Analyzing time series data that exhibits seasonal effects

• US 20090024427A1
• Filed: 07/19/2007
• Published: 01/22/2009
• Est. Priority Date: 07/19/2007
• Status: Active Grant

• Current Assignee: Meizu Technology Company Limited
• Original Assignee: Hewlett-Packard Development Company, L.P. (HP Inc.)
• Inventors: Shan, Jerry Z.
• Granted Patent: US 7,865,389 B2
• Time in Patent Office: Days
• US Class Current: 705/7
• CPC Class Codes: G06F 17/18 for evaluating statistical data , e.g. average values, frequency distributions, probability functions, regression analysis forecasting specially adapted for a specific administrative, business or logistic context G06Q10/04
• CPC Class Codes: G06Q 10/00 Administration; Management
• CPC Class Codes: G06Q 30/00 Commerce
• CPC Class Codes: G06Q 30/0201 Market modelling; Market analysis; Collecting market data
• CPC Class Codes: G06Q 30/0202 Market predictions or forecasting for commercial activities

Abstract

To analyze a time series of data that exhibits seasonal effects, the time series is processed to obtain a representation in the frequency domain. According to the representation, plural cycle lengths are identified as representing different seasonal effects of the data in the time series, where a first of the plural cycle lengths is greater than a second of the plural cycle lengths.

Claims

1. A method executed by a computer to analyze a time series of data that exhibits seasonal effects associated with an enterprise, comprising:

processing the time series to obtain a representation in a frequency domain; and

according to the representation in the frequency domain, identifying plural cycle lengths as representing different seasonal effects of the data in the time series, wherein a first of the plural cycle lengths is greater than a second of the plural cycle lengths.

2. The method of claim 1, wherein processing the time series comprises:

estimating a spectral density of the time series in the frequency domain, wherein the representation comprises the spectral density; and

identifying plural peaks at plural corresponding frequencies according to the estimated spectral density,

wherein the plural cycle lengths are based on the frequencies corresponding to the plural peaks.

3. The method of claim 2, wherein estimating the spectral density of the time series in the frequency domain comprises deriving a periodogram of the time series.

4. The method of claim 2, further comprising normalizing the spectral density of the time series to produce a normalized spectral density, wherein identifying the plural peaks is based on the normalized spectral density.

5. The method of claim 2, further comprising converting the frequencies corresponding to the plural peaks to the plural cycle lengths.

6. The method of claim 1, further comprising:

receiving the time series; and

cleansing the time series by performing outlier analysis prior to processing the time series to obtain the representation in the frequency domain.

7. The method of claim 1, further comprising confirming at least one of the plural cycle lengths.

8. The method of claim 7, wherein confirming the at least one of the plural cycle lengths comprises:

removing an effect of a cycle length more significant than the at least, one of the plural cycle lengths from the time series, wherein removing the effect causes production of a modified time series; and

processing the modified time series to obtain a second representation in the frequency domain; and

according to the second representation, identifying a most significant cycle length to compare to the at least one of the plural cycle lengths for confirming the at least one of the plural cycle lengths.

9. The method of claim 1, further comprising building a model that is calibrated for the identified plural cycle lengths.

10. The method of claim 9, wherein building the model comprises:

dividing the time series into a training sample part and a test sample part;

building an initial model based on the training sample part;

verifying the initial model using the test sample part; and

in response to successful verification, extending the model to cover the entire time series.

11. The method of claim 1, further comprising communicating the identified cycle lengths to a decision support system to perform a decision support task.

12. The method of claim 1, wherein processing the time series comprises processing the time series containing one of sales data, profit data, revenue data, cost data, data relating to enrollment of students, and data associated with operations of a government agency.

13. A method executed by a computer to analyze a time series of data that exhibits a seasonal effect associated with an enterprise, comprising:

producing a spectral density of the time series;

normalizing values in the spectral density with respect to an aggregate of the values of the spectral density at corresponding frequencies to produce a normalized spectral density; and

determining a cycle length corresponding to the seasonal effect based on identifying a peak in the normalized values of the normalized spectral density.

14. The method of claim 13, further comprising computing the aggregate of the values of the spectral density by computing a sum of the values of the spectral density, and

wherein normalizing the values in the spectral density comprises one of:

(1) subtracting the sum from each value of the spectral density; and

(2) dividing each value of the spectral density by the sum.

15. The method of claim 13, further comprising:

performing outlier analysis of the time series to replace one or more outlier data values in the time series prior to producing the spectral density.

16. The method of claim 15, wherein performing the outlier analysis comprises defining upper and lower quantiles, and identifying data values in the time series outside the quantiles as being outliers.

17. The method of claim 15, wherein replacing the one or more outlier data values comprises replacing the one or more outlier data values with predetermined one or more values.

18. The method of claim 13, wherein producing the spectral density comprises computing a periodogram of the time series.

19. The method of claim 13, further comprising receiving the time series that contains one of sales data, profit data, revenue data, cost data, data relating to. enrollment of students, and data associated with operations of a government agency.

20. Instructions on a computer-usable medium that when executed cause a computer to:

process a time series to obtain a representation in a frequency domain; and

according to the representation, identify plural cycle lengths as representing different seasonal effects of data of the time series, wherein the seasonal effects are associated with an enterprise, and wherein a first of the plural cycle lengths is greater than a second of the plural cycle lengths.

21. The instructions of claim 20, wherein processing the time series to obtain the representation comprises:

estimating a spectral density of the time series in the frequency domain, wherein the representation includes the spectral density;

identifying plural peaks at plural corresponding frequencies according to the estimated spectral density,

wherein identifying the plural cycle lengths is based on the frequencies.

22. The instructions of claim 20, which when executed cause the computer to convert the frequencies to the corresponding cycle lengths.