Advance warnings of business cycle contractions and the corresponding market pullbacks would be invaluable. Toward that end, I have used the Economic Cycle Research Institute's (ECRI) recession forecasts to moderate my equity exposure during probable recessionary environments.

While ECRI has an excellent long-term record in business cycle forecasting, its controversial recession call in September of 2011 was premature, counterproductive, and resulted in considerable opportunity costs. In addition, ECRI does not share its proprietary methodology, which makes it challenging to integrate ECRI's forecasts into an investment process. As a result, I became interested in developing a more systematic approach to U.S. recession forecasting.

## A New Framework

I was fortunate to stumble across the work of James Picerno and his articles on the Capital Spectator Economic Trend Index (CS-ETI) and the use of probit models to estimate the probability of a recession. I used his work as the foundation for my own recession forecasting models, which will be presented below.

Picerno uses 18 variables (see Figure 1 below) to construct a diffusion index, which sounds complicated, but is actually relatively simple. His diffusion index represents the percentage of the 18 explanatory variables that are trending higher, consistent with a growing economy.

## Figure 1: CS-ETI December 2012 - Reprinted with permission by Capital Spectator

This is a simple, intuitive framework, but one that does not automatically translate index values to recession risk. It would still be helpful to convert the CS-ETI values into actual recession probability estimates, which can be accomplished with a probit model. Picerno explains his process:

"I'm using a standard probit model that uses the monthly data for the 3-month average of CS-ETI as the independent variable and NBER's monthly recession readings (0 = no recession, 1 = recession). I estimate the cumulative normal distribution of the alpha and beta coefficients via a maximum likelihood technique in both Excel and R."

The resulting probit model converts the CS-ETI diffusion index values into more intuitive recession probability estimates ranging from 0% to 100%.

## New Model Construction

Picerno's work was an excellent place to start. His model was easy to understand and has performed very well historically. Nevertheless, I had a few ideas for improvements. First, instead of building one model, I created two. The first is the UNIT recession model, which predicts the probability of being in a recession, as defined by the National Bureau of Economic Research (NBER). This is the same dependent variable used by Picerno.

The second model was more difficult to estimate, but is potentially more useful. Markets typically peak before recessions begin and reach their troughs before recessions end. As a result, the UNIT peak-trough model attempts to forecast the probability of being between the peak and trough of an NBER-defined recession. Peaks and troughs not associated with NBER recessions were ignored.

I termed the resulting forecasting tools UNIT models, because by definition, the dependent variable probability estimates for the underlying models fall between 0.0 and 1.0 (0% and 100%).

## Diffusion Index Development

To calculate his diffusion index, Picerno uses a 12-month look-back period for every variable, which eliminates possible seasonal adjustment biases, but does not necessarily minimize forecasting errors. Instead, I calculated the optimal look-back period and recession threshold for each independent variable in isolation - to best explain the behavior of the dependent variables. Based on this research, I discarded several of Picerno's variables and added three new variables that were derived from different leading economic indicators.

Picerno's diffusion index (CS-ETI) represents the percentage of independent variables that are trending higher. I reversed this convention for my models. My diffusion index represents the percentage of independent variables that are indicating a recession. All of my models use the same diffusion index, which is based on a common set of 16 independent or explanatory variables (red line in Figure 2 below). The gray shaded regions represent NBER recessions and the blue line represents the log value of the S&P 500 index (right vertical axis). Currently three out of 16 variables indicate a recession, resulting in a diffusion index value of 18.8%. This ties the highest diffusion index reading since July 2009.

## Figure 2 - Trader Edge Recession Diffusion Index

## UNIT Model Development

Picerno's probit model uses a single independent variable: "the 3-month average of CS-ETI." Instead, I use the most recent value of the diffusion index, which allows the model to respond faster. I also added a second independent variable to both of my models: the change in the diffusion index over the past several months. This helps the models differentiate between entering a recession (when the diffusion index is increasing) and exiting a recession (when the diffusion index is decreasing). This allows the models to respond directly to changes in the diffusion index, which was especially advantageous in estimating the peak-trough model.

For each UNIT model, I estimated the probit model, but I also estimated a logit model. Logit models are very similar to probit models, but use a slightly different distribution. The UNIT model represents the average of the probit and logit model forecasts.

## UNIT Recession Model Results

The UNIT recession model estimates are depicted in Figure 3 below (red line - left vertical axis). Again, the gray shaded regions represent NBER recessions and the blue line represents the log value of the S&P 500 index (right vertical axis). When the recession probability estimates exceed 40% (horizontal green line), the U.S. has a material chance of entering a recession. Lower recession warning thresholds (e.g. 30%) could also be used, but would result in more false positives. The probability that we are currently in a recession increased from 0.2% last month to 3.4% based on the November data.

## Figure 3 - Trader Edge UNIT Recession Model

## UNIT Peak-Trough Model Results

In Figure 4 below, the peak-trough estimates (red line - left vertical axis) represent the probability that the S&P 500 is currently between a peak and trough associated with a NBER recession. These probability estimates should increase before a recession begins and fall before a recession ends.

The gray shaded regions in Figure 4 below represent the peak-trough periods associated with NBER recessions - NOT the recession periods that were depicted in the previous charts. To determine the peak-trough periods, I identified the highs and lows of the S&P 500 within 6-9 months of the NBER recession periods.

According to the UNIT peak-trough model, the probability that the S&P 500 is between a peak and trough associated with an NBER recession increased from 6.4% last month to 23.6%, based on data through November 2012.

## Figure 4 - Trader Edge UNIT Peak-Trough Model

## Neural Network Peak-Trough Model Results

Due to the difficulty of estimating the peaks and troughs associated with NBER recessions on a timely basis, I also constructed a neural network peak-trough model. The neural network peak-trough model represents the average of five different neural network models, each using a unique architecture and different independent variables (all based on the diffusion index).

Neural networks are extremely powerful and great care must be used to avoid over-fitting the data. As a result, before constructing the models, I divided the data into three separate groups: training, cross-validation, and testing. The training data was used to train the neural network models. The cross-validation data was used (in conjunction with the training data) to identify the best variable combinations and the optimal number of processing elements. Finally, the testing data was used to ensure generalized solutions that were applicable to data outside the training data-set.

According to the neural network peak-trough model, the probability that the S&P 500 is between a peak and trough associated with an NBER recession increased from 5.1% last month to 27.4% this month, which is generally consistent with the UNIT peak-trough estimate. The neural network peak-trough model forecasts are illustrated in Figure 5 below, which has the same format as Figure 4.

## Figure 5 - Trader Edge Neural Network Peak-Trough Model

## Conclusion

There is no question that the risk of an impending U.S. recession increased significantly in November, but the model forecasts are still below the 30%-40% warning thresholds. In addition, the data was affected by hurricane Sandy, which means the slowdown could be temporary. Fear of the fiscal cliff could also have influenced the data.

While these types of models show promise, they do have their limitations. Forecasting models in general cannot deal with external shocks that are not directly captured by the data. This includes terrorist attacks, conflict in the Middle East, political disruptions, exits from the euro, country defaults, etc.

Given the precarious state of the global economy, if a U.S. recession were to occur, it could come on quickly and it could be severe. Failure to resolve the fiscal cliff would only accelerate that process, making it even more challenging for the models to make timely predictions.

Even with these limitations, the UNIT and neural network model forecasts over the next few months should be very revealing.

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