Trend (Hodrick-Prescott Filter)
The Hodrick-Prescott filter is a method of smoothing temporal series. It is used to highlight long-term trends (seasonal fluctuations and trends) of a temporal series. This method was first used by the economists Hodrick and Prescott to analyze the business cycles of the post-war U.S. macroeconomic.
By itself, the filter is the solution of the optimization task. The smoothed series, on one hand, must be close enough to the original series, that it is necessary to minimize the sum of squared deviations: On other hand, the smoothed series must be sufficiently smooth , that the series itself is subject to minimal dramatic change.
Thus, the filter is a double-sided and linear and calculates the smoothed series of the temporal series by minimizing the dispersion of the elements of series around at the condition of a minimum sum of the elements of double-differential series . The elements of the smoothed series are selected in order to minimize the following expression:
Different initial data is required to specify different lambda, whose values are determined according to the period analyzed:
— For a daily trend, lambda = 43,200
— For a weekly trend, lambda = 14,400
— For a monthly trend, lambda = 1,600
— For a yearly trend, lambda = 100
Mycroft Assistant uses a trend highlighted by the trend (Hodrick-Prescott filter) for several purposes:
– to provide visual trend analysis – for the point of sales analysis;
– to identify trend reversal – for the notification system;
– to adjust the sales forecast for future periods according to any change of the trend – for inventory management and planning.
— Demand forecasting – information about it you can find HERE
— Sales analysis – information about it you can find HERE ;
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