Thursday, January 2, 2014

What’s with Seasonal Adjustments Already?

Eric Martinson, Economist

One of the fascinating characteristics of the human mind is our collective and individual ways of assessing the world around us. From infancy, we establish relationships and patterns to make sense of our environments. We test our observations and, hopefully, adjust our internal models as our understanding is enhanced. Today, with the tsunami of data that technology has created and the immediacy of communication, making sense of markets can be a daunting task. How does one discern the relevance, if any, of a particular statistic in relation to another piece of information?  How do we separate random (or even determined) “noise” from meaningful insights and relationships?

One sentence from the most recent Employment Summary (November 2013) press release for the state of Utah released by DWS provides a case in point: “The seasonally-adjusted unemployment rate for the state registered 4.3 percent” [emphasis added]. There is rarely an occasion during which I present to a given audience about the labor economy where I am not asked, when providing some relevant statistic, about the meaning and the need for seasonally-adjusted data. What types of data are seasonally-adjusted and why?

Seasonal adjustment is a statistical technique that attempts to measure and remove the influences of predictable seasonal patterns. Some data series have noticeable movements across various months due only to different seasons, such as construction employment being up in summer and down in winter, or elementary education employment being down during summer and winter breaks. The goal is to remove the seasonal movements and instead look for non-seasonal movements. The non-seasonal movements tell the underlying story of what is changing or not in construction, education, etc.

The adjustment essentially extracts from the data a trend where we can evaluate these underlying movements from period to period. In our example above, the unemployment rate (the proportion of the civilian, non-institutionalized labor force that is unemployed and desires to be employed) is seasonally adjusted from month to month. Over the course of a year, the size of the labor force, the levels of employment and unemployment, wages and other measures of labor market activity undergo fluctuations largely due to seasonal events including changes in weather, harvests, major holidays, or school schedules. Because these seasonal events generally follow a regular pattern each year, their influence on statistical trends can, for certain analyses, be ignored and eliminated by seasonally adjusting the statistics from month to month. These seasonal adjustments make it easier to observe the underlying cyclical and structural trends, or other non-seasonal influences in the series.

Depending on the data being observed, there are other patterns of seasonality besides the 12-month seasonality of monthly employment. When the data permits, adjustments can be applied weekly, quarterly, and so on. Figure 1 shows Utah’s non-seasonally-adjusted unemployment rate (the blue wavy line) with a seasonally-adjusted rate (the smoother dark red) superimposed on the non-adjusted series. Figure 2 shows the same series for January 2009 through December 2009. This closer detail illustrates how despite a decrease in the actual unemployment rate from March to April, when seasonally adjusted, the underlying trend of the unemployment rate is instead increasing. In other words, when the seasonal employment factor is taken out of the actual employment series, the trend is opposite of what the series shows for the month of March 2009.

There are many different ways, some relatively simple while others being rather complex, to approach seasonally adjusting data. But the general idea is to compute a moving average of a specified number of periods. This process essentially decomposes the data into three components in a data time series: “trend,” “seasonal,” and “remainder” (or “random error”–small portions that have some other explanation).  The trend component shows the long-term movements (increases or stagnations) of the data. It is this component that essentially serves the basis for seasonally-adjusted data. The constant fluctuation in the data that is taken out as a result of the moving average computation, leaving the seasonal component. This can be seen in Figure 1 where the variation of the actual unemployment rate (blue) is “smoothed” to an underlying trend (dark red). Depending on the data, the amplitude of seasonality can be small or large. Also, we can determine any cyclical movements in the data by analyzing the trend line once the seasonality is eliminated. That is, any patterns exhibiting rises and falls in the data that are not fixed to a particular season.

Once the trend is extracted, it essentially serves as the basis for seasonally-adjusted data. Some sophisticated models may add a few more steps to this procedure, but the underlying process is fundamentally the same in any seasonal adjustment process.

 Click graphs to enlarge 

Below is output from one statistical software that illustrates the various components of employment data. They are separated into seasonal, trend, and any remainder. Worth repeating is that the process for seasonal adjustment varies from one model to the next. One model’s output may be slightly different than another’s depending on which model is being used. For instance, the Bureau of Labor Statistics incorporates what is called an X-12 ARIMA model to determine seasonally-adjusted employment and unemployment data.

Click graph to enlarge 

Seasonal adjustments are helpful in allowing an observer to filter a time series in order to identify the fundamental trends that may be otherwise more difficult to see in the actual data.  Isolating the trend reveals the underlying story within the data, unmasking the real movements in a data series.

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