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Practical Time Series Analysis by Dr. PKS Prakash, Dr. Avishek Pal

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First-order differencing

First order differencing implies taking differences between successive realizations of the time series so that the differences Δxt 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 xt = xt-l + Єt where Єt 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 (Δxt of a random walk are equal to the random noise Єt. Hence the residuals remaining after first-order differencing ...

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