Non-Stationary Time Series Demand Forecasting Model
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Solution Overview
Problem
Existing economic models struggle to accurately predict demand in non-stationary micro-economic systems due to assumptions of stationary processes and failure to account for time-dependent product-level factors, leading to biased parameter estimates and distorted price elasticity measures.
Innovation Solution
A Bayesian framework is used to model non-stationary processes with a non-parametric demand profile, integrating time-varying parameters directly into the likelihood function, allowing for accurate modeling of micro and macro-economic systems and accounting for product-level factors such as new product introductions, discontinuations, and unique seasonal responses.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If ad-hoc methods like category seasonality index are used to address non-stationary processes, then the modeling process is simplified, but parameter estimates become biased and price elasticity measures are distorted
Solution Approach 1:
The patent transforms the stationary demand parameters into time-varying parameters that adapt to non-stationary conditions. By allowing parameters to change over time according to their underlying non-stationary processes, the model maintains measurement precision while accommodating changing demand patterns without requiring ad-hoc seasonal adjustments.
Solution Approach 2:
The invention introduces dynamic elements to the demand model by representing demand as a non-stationary process where parameters evolve over time. This dynamic approach replaces static parametric assumptions with time-adaptive modeling, eliminating the need for separate seasonal indexing while maintaining operational simplicity through unified mathematical framework.
2Device complexity
If parametric models with stationary assumptions are used, then the model structure remains simple, but the model fails to capture time-dependent product-level factors
Solution Approach 1:
The patent changes the fundamental assumption about demand parameters from stationary to non-stationary, allowing them to evolve over time. This parameter transformation enables the model to capture time-dependent factors like new product introductions and discontinuations while maintaining a relatively simple parametric structure through Bayesian framework and conjugate priors.
Solution Approach 2:
The invention segments the demand process into product-level components that can have unique time-varying characteristics. By allowing each product or category to have its own non-stationary demand profile rather than forcing a single stationary parameter set, the model captures diverse time-dependent behaviors without requiring complex individual modeling for each product.
3Productivity
If category-level seasonal adjustments are applied, then overall category trends are captured, but unique product demand profiles and causal factors are absorbed into the seasonality index
Solution Approach 1:
The patent applies local quality by allowing different parts of the demand system (individual products within categories) to have different time-varying parameters rather than forcing uniform seasonal adjustments. This enables each product to maintain its unique demand profile characteristics while still benefiting from category-level trend capture, preventing information loss at the product level.
Solution Approach 2:
The invention segments the demand modeling at the product level rather than applying blanket category-level adjustments. By allowing each product to have its own non-stationary demand process with unique time-varying parameters, the model preserves product-specific information while still capturing overall category trends through the hierarchical Bayesian framework.
Data Source
AI summary
A non-stationary time series model using a likelihood function as a function of input data, base demand parameters, and time dependent parameter. The likelihood function may represent any statistical distribution. The likelihood function uses a prior probability distribution to provide information external to the input data and is used to control the model. In one embodiment the prior is a function of adjacent time periods of the demand profile. The base demand parameters and time dependent parameter are solved using a multi-diagonal band matrix. The solution of base demand parameters and time dependent parameter involves making estimates thereof in an iterative manner until the base demand parameters and time dependent parameter each converge. A non-stationary time series model is provided from an expression using the solution of the base demand parameters and time dependent parameter. The non-stationary time series model provides a demand forecast as a function of time.