Views > Data visualization > To find seasonality use cycle plots

“Time discovers truth.”

Lucius Annaeus Seneca
Roman philosopher

We've always been fascinated by the concept of “time”. It's probably the most important concept known to mankind and has long been a major subject of study in religion, philosophy, and science.

No wonder that our ancestor's oldest attempt to represent data graphically was a time series. The graph below—dating from the tenth or eleventh century—illustrates the movement of planets as a function of time.

Source: “A Note on a Tenth Century Graph”, H. Gray Funhouser, Osiris Vol. 1, (January, 1936), pp. 260-262.

Moving forward to our modern history, time-series chart is the most frequently used form to display data. According to Edward Tufte, time series made 75 percent of the charts in a random sample of 4,000 graphics published in leading international newspapers between 1974 and 1980—R. Edward Tufte, “The Visual Display of Quantitative Information”, 2001, Graphics Press.

To understand the popularity of the time-series we need to look no further than one of the manager's most important roles: forecaster. Indeed, the primary goal of the analysis of a time series is forecasting—Hence, its high frequency of appearance in business reports. But in order to forecast we first need to identify patterns in the observed data. Once patterns are identified, valuable insights into the movement of the data might be gained and forecasting into the future becomes an easier task.

Different patterns—trend, cyclicality, seasonality and irregularity—are of interest to the forecaster. But we're going to focus here on seasonality. By seasonality, we mean periodic fluctuations. For example, a coastal resort located on the Mediterranean experiences higher occupancies in the summer compared to a ski resort in the Alps where winter is the high season. So time series of hotel occupancies will typically show peaking of demand at different times of the year.

Luckily there are different graphical techniques that can be used to detect seasonality. To illustrate the techniques we're going to use the data shown in the table below. The numbers represent overall market hotel room occupancies of a hypothetical tourism destination from 2006 through 2013 and for twelve months of the year.

In summary, the presentation of data in numerical form is often hard to follow, especially if there are many values involved. Graphing and charting numerical values is usually a more effective way to present a data collection. However, choosing the appropriate chart form to represent the data is key to clear communication. In the above analysis, we showed you different ways to represent seasonality. Each technique has its pros and cons. However, we believe that cycle plots are the most suitable to detect seasonality in large data sets.



cycle plots for seasonality 2
cycle plots for seasonality 3

The clearest way to examine a regular time series is with either a column chart or a line chart such as the ones shown below depicting the monthly hotel occupancy for year 2013. Deciding on which graph to use depends on the number of data points to be presented. For small data sets—say up to 10 or 12—use the column chart, otherwise use the line chart. As you can see we can very quickly spot that occupancy was highest in November and lowest in July.

cycle plots for seasonality 4

It is often useful to superimpose the time series for multiple data sets in a single graph. The result is a "graph envelope overview" as shown below. The advantage of this solution is that it increases our ability to detect the seasonality in the data over several years. For example, summer seems to be persistently a quiet period of the year at the subject destination. However, when the number of lines increases, the display becomes cluttered—which makes the task of isolating any one line from the others to analyze its form a difficult one. For example, can you easily say that the market has declined from a peak in 2006 to reach a trough in 2010 and seems to be on the road to recovery in 2013? We bet it's going to be a tough task—As you'll see, this pattern will become obvious in the "run sequence chart" that will follow.

cycle plots for seasonality 5

By presenting the data using “the run sequence plot” shown in the graph below, the pattern that we were looking for—peak-trough-rebound sequence—becomes apparent. This pattern was difficult to detect in the previous chart. The advantage of this solution is to detect trends over many years, but it makes the task to detect seasonality difficult.

cycle plots for seasonality 6

Now the question that arises is the following: is there a way to combine the strengths of both the “graph envelope overview” and the “run sequence chart” into one graph? That is, a graph that simultaneously shows the seasonality throughout the year as well as the trend between the years? The answer is yes and it's called: “The cycle plot”. The cycle plot reveals a seasonality pattern and at the same time allows us to see trends that extend across multiple periods.

In the graph below, each month of the year is plotted separately for the period 2006-2013. The short horizontal red lines represent the weighted average of occupancies for each month of the year between 2006 and 2013.

Two fundamental characteristics of the data are apparent in one single graph:

  • Occupancy rates are lowest during summer and peak slightly after the beginning of the year and slightly before the end of the year.

  • With the exception of the month of July, the market rebounded from a trough in 2009-2010 but still didn't come back to the peak of 2006.

cycle plots for seasonality 7
cycle plots for seasonality 1