Last week's update of the Capital Spectator Recession Risk Index (CSRRI)- a simple but revealing diffusion index based on a broad spectrum of economic and financial indicators- suggested that the probability was low that July will mark the start of a new recession. A broad review of recent history can reveal quite a lot about the business cycle, but it's only a beginning. In an effort to peek ahead by projecting CSRRI's readings for the next several months, modern econometric modeling techniques can help.

In particular, by torturing the data with what's known as an ARIMA model (short for autoregressive integrated moving average), we can develop a robust benchmark for peering forward. Yes, all the standard caveats apply: Forecasting, like playing with matches at a gasoline station, can be dangerous in the wrong hands. But with a bit of adult supervision, predicting can help us to think productively about what may or may not be coming. With that in mind, let's kick the tires on the possibilities.

As a preview, crunching the numbers with a series of ARIMA estimates for each of the 17 indicators in CSRRI, and aggregating the results, implies that recession risk will remain low for August. That's no guarantee, of course, but it's one signal (and arguably a robust one) that the slow-growth momentum will roll on for the near-term.

For some of the details behind this forecast, read on. But first, some perspective on where we've been. Here's how the latest reading on CSRRI's indicators stack up via the published data so far:

*(click on charts below to enlarge)*

Why should we care about this menu of numbers? This chart below explains:

As you can see in the graph above, the 80%-plus reading implies that the economy was comfortably above the tipping point. How confident should we be for expecting more of the same for the next month? Here's where an ARIMA model can provide some guidance. The basic procedure is to apply the model to each data series to generate forecasts, one indicator at a time. With those forecasts in hand, the data can be aggregated to compute future expected values for CSRRI.

The challenge with ARIMA-based forecasting is selecting an optimal (or near-optimal) set of parameters for the model. Fortunately, there has been progress in automating the process to a degree by letting the data, in effect, choose the parameter mix. The optimal mix for, say, employment, will differ from the modeling details for industrial production. For projecting CSRRI values, I use Professor Rob Hyndman's forecasting package, which runs on R, a software tool for statistical computing. Cutting to the chase, let's compare the CSRRI forecasts with recent historical data:

As with any forecast, we should treat this one cautiously. Nonetheless, I've taken some precautions to keep the usual hazards to a minimum. First, the future values of CSRRI are estimated by forecasting each of the underlying 17 variables individually via ARIMA. Inevitably, each forecast will likely suffer from a fair amount of uncertainty; the standard errors at, say, the 95% confidence level, are wide enough to drive a truck through compared with the point forecasts. But a portion of this uncertainty is addressed by generating predictions for a broad mix of indicators. As a result, some of the errors in looking ahead are likely to cancel each other out. In other words, the excessively optimistic predictions will be offset by the overly pessimistic ones.

In addition, I'm only looking ahead by three months. As usual in the murky realms of forecasting, the further out in time you look, the wider the band of standard errors. To the extent that we treat forecasts with respect, the highest level of confidence is reserved for the next period ahead, in this case the August 2012 estimate for CSRRI.

By that standard, there's a good case to argue that the broadly positive readings for the nearly complete report card for July will spill over into August. What might derail this rosy outlook? A shock of some magnitude would do the trick. If the euro collapses, for example, the blowback across the Atlantic might be enough to push the U.S. economy over the edge. A greater level of mayhem in the Middle East that sends oil prices skyrocketing should also be on the short list of exogenous shocks that might trip up the modest growth momentum in the U.S.

There are, as always, monsters lurking in the shadows in the delicate art/science of predicting the economy, especially when growth is precarious and relatively sluggish. But based on the numbers in hand, and using the published data to make some conservative forecasts for the next month or so, the case for cautious optimism still looks like a reasonable assumption.