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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

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Published on: July 3, 2020

General simulation algorithm for autocorrelated binary processes.

Francesco Serinaldi^1,2, Federico Lombardo³

¹School of Civil Engineering and Geosciences, Newcastle University, Newcastle Upon Tyne, NE1 7RU, United Kingdom.

Physical Review. E

|March 17, 2017

Summary

This study presents a novel method for generating binary sequences with specific autocorrelation. The approach models the underlying continuous process, enabling effective simulation of complex binary signals.

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Area of Science:

Physics
Stochastic Processes
Data Science

Background:

Binary random processes are common in various scientific fields.
Generating binary sequences with controlled autocorrelation is difficult due to discrete distributions.
Classical spectral techniques are problematic for discrete binary processes.

Purpose of the Study:

To develop an effective method for simulating binary sequences with prescribed autocorrelation.
To overcome the limitations of classical spectral techniques for discrete binary processes.

Main Methods:

Modeling the parent continuous process with beta-distributed transition probabilities.
Adapting spectral techniques, specifically the iterative amplitude-adjusted Fourier transform method, for continuous processes.
Applying this paradigm shift to simulate binary signals.

Main Results:

The proposed method effectively simulates binary signals with power-law and exponential autocorrelation functions.
The algorithm successfully models processes like Hurst-Kolmogorov and Markov processes.
Demonstrated application in simulating rainfall intermittency data, preserving empirical autocorrelation.

Conclusions:

A novel and generalizable algorithm for simulating binary sequences with controlled autocorrelation has been developed.
The method offers a significant advancement over traditional techniques by focusing on the continuous parent process.
The algorithm has practical applications in modeling complex natural phenomena and generating realistic surrogate data.