The process of subtracting successive terms in a series of equi-spaced observations. Used in numerical analysis and as a simple method for removing trends in time series. Suppose, for example, that yt , the value at time t, is given (for t=1, 2, 3,…) by yt=a + bt. Then, for each value of t>1, the first difference, Δyt, is given by
which is no longer dependent on t. In the same way, further differences will remove higher polynomial dependencies on time. For example, the second difference, Δ2yt (=Δyt−Δyt−1), will remove any quadratic dependence on time.
Subjects: Probability and Statistics.