Time Series Forecasting with Gaussian Mixture Models
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing methods for forecasting time series data, particularly non-stationary data with extreme values, are inaccurate as they either remove extreme values, leading to loss of critical information, or fail to account for the rate of change in the data, and do not provide both point and probability estimates.
Innovation Solution
A system and method that processes both stationary and non-stationary time series data to form a unified data set by differencing non-stationary data, representing it as a mixture of Gaussian distribution models, and assigning weights using Maximum Likelihood Estimation or Expectation Maximization algorithms to generate forecasted time series data.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If extreme values are removed from historical time series data, then forecasting accuracy for general patterns is improved, but critical information is lost
Solution Approach 1:
The patent segments the time series data into stationary and non-stationary components, applying different processing approaches to each. The non-stationary component containing extreme values is handled separately through differencing operations, allowing the extreme values to be preserved in the transformed data while the stationary component provides the general pattern structure.
Solution Approach 2:
The patent applies differencing operations to transform the non-stationary time series data, changing the parameters of the data representation. This transformation allows extreme values to be retained in a form that can be properly modeled, converting the problematic non-stationary data into a stationary form suitable for Gaussian mixture modeling.
2Device complexity
If traditional forecasting methods are applied to non-stationary time series data, then simplicity of method is maintained, but forecasting accuracy deteriorates
Solution Approach 1:
The patent divides the forecasting approach into distinct segments: differencing non-stationary data to make it stationary, modeling with Gaussian mixture models, and combining results. This segmentation allows each component to be handled with appropriate methods, improving accuracy without overwhelming complexity.
Solution Approach 2:
The patent introduces differenced stationary series data as an intermediary between the original non-stationary data and the final forecast model. This intermediary transformation enables the use of standard stationary time series modeling techniques on non-stationary data, bridging the gap between simplicity and accuracy.
3Loss of information
If extreme values are replaced with most likely values, then data completeness is improved, but critical characteristics are lost
Solution Approach 1:
Instead of replacing extreme values with most likely values (the conventional approach), the patent inverts the approach by using differencing to transform the data so that extreme values are preserved in the transformed stationary series. This inversion allows extreme values to be maintained rather than replaced, preserving critical system characteristics.
4Loss of information
If mixed or multiple data distributions are employed to capture extreme values, then information retention is improved, but model complexity increases
Solution Approach 1:
The patent applies differencing operations to change the parameters of the non-stationary data, transforming it into stationary form. This parameter change simplifies the modeling task, allowing the use of Gaussian mixture models on the transformed data rather than requiring complex non-stationary models, thus reducing overall model complexity while retaining information.
Data Source
AI summary
Systems and methods for forecasting a time series data are disclosed. The methods include receiving a historical time-series data including a series data and a non-stationary series data. The historical time-series data is processed to obtain a unified time series data. On the unified time series data, a data distribution is plotted and the data distribution is validated based upon a rate function associated with a Large Deviation Theory (LDT). The unified time series data is split validated into vectors based on autocorrelation function (ACF). The unified time series data is further validated. A mixture of Gaussian distribution models is applied and weights are assigned to each of the Gaussian distribution model. By controlling the weights based upon various what-if scenarios, a resultant Gaussian time series data is generated. The resultant Gaussian time series data indicates forecasted time series data of the historical time series data.