Appropriate time scales for nonlinear analyses of deterministic jump systems

Area of Science:

• Complex Systems Analysis
• Time Series Analysis
• Nonlinear Dynamics

Background:

• Many real-world phenomena arise from deterministic systems but exhibit non-uniform temporal fluctuations.
• Financial markets are a prime example, with price movements occurring at irregular intervals.
• Current research often applies uniform time scales (e.g., 1-min, 1-h data) to analyze such systems.

Purpose of the Study:

• To investigate the appropriateness of uniform time scales for analyzing systems with non-uniform time intervals.
• To assess the validity of using uniform sampling for nonlinear analyses in financial markets.
• To compare the effectiveness of uniform sampling for different types of data, including neural spikes and internet traffic.

Main Methods:

• Utilized surrogate data tests to evaluate the identification of deterministic properties from uniformly sampled data.
• Examined financial market data, neural spikes, and internet traffic packets.

Main Results:

• Uniform time sampling is frequently inappropriate for nonlinear analyses of systems with non-uniform fluctuations.
• Uniform sampling proved effective for extracting properties from neural spikes and internet traffic data.
• Uniform sampling can lead to overlapping data, potentially causing false rejections in surrogate data tests.

Conclusions:

• The choice of time scale is critical for accurate analysis of deterministic systems with irregular fluctuations.
• Uniform time scales may not be universally applicable and their suitability depends on the specific system characteristics.
• Further research is needed to refine sampling methodologies for complex, non-uniformly sampled data.