Criterion of Existence of Power-Law Memory for Economic Processes

Area of Science:

• Economics
• Mathematical Modeling
• Time Series Analysis

Background:

• Economic processes often exhibit complex dependencies that are not captured by traditional models.
• Understanding long-range dependence is crucial for accurate economic forecasting and policy-making.
• Power-law type (PLT) memory represents a specific form of long-range dependence with significant implications.

Purpose of the Study:

• To propose novel criteria for identifying the existence of PLT memory in economic processes.
• To provide methods for detecting power-law long-range dependence in both time and frequency domains.
• To facilitate the application of fractional calculus in economic modeling.

Main Methods:

• Analogy with long-range alpha-interaction for time domain analysis.
• Concept of non-integer dimensions for frequency domain analysis.
• Illustration of proposed criteria with diverse economic examples.

Main Results:

• Established criteria for identifying PLT memory in economic time series.
• Demonstrated the utility of these criteria in distinguishing between different memory types.
• Showcased the applicability of the criteria for endogenous-exogenous variable relationships.

Conclusions:

• The proposed criteria effectively detect PLT memory in economic systems.
• These criteria enable the use of fractional calculus for constructing advanced dynamic economic models.
• The criteria can identify linear integro-differential operators relevant to fractional calculus.