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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

The stock market is not the economy

Taking a "random walk" through the data

Does the stock market tell us anything about the economy? The stock market seems to react continually to various data and economic news, and many of us follow its day-to-day changes, especially if we’re invested in it. But do fluctuations in the stock market actually reflect economic health?

The best measure we have for measuring total economic activity is GDP. But GDP is measured only quarterly and with a considerable lag. With the help of FRED, though, we can look at a decade’s worth of data to see how closely GDP relates to the stock market.

The graph above looks at quarter-to-quarter percent changes in the Dow Jones Industrial Average (DJIA), deflated to remove general price increases, and real GDP, which is by definition also deflated to remove general price increases. Of course, the stock market is very volatile, but it’s too hard to see any relationship in this line graph. A better way to visualize connections (or a lack of connections) is a scatter plot, shown below, with the same data.

If the two measures were related, we would see the points clustered in the lower left, middle, and upper right. But we don’t see that. One reason may be that the DJIA covers only 30 firms. While they’re large firms, they make up only a fraction of the economy. So we built the same graph (below) with data from the S&P500, which encompasses the 500 largest firms on the stock market. But no luck: We still don’t see any relationship.

So why are GDP and the stock market graphically unrelated? First, it’s important to understand what the value of a stock measures: the sum of discounted expected dividends plus a liquidation value of capital. In other words, what the market thinks the future dividends of the firm will be, evaluated at current prices, and what could be obtained from liquidation if the firm goes bankrupt. Note that dividends are only a small part of the firm’s income; dividends don’t account for any income that’s directed toward taxes, servicing loans and bonds, and (maybe most importantly) wages. The labor income share of total income in the economy is about 60%. And, as recently noted on this blog, the labor income share has decreased. Now, if regulation or laws reduce the bargaining power of labor, for example, labor income decreases, capital income and dividends increase, but total income may not have changed or even decreased.

How these graphs were created: Search for “Dow Jones,” select the Industrial Average series, and click on “Add to Graph.” Click on “Edit Graph,” add the “GDP deflator,” apply formula a/b, and set units to “Percent change.” From the “Add Line” tab, search for and select “real GDP,” and set units to “Percent change.” Once you restrict the sample to the last 10 years, you have the first graph. For the second, take the first, use the “Edit Graph” panel to open the “Format” tab and select type “Scatter.” For the third graph, replace the DJIA with SP500. You can then expand the sample.

Suggested by Christian Zimmermann.

View on FRED, series used in this post: DJIA, GDPC1, GDPDEF, RU3000TR, SP500

20/19 Hindsight

Checking policymakers’ economic predictions against the data

Since 2007, the Federal Open Market Committee (FOMC) has published individual members’ assessments of the economy in the Summary of Economic Projections (SEP). The SEP was one of Chairman Bernanke’s communication innovations in an effort to increase transparency after the 2007-09 Great Recession.

This expanded forward guidance includes predictions of the changes in the federal funds rate, GDP, the unemployment rate, personal consumption expenditures (PCE) inflation, and core PCE inflation. It’s released along with the minutes of selected FOMC meetings. Each policymaker submits an estimate for each indicator for the next three years as well as a longer-run estimate.

A recent St. Louis Fed Review article cites a survey of economists and other Fed watchers: 33% found the SEP “useful,” 29% found it “somewhat useful,” and 38% found it “useless.” Investors and economic journalists use the projections as a forecast for the economy and monetary policy changes—in particular, the federal funds rate predictions. Investigating the success of the SEP at predicting indicators could give insight into the effectiveness of this FOMC communication channel.

Thankfully, ALFRED tracks changes in policymakers’ SEP forecasts across time. By placing different vintages of predictions on the same graph (as we did above), we can see how policymakers may have shifted their views over time. Policymakers consistently overshoot the effective federal funds rate by a good margin. What’s going on there? Well, as the note on the FRED page for this series explains, the SEP tracks participant projections for the end of a calendar year. So we should use the annual and year-end settings (instead of daily data for the federal funds rate), as in the graph below.

This looks much better. FOMC predictions match the data well, especially over the short-run. (As in the first graph, the thick red line shown above is the effective federal funds rate for 2019-06-18.) This close alignment isn’t surprising, given that these are the median data points for projections and the Committee sets interest rate targets by voting. However, the median for the dot plot was tracked only beginning in 2015 and the yearly nature of the projections means a small sample size. Predictions in 2015 and 2016 favored a steadily increasing federal funds rate, but more recent predictions favor a slower increase in rates. If interest rates begin falling, the SEP may look very different.

Now let’s look at a different prediction reported on the SEP: the growth rate of real GDP. (The thick red line shown above is real GDP for 2019-06-18.) There are more data points for this graph because this measure was reported starting in 2007. A representative prediction was selected from Q4 of each calendar year for (slightly) less graph clutter. Again, policymakers’ predictions are generally closely aligned with the actual data, especially for shorter-term predictions. Between 2009 and 2014, the two- and three-year predictions tended to overshoot the actual data—that is, they were more “optimistic.” Since 2015, however, policymakers’ projections have appeared more “pessimistic” in the medium- and longer-term, trending closer to or even below the reported GDP growth rate.

How these graphs were created: For the federal funds rate graphs: From ALFRED, search for “FOMC Summary of Economic Projections for the Fed Funds Rate, Median.” Check the appropriate series in the search results and click “Add to Graph.” By default, ALFRED creates a bar chart; to change to a line graph, use the “Graph type” menu under the “Format” tab. To include the earliest vintage, click on the “Edit Graph” button, go to the “Edit Line 1” tab, and select vintage 2015-12-16. To add the next vintage, go to the “Add Line” tab, search for and select the correct series, click “Add data series,” go to the “Edit Line 2” tab, and select vintage 2016-03-16. Repeat this process until all desired vintages have been added. Then, to add the federal funds rate line, go to the “Add Line” tab, search for and select “Effective Federal Funds Rate,” click “Add data series.” Adjust the range of the plot so the start date is 2016-01-01 and the end date is 2020-01-01. For the second graph, go to the tab for the federal funds rate line (Line 12, in this case), select “Annual” in the “Modify frequency” dropdown menu, and select “End of Period” in the “Aggregation method” dropdown menu.

The process was similar for the growth rate of GDP graph, but search for “FOMC Summary of Economic Projections for the Growth Rate of Real Gross Domestic Product, Central Tendency, Midpoint” instead. Note that FRED supports a total of 12 lines, so a representative vintage from Q4 of each year was selected. To add the growth of real GDP line, go to the “Add Line” tab, search for and select “Real Gross Domestic Product,” click “Add data series,” go to the tab for the real gross domestic product (Line 11, in this case), select “Percent Change from Year Ago” in the “Units” dropdown menu, and select “Annual” in the “Modify frequency” dropdown menu. In the “Format” tab, remove the titles to dispense with the clutter from two-line legends. Finally, adjust the range of the plot so the start date is 2007-01-01 and the end date is 2020-01-01.

Suggested by Darren Chang and Christian Zimmermann.

View on FRED, series used in this post: EFFR, FEDTARMD, GDPC1, GDPC1CTM


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