Inflection points

I’ve been aware of various economic forecasts that pop-up from time-to-time in the popular press. There is no consensus, of course, but one would at least expect some coherency. This expectation, sadly, is unlikely to be met. Why?

Inflection points. For my purpose here, an inflection point is a point in a data series where the data stops going in one direction (increasing or decreasing) and starts going in the other direction (decreasing or increasing).  In the case of current economic forecasts, it is the point when the “economic data” stops decreasing and starts increasing.

Most economic forecasters are terrible when it comes to forecasting these inflection points. Why is that? Most economic forecasts are made using trends in the data and it is pretty easy to get a good forecast if the data is moving in only one direction. Also, most economic data series are highly correlated (they tend to move in the same direction at about the same rate), so it’s tough to find evidence that a data series is about to change direction even by looking at evidence from other data series.

To illustrate this point I went to the census.gov website (governments are a great source of data) and downloaded the most recent history of Retail Sales data. This series includes total retail sales from January 1992 through October 2010 (October is listed as provisional). This data series illustrates another couple of points. One is that it’s almost January 2011, but the latest provisional month of data is for October. Yes, the data lags. The second point is this notion of provisional. Yes, the data history changes as we move forward. It can change a lot. Nearly all of these data series are “estimated” in the sense that the totals from a given series are derived from survey samples.

I took the monthly retail sales data history and used it to forecast retail sales for the next 36 months (November 2010 through October 2013). There are many ways to forecast this series, but all involve the interaction between the forecaster, the data and some form of statistical software. What I did with this forecast was to intervene as little as possible in this process. The process took several steps and the end result is this graph.

In the graph, the data history are to the left of the vertical line, the forecast data are to the right. As I noted, I had very little to do with this forecast. I chose the basic method, but just kept the results from that model. If you’re interested, the model was (1) remove the seasonality (the various spikes – they line up by month) and trend (basically up and then down), (2) fit an ARIMA model  to what’s left (the residuals). There are various ways to remove the seasonality and trend, but what I did was use regression on a time trend, a squared time trend and a cubed time trend, and I included a “dummy variable” for each month. The best fitting ARIMA model turned out to be a 2, 1, 2.

This forecast illustrates the problem in that the prediction is for some modest improvement in retail sales through much of 2011 and then things slowly get worse.  Is this a reasonable forecast? One way to gauge is to see how well the model fits the data.

The model looks pretty good (red is the model, blue is the actual data). So, as a forecaster I could say that things aren’t looking so bright for the economy. This is only retail sales, but retail sales tell a fair amount about economic activity. Because consumer spending accounts for roughly two-thirds of economic activity and forms the basis for much of state and local tax revenue (with their usual balanced budget requirements), retail sales are an important indicator of the health of the economy. But can we trust this model?

To help answer this question, we could look at monthly year-over-year growth rates. Looking at these, we see that one possible inflection point was around February and March of 2008 (that was when retail sales levels started shrinking), and another was around November and December of 2009 (retail sales levels started growing again). Looking at 2010 retail sales data, the monthly year-over-year growth rates look pretty robust, but the problem is that 2008 and 2009 were so bad that although the growth rates look good, the changes in dollar values are relatively small, which could be one reason why our the forecast model is not picking up a true inflection point.

At this point there are three basic choices. One, simply put faith in the forecast model and use the forecast generated by that model.  Two, throw out this model and try a different model. Three, use judgment to simply adjust the forecast. What would I do? I would most likely go back and adjust the model. But the overall problem remains – how to accurately forecast an inflection point (and the related problem of determining the new trend after that point).

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