In a previous article on improving-data-quality-through-exploration, I show how Tukey’s exploratory data analysis (EDA) offers an opportunity towards a smarter demand forecasting process. I will now focus on how business cycle time series data can better prepare the forecaster in dealing with economic cycles.

The first known time series using economic data was published in Playfair’s 1786 book and beautifully reprinted in Ed Tufte’s masterful The Visualization of Quantitative Information (1983). William Playfair (1759 – 1823), an English political economist, preferred graphs to tabular displays because he could better show the shape of the data in a comparative perspective. The diagram shows how Playfair plotted the weekly wages of a good mechanic and the price of a quarter of wheat over time.

Playfair commented: “You have before you, my Lords and Gentlemen, a chart of the prices of wheat for 250 years, made from official returns; on the same plate I have traced a line representing, as nearly as I can, the wages of good mechanics, such as smiths, masons, and carpenters, in order to compare the proportion between them and the price of wheat at every different period.”

When item sales, revenue volumes, inventory counts, and such are reported or observed as time series, the data may contain important detail that we can effectively analyze, quantify, and create models for. Time series analysis is a useful tool for identifying essential components in historical data so that we can select the most appropriate model for the problem at hand

Business forecasters and planners commonly assume that variation in a time series can be expressed in terms of several basic components: a long-term trend plus an economic cycle, seasonal factors, and an irregular or random term. It forms the basis of the Ratio-to-Moving Average (RMA) decomposition method developed in 1922 by Frederick R. Macauley (1882-1970) of the National Bureau of Economic Research and is still widely used today.

By comparing a number of traditional and innovative analytical models, we can enhance our understanding of data that are typical or representative of the problem being studied, Such data should be accurate in terms of reporting accuracy and also have been adjusted, if necessary, to eliminate unusual or extreme values.

For a given time series, it may not be possible to observe a particular component directly due to the existence of other components that are more dominant. If appropriate, it is also desirable to correct, adjust, and transform data before creating forecasting models.

Trends and Cycles

It is not uncommon for practicing forecasters to use the term trend when referring to a straight-line projection. But a trend does not need to be a straight-line pattern; a trend may fall or rise and can have a more complicated pattern than a straight line. The US Federal Reserve Board (FRB) index of industrial production (Source: Board of Governors of the Federal Reserve System) highlighting the shaded areas for business recession periods, is a good example of a time series that is predominantly upward trending. The industrial production index measures outputs in the manufacturing, mining, durable goods and electric and gas utilities industries; the reference period for the index is 2007.

How do we know a time series is trending? The inspection of a time series plot often indicates strong trend patterns. Fitting trend lines is a simple and convenient way of exposing detail in data. A useful way of presenting the FRB index is to compare it to some trend line, such as an exponential or straight line trend. This type of analysis brings out sharply the cyclical movements of the FRB index, and it also shows how the current level of output compares with the level that would have been achieved had the industrial sector followed its historical growth rate.

Although this may not be the best or final trend line for the data, the straight-line trend is a simple summary tool. In order to assess the value of this simple procedure, the deviations of the data from this trend line (known as residuals) of the FRB data are shown below. The shaded areas are periods of Business Recession as defined by the US National Bureau of Economic Research (NBER). It is evident that elimination of trend in the data now reveals a cyclical component that appears to correspond to economic expansions and contractions. Modeling can often be thought of as a process of stripping away the essential variation to expose some hidden detail, as in peeling an onion.

Some financial data can also be useful for analyzing and predicting economic cycles. For example, the Treasury yield curve (a plot of the interest rates paid on U.S. securities ranging from 3-month bills to 30-year bonds) has been used by investors and market analysts to decide which Treasury bond or note offer the best interest rate. Typically, 10-year notes yield between one and two percentage points more than 3-month bills and the yield curve bends up. However, if long-term rates fall below the short-term rates, the curve inverts and arcs downward. Economist Frederic Mishkin (1951- ) of the Federal Reserve Bank of New York has discovered that every time the yield curve has inverted, a recession followed a year or so later. A way of looking at this is to plot the difference between the 3-month and 10-year Treasury rates. Every time the difference has sunk below zero, a recession followed roughly 12 months later. Business cycle analysis, leading indicators and a method of cycle forecasting are described in Chapter 7 of my book Change & Chance Embraced: Achieving Agility with Smarter Forecasting in the Supply Chain.

The definition of a cycle in demand forecasting is somewhat specialized in that the duration and amplitude of the cycle are not constant. This characteristic is what makes cycle forecasting so difficult. Although a business cycle is evident in so many economic series, its quantification is one of the most elusive in economic time series analysis.

Other time series data that are not strongly dominated by seasonal and trend effects include the University of Michigan Survey Research Center’s (SRC) index of consumer sentiment, shown below. In this case, the dominant pattern is a cycle corresponding to contractions and expansions in the economy. Of course, a large irregular component is present in this series because there are so many unknown factors that significantly affect the behavior of consumers and their outlook for the future.

Based on an exploratory ANOVA decomposition method (Excel Add-in> Data Analysis> ANOVA: Two-way without replication > OK èview output: SS column in percentages), as described in my book. From this analysis, we determine that the total variability in the consumer sentiment index is made up of 80% trend-cycle effect, 3% seasonal and 17% other (unknown, yet to be identified). When using this index as a factor in a forecasting model, the driver would not have to be seasonally adjusted, while the demand variable to be forecasted may need to be seasonally adjusted first.

Similar consumer sentiment indices are available online for many countries. In this situation, the dominant pattern is a cycle corresponding to contractions and expansions in the economy. (Contrast this with the index of industrial production (above) and monthly housing starts, shown below. Of course, a large irregular component (the uncertainty factor) is present in this series because there are many unknown factors that can significantly affect the behavior of consumers and their outlook on future spending.

In the consumer goods industry, housing starts can be used as a driver of the demand for hard goods (e.g. refrigerators, dishwashers and washing machines). The housing starts over time are also subject to the business cycle fluctuations as do consumer hard goods. Even visually, there appears to be a close association between housing starts and the consumer sentiment index. There are other industries where demand forecasters can establish such linkages with economic or demographic factors.

Many economic series also show seasonal variation. For example, income from a farm in the United States may rise steadily each year from early spring until fall and then drop sharply. In this case, the main use of a seasonal adjustment procedure is to remove such fluctuations to expose an underlying trend-cycle. Many industries also have to deal with similar seasonal fluctuations. To make decisions about price and inventory policy and about the commitment of capital expenditures, the business community wants to know whether changes in business activity over a given period of time were larger or smaller than normal seasonal changes. It is important to know whether a recession has reached bottom, for example, or whether there is any pattern in the duration, amplitude, or slope of business cycle expansions or contractions.

Clearly, to make sense of business cycle indicators we often require a seasonal adjustment of a ratio of variables or a seasonal adjustment of the components of the ratio. Seasonal adjustment procedures are treated in Chapter 6 of my book.

Hans Levenbach, PhD is Executive Director, CPDF Training and Certification Programs. He conducts hands-on Professional Development Workshops on Demand Forecasting for multi-national supply chain companies worldwide. He is group manager of the LinkedIn groups (1) Demand Forecaster Training and Certification, Blended Learning, Predictive Visualization, and (2) New Product Forecasting and Innovation Planning, Cognitive Modeling, Predictive Visualization.