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:222.jpg On other hand, the smoothed series must be sufficiently smooth 223.jpg, that the series itself is subject to minimal dramatic change.

Thus, the filter is a double-sided and linear and calculates the smoothed series image224.png of the temporal series 224-y.jpg by minimizing the dispersion of the elements of series image224.png around 224-y.jpg at the condition of a minimum sum of the elements of double-differential series  image224.png. 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


Sales history with Hodrick-Prescott Filter

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.


Sales history with Hodrick-Prescott Filter

Know more:

— Demand forecasting – information about it you can find HERE

— Sales analysis – information about it you can find HERE ;

— Planning – information about it you can find HERE and HERE ;

If you want to get started with the Mycroft Assistant – where we have implemented everything necessary for you to work effectively, simply sign up HERE and follow the provided instructions.