Practical Time-Series Analysis

First-order differencing

First order differencing implies taking differences between successive realizations of the time series so that the differences Δx_t are irregular variations free from any long run trend or seasonality. The random walk model discussed in the last chapter is a sum of subsequent random variations and is given by x_t = x_t-l + Є_t where Є_t is a zero mean random number from normal distribution. Random walks are characterized by long sequence of upward or downward trends. Besides, they take unforeseen changes in direction. Based on these characteristics, random walks are non-stationary. However, the first differences (Δx_t of a random walk are equal to the random noise Є_t. Hence the residuals remaining after first-order differencing ...