Smoothing Methods

As a first step in time series analysis it is often helpful to neutralize the effects of the random irregular component and thereby more clearly visualize the behavior of the other three components. Perhaps the simplest method of summarizing a time series is known as a moving average. As the name suggests, the method relies on computing means. We begin by computing the average of the first few observations from, say, y₁ through y_m. That average then corresponds either to the chronological center of the first m observations or serves as the "prediction" for y_m+1. We then move along in the series, computing the average of observations y₂through y_m+1. This continues until we've passed through the entire sample, continually taking averages of m observations at a time, but always a different group of observations.

Moving averages are commonly used, perhaps chiefly for their simplicity and computability if not for their usefulness as a forecasting method. In JMP, simple moving averages are featured among the control chart methods discussed in Chapter 19 of this book. To introduce the concept of a smoothing method, we'll turn first to three techniques known as exponential smoothing methods. JMP offers six variations of exponential smoothing, and we'll consider three of them.