Results

Finally, I perform validation tests by testing my model residuals for a unit root using the PP test. As shown by the test below, the residuals have a unit root. However, if I were to perform a multivariate regression with more than one economic variable, I would greatly reduce the size of the residuals and mostly eliminate the autocorrelation of the residuals.

Phillips-Perron Unit Root Test