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 (see moving average) in time series. Suppose, for example, that y_t , the value at time t, is given (for t=1, 2, 3,…) by y_t=a+bt. Then, for each value of t>1, the first difference, Δy_t, is given bywhich is no longer dependent on t. In the same way, further differences will remove higher polynomial dependencies on time. For example, the second difference, Δ²y_t (=Δy_t−Δy_t−1), will remove any quadratic dependence on time.