Detecting Patterns Over Time
For much of this book, we have examined variation across individuals measured simultaneously. This chapter is devoted to variation over time, working with data tables in which columns represent a single variable measured repeatedly and rows represent regularly spaced time intervals. In many instances, time series data exhibit common, predictable patterns that we can use to make forecasts about future time periods. As we move through the chapter, we'll learn several common techniques for summarizing variation over time and for projecting future values.
Typically, we classify patterns in a time series as a combination of the following:
Trend: Long-term movement upward or downward.
Cycle: Multi-year oscillations with regular frequency.
Season: Repeated, predictable oscillations within a year.
Irregular: Random movement up or down, akin to random disturbances in regression modeling.
To illustrate these patterns, we'll first consider industrial production in India. India is one of the largest and fastest-growing economies [1]in the world. Industrial production refers to the manufacture of goods within the country, and is measured in this example by India's Index of Industrial Production (IIP). The IIP is a figure that compares a weighted average of industrial output from different sectors of the economy (for example, mining, textiles, agriculture, manufacturing) to a reference year in which the index is anchored at a value of 100. As a result, we can interpret a value of the IIP as a percentage of what industrial output was in the base year. So, for instance, if the IIP equals 150 we know that production was 50% higher at that point than it was in the base year.
[1] In 2005 India was ranked 12th in the world in terms of total Gross Domestic Product (GDP), as reported by the World Bank.
Open the table called India Industrial Production.
This table contains IIPs for different segments of the Indian economy. All figures are reported monthly from January 2000 through June 2009.
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In this data table, the last three rows are initially hidden and excluded. Standard practice in time series analysis is to hold some observations in reserve while building predictive models, and then test the performance of the models comparing forecasts to later observations. |
Let's look at the variability in production of basic goods (processed goods such as paper, lumber, and textiles valued for their use in the manufacture of other products). We'll look at the variation using a Run Chart, which simply plots each observed data value in order.
Select Analyze → Modeling → Time Series. As shown in Figure 17.1, select BasicGoods as the Y, Time Series to analyze, and identify the observations by Month.
In the lower left of the dialog box, change both the Autocorrelation Lags (which we'll define in a later section) and the number of Forecast Periods to 3.
Click ok.
Figure 17.1. Launching the Time Series Platform
Look at the first simple time series chart (enlarged in Figure 17.2). The horizontal axis shows the months beginning in January 2000 and the vertical axis shows the values of the Index of Industrial Production for basic goods. The upward trend is visible, but it is not a steady linear trend; it has some curve to it as well as some undulation that suggests cyclical movement. Also visible is a sawtooth pattern of ups and downs from month to month, indicating some irregular movement and possibly a seasonal component. In short, this first example exhibits all four of the elements often found in time series data.
Figure 17.2. Time Series Graph of Production of Basic Goods
Below the graph are two graphs and a table of diagnostic statistics. Although these are a basic feature of the JMP Time Series platform, they go beyond the typical content of an introduction to these techniques. We'll bypass them for now.
In the next two sections of the chapter we'll introduce two common methods for smoothing out the irregular sawtooth movement in a time series, both to better reveal the other components and also to develop short-term forecasts. We'll also introduce some statistics to summarize the performance of the models.
It is valuable to understand at the outset that the techniques of time series analysis share a particular logic. In each of the techniques presented in this chapter, we'll apply the method to a sample of observations to generate retrospective "forecasts" for all or most of the observed data values. We then compare the forecasts to the values that were actually observed, essentially asking "if we had been using this forecasting method all along, how accurate would the forecasts have been?" We'll then select a forecasting method for continued use, based in part on its past performance with a particular set of data.