Non-parametric tests for serial dependence in time series based on asymptotic implementations of ordinal-pattern...

Area of Science:

• Time Series Analysis
• Non-parametric Statistics
• Data Mining

Background:

• Real-valued time series often exhibit complex serial dependence.
• Discovering non-linear dependencies is crucial for accurate time series modeling.
• Existing methods may not fully capture intricate temporal patterns.

Purpose of the Study:

• To develop and validate non-parametric hypothesis tests for detecting serial dependence in time series.
• To provide easily implementable statistical tests based on ordinal patterns.
• To illustrate the practical application of these tests using real-world environmental data.

Main Methods:

• Construction of hypothesis tests utilizing ordinal patterns.
• Derivation of the asymptotic distribution for sample frequencies and test statistics.
• Implementation of tests based on asymptotic approximations.
• Monte Carlo simulations to evaluate finite-sample performance and power.

Main Results:

• The asymptotic distribution of ordinal pattern frequencies and test statistics is derived.
• The proposed tests are shown to be implementable using asymptotic approximations.
• Simulations confirm the finite-sample performance and power of the tests against various alternatives.
• The methodology is successfully applied and interpreted using an environmental dataset.

Conclusions:

• Ordinal pattern-based hypothesis tests offer a robust approach for detecting serial dependence in time series.
• The derived asymptotic properties facilitate practical implementation and application.
• The study provides a valuable tool for analyzing complex temporal dynamics, as demonstrated by the environmental data example.