The nature of predictions
To paraphrase John Allen Paulos, author of A Mathematician Reads the Newspaper, all expert predictions can be essentially restated in one of two ways: “Things will continue roughly as they have been until something changes”; and its corollary, “Things will change after an indeterminate period of stability.” Although these statements are both true and absurd, they contain a kernel of wisdom: simply assuming a relative degree of stability and painting a picture of the future based on current trends is the first step of scenario planning. The trick, of course, is to never completely forget the “other shoe” of Paulos’s statement: as the disclaimer states on all investment offerings, “Past performance is not a guarantee of future results”; at some point in the future our present trends will no longer accurately describe where we are headed. (We will deal with this as well, with a few “safety valves.”)
From the second stage of the Rational Planning Paradigm (covered in the background sections of the book) we should have gathered information on both past and present circumstances related to our planning effort. If we are looking at housing production, we might have data on annual numbers of building permits and new subdivision approvals, mortgage rates, and housing prices; if we are looking at public transportation we might need monthly ridership numbers, information of fare changes, population and employment figures, and even data on past weather patterns or changes in vehicle ownership and gas prices. The first step of projection, therefore, is to gather relevant information and get it into a form that you can use.
Since we will be thinking about changes over time in order to project a trend into the future, we’ll need to make sure that our data has time as an element: a series of data points with one observation for each point or period of time is known as a time series. The exact units of time are not important—they could be days, months, years, decades, or something different—but it is customary (and important) to obtain data where points are regularly spaced at even intervals.1 Essentially, time series data is a special case of multivariate data in which we treat time itself as an additional variable and look for relationships as it changes. Luckily,
R has some excellent functions and packages for dealing with time-series data, which we will cover below in passing. For starters, however, let’s consider a simple example, to start to think about what goes into projections. Continue reading…