Count Series Forecasting with Discrete Probability Distributions
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Solution Overview
Problem
Traditional time series analysis techniques are inadequate for predicting future events in count series data, as they assume continuous distribution, which is unrealistic for discrete-valued data points, leading to inaccurate forecasts and unrealistic confidence intervals.
Innovation Solution
A system and method that analyze count series data by generating counts of discrete values, selecting an optimal discrete probability distribution, and using it to adjust predicted future data points, enabling more accurate forecasting by employing statistical models tailored to discrete probability distributions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional continuous distribution time series analysis techniques are used, then the analysis can be performed with existing methods, but the prediction accuracy deteriorates because the assumption of continuity is unrealistic for discrete-valued count data
Solution Approach 1:
The patent transforms the fundamental parameter assumption from continuous distribution to discrete distribution. It employs discrete probability distributions (Poisson, Negative Binomial, Zero-Inflated Poisson, Zero-Inflated Negative Binomial) instead of continuous distributions, fundamentally changing the mathematical parameter space to match the discrete nature of count data, thereby resolving the contradiction between prediction accuracy and adaptability to discrete data
Solution Approach 2:
The patent inverts the traditional approach by not forcing discrete data into continuous models, but rather developing models specifically tailored for discrete data. It reverses the conventional wisdom by treating discrete distributions as the primary approach and continuous approximations as secondary, thus improving both prediction accuracy and theoretical appropriateness for count series data
2Measurement precision
If discrete probability distributions are used to model count series data, then the prediction accuracy improves, but the model complexity increases due to multiple distribution types and parameter selection
Solution Approach 1:
The patent implements dynamic model selection through automated information criteria (AIC, BIC) that dynamically determine the optimal discrete probability distribution based on the characteristics of the input data. The system adapts between different distribution types (Poisson, Negative Binomial, Zero-Inflated variants) and adjusts parameters dynamically, resolving the contradiction by making the complexity adaptive rather than static
Solution Approach 2:
The system performs self-service through automated model selection and parameter estimation. It automatically selects the appropriate discrete probability distribution and estimates parameters without requiring manual intervention, thereby managing model complexity internally while maintaining high prediction accuracy. The automated selection process serves the user need for accurate predictions without exposing them to the underlying complexity
3Ease of operation
If confidence intervals are generated using continuous distribution assumptions, then the calculation is straightforward, but the confidence intervals become unrealistic and may include negative or non-integer values
Solution Approach 1:
The patent changes the parameter space for confidence interval generation from continuous to discrete. By using discrete probability distributions and their corresponding quantile functions, the system generates confidence intervals that are constrained to integer values within the valid range of the distribution, ensuring realism while maintaining calculation feasibility through automated computational methods
Data Source
AI summary
Systems and methods are included for adjusting a set of predicted future data points for a time series data set including a receiver for receiving a time series data set. One or more processors and one or more non-transitory computer readable storage mediums containing instructions may be utilized. A count series forecasting engine, utilizing the one or more processors, generates a set of counts corresponding to discrete values of the time series data set. An optimal discrete probability distribution for the set of counts is selected. A set of parameters are generated for the optimal discrete probability distribution. A statistical model is selected to generate a set of predicted future data points. The set of predicted future data points are adjusted using the generated set of parameters for the optimal discrete probability distribution in order to provide greater accuracy with respect to predictions of future data points.