Seasonal Length Detection via Power Spectrum Interpolation
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Solution Overview
Problem
Accurate detection of seasonality in time series data is challenging due to the presence of numerous periodic patterns and noise, making it difficult to identify representative seasonal patterns.
Innovation Solution
A method that involves generating a power spectrum from time series data, selecting peaks indicative of seasonal patterns, performing interpolation around these peaks, and determining seasonal length based on the frequency at the identified peak, while filtering out harmonics and noise to enhance accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional seasonality detection methods are used on time series data with numerous periodic patterns, then the detection process becomes complex and computationally intensive, but the accuracy of identifying representative seasonal patterns deteriorates due to noise and multiple periodicities
Solution Approach 1:
The patent segments the time series data into multiple windows and performs Fourier transforms on each window separately. This division allows the complex problem of detecting seasonality in the entire dataset to be broken down into simpler sub-problems, each handling a specific time window with its own periodic patterns, thereby reducing overall computational complexity while maintaining detection accuracy.
Solution Approach 2:
The patent introduces an intermediary process of generating a power spectrum from Fourier transform results and performing interpolation to identify peaks. This intermediary representation transforms the raw time series data into a frequency domain power spectrum, making it easier to identify seasonal patterns by focusing on peak frequencies rather than directly analyzing the complex time series with multiple periodicities.
2Loss of information
If all periodic patterns in the time series data are analyzed, then comprehensive seasonality information is obtained, but the computational resources and time required increase significantly
Solution Approach 1:
The patent applies local quality by performing interpolation specifically around identified peak regions in the power spectrum rather than uniformly across the entire frequency range. This localized approach concentrates computational resources on the most relevant frequency regions where seasonal patterns are present, maintaining information completeness while significantly reducing overall computation time.
Solution Approach 2:
The patent performs partial action by selectively analyzing only the peak regions in the power spectrum that correspond to significant periodic patterns. Instead of exhaustively analyzing all possible frequencies, the method focuses computational effort on identifying and interpolating around peak frequencies, which represent the dominant seasonal patterns in the data, thereby achieving adequate seasonality detection with reduced computational time.
Data Source
AI summary
A method of detecting seasonality in time series data includes receiving a set of time series data, analyzing the time series data to generate a power spectrum, the power spectrum indicative of power as a function of frequency, and selecting a peak in the power spectrum, the selected peak having a peak power. The method also includes performing an interpolation around the selected peak, and selecting a number of additional peaks having powers within a selected proportion of the peak power. The method further includes, based on the number of additional peaks being less than a threshold number, identifying the selected peak as representing a season having a seasonal length, and determining a seasonal length of the season based on a frequency at the identified peak.