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A lesson on time series to get you started with FREDcast

Learn how to go from zero to forecasting hero

Two years ago, the St. Louis Fed introduced FREDcast, a forecasting game in the style of fantasy sports. In FREDcast, users enter a forecast for four economic time series each month: GDP, payroll employment, the unemployment rate, and CPI. Now in its third year, FREDcast is growing in popularity and taking hold at some major universities.

The motivation behind FREDcast has been to lower the barriers of forecasting macroeconomic time series, and the game is designed so that anyone with a basic understanding of data can join the game and start forecasting. One of the major challenges, though, is establishing that common, basic understanding of time series data. So let’s lay out a few concepts and definitions to get you started.

What is a time series?

In plain English, a time series is a sequence of data observations collected over time. For example, a collection of the daily closing values of the Dow Jones Industrial Average is a time series. Time series data differ from cross-sectional data, which are observed over many subjects either at the same time or where time is not a factor. Test scores from a statistics class mid-term would be an example of a cross-sectional dataset.

The FRED graph above plots the level values of a time series: real gross domestic product (GDP). Real GDP is the value of an economy’s production of goods and services—a prominent economic variable. In FREDcast, users forecast the growth rate of real GDP, but for illustration purposes we’ll look at the levels here. On the horizontal axis are the quarters of the year when GDP is measured, and on the vertical axis are the values of GDP collected in those quarters. The units of the series are listed on the vertical axis, so we can see that GDP here is measured in billions of 2012 dollars.

The data show some patterns. The most striking pattern is that the value of GDP increases. A secondary pattern involves the smaller movements in GDP up and down. These patterns represent two of the four core properties of time series data:

1. The trend. In any time series, the trend is the slow change in the series over a long period. In this case, it’s a slow increase over time. In the natural world, this is analogous to, say, climate change: how temperatures have been rising slowly over time.

2. The cycle. In most economic forecasting and in FREDcast, we’re interested in the growth rate of a variable. Growth rates can be calculated in a variety of ways, but the core idea is to look at the change in the value of the series from one period to another. As these periods are typically close together (e.g., month to month or year to year), the growth rate captures the smaller, short-term movements in the series instead of the long-term trend movements. These short-term movements are called the cycle, which represents predictable increases and decreases in the data that occur in sync with another process (e.g., the business cycle). In the graph above, the smaller movements in the data occur in sync with the recessions (gray shading). To continue with our weather analogy, cycles could be thought of as heating and cooling in the atmosphere that result in distinct periods of both fair weather and storms.

3. Seasonality. There are cyclical patterns that repeat over units of time (e.g., daily, weekly, monthly). Think about the weather in general in your hometown for an entire year: The temperature displays the same basic seasonal pattern, right? GDP does have a seasonal pattern, but the agency that collects GDP )the Bureau of Economic Analysis) removes the seasonal pattern before publishing the data. For most economic data, we care about the trend and the cycle but not the seasonal variation, since that represents patterns in the data that are independent of overall economic health.

4. Random variation. The last property of time series data is random variation. Not every part of a time series can be explained by a trend, cycle, or seasonal pattern. What’s left over are just random movements that can’t be predicted. Consider, say, a chilly day in mid-July or a warm sunny day in the dead of winter.

What are the time series in FREDcast?

With the exception of the unemployment rate, all the variables used in FREDcast are either changes or growth rates. The variables have also been seasonally adjusted to remove seasonal variation. The leftover components in the FREDcast variables, then, are the cycle and the random variation. Because we can’t predict random variation, FREDcast forecasts are really focused on forecasting the cycle of the four variables.

A simple method to start forecasting is to plot the growth rate of the FREDcast variable* and look at how the cycle relates to the business cycle. Forecasters should then consider the context of the overall economy when making forecasts and draw on their economic knowledge to make a prediction.

Time series data may seem like an unapproachable subject to a new student of economics, but we hope short, simple lessons like these can help anyone become more comfortable with the data.

How this graph was created. Search for “real GDP” on FRED, select the first result, and click “Add to Graph.”

*FREDcast players forecast CPI inflation, for example. Now, CPI is the consumer price index, which, as the name indicates, is an index. But a more common way to talk about inflation is as a growth rate. From the CPI series page in FRED, go to the “Edit Graph” panel and then to the “Units” menu: Change the units from “Index 1982-1984=100” to “Percent Change from Year Ago” and you have a growth rate.

Suggested by Diego Mendez-Carbajo and Hannah Shell.

View on FRED, series used in this post: GDPC1

Where do states get their tax revenue?

Income, sales, fuel, corporate, property, license, tobacco, alcohol...

State governments run on tax revenue in much the same way the federal government does. The FRED graph above shows the specific shares of state tax revenue from many sources. The two major sources are sales tax and individual income tax. While there’s a clear seasonal pattern (mostly from income taxes), there are no strong trends: The shares seem rather stable. If we look a little more closely, though, we can see a shift from corporate income tax to individual income tax and a decrease in motor fuel tax revenue. Granted, it’s not perfectly clear unless you look at the numbers directly. So, if you’re using a mouse, hover over the graph to reveal the values for each series for a particular date, including the percentages. Given the seasonal pattern, it’s best to compare the same quarter over several years—say, the yearly peaks in the second quarter.

How this graph was created: From the release table on State and Local Tax Revenue, click on “national totals of state government tax revenue,” select the quarterly taxes, and click on “Add to Graph.” From the “Edit Graph” panel, open the “Format” tab, select graph type “Area” and stacking “Percent.”

Suggested by Christian Zimmermann.

View on FRED, series used in this post: QTAXT01QTAXCAT2USNO, QTAXT09QTAXCAT2USNO, QTAXT10QTAXCAT2USNO, QTAXT13QTAXCAT2USNO, QTAXT16QTAXCAT2USNO, QTAXT24T25QTAXCAT2USNO, QTAXT40QTAXCAT2USNO, QTAXT41QTAXCAT2USNO

Zoom in on unemployment

GeoFRED maps and BLS data help us view unemployment up close

The U.S. is a large, diverse country with many differences in sectoral composition, demographics, geography, labor mobility, climate, and much more. FRED recently added a bunch of data on U.S. unemployment rates, which is a dataset with its own diverse set of differences and facets. This post explores one of those facets: geographies. We often hear about the national unemployment rate, but the Bureau of Labor Statistics provides a decomposition of unemployment at many geographic levels. Zooming in to these specific areas can help us better understand the country’s economic challenges.

The first two maps look at different ways the Census Bureau has divided up the country: The first has four U.S. Census regions, and the second has nine Census divisions.

The next map shows the 48 continental U.S. states, which obviously vary in size and population density; so, one has to be careful when interpreting the visuals. But clearly, interstate differences can be stark, even for neighboring states. Now let’s go a step further.

The next map show county-level data. In a few cases, the boundaries of a state can be recognized. But, for the most part, counties have their own unemployment experiences beyond any state averages. There are also streaks of color that span over several parts of states, like the ones that run from the Southwest to the Northwest and from the Gulf of Mexico to Lake Erie.

The last graph includes metropolitan statistical areas, which usually span several counties and sometimes multiple states. Not all U.S. territory is encompassed by MSAs, so you’ll notice that many areas don’t have an unemployment rate in this map.

How these maps were created: For each of them, go to GeoFRED, select the geographic unit, and in the cogwheel menu in the upper left select “unemployment rate” as the data.

Suggested by Christian Zimmermann.



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