<p>This study examines the long-term dynamics of Australia’s net overseas migration (NOM) from Sept-04 to Sept-24 and reveals a persistent time series structure, with a Hurst exponent of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$H = 0.814$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>H</mi> <mo>=</mo> <mn>0.814</mn> </mrow> </math></EquationSource> </InlineEquation>, indicating long-range correlations. Box-dimensional analysis shows that inclusion of major global crises elevates structural complexity: the full period yields a box dimension of 1.663, compared to 1.367 when both the Global Financial Crisis (GFC) and COVID-19 periods are excluded. Sliding-window permutation entropy (PE) (window sizes 8–20 quarters) reveals a window-invariant trough in 2020–2021 aligned with pandemic border closures, followed by a post-2022 rebound that is strong at short horizons yet stabilizes below pre-2019 complexity at longer horizons. Event-aligned magnitudes confirm this pattern: The <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\Delta \textrm{PE}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Δ</mi> <mtext>PE</mtext> </mrow> </math></EquationSource> </InlineEquation> for GFC is positive (standardized effects 0.7–1.5), the <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\Delta \textrm{PE}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Δ</mi> <mtext>PE</mtext> </mrow> </math></EquationSource> </InlineEquation> for COVID-19 is negative (standardized effects down to <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$-2.1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>-</mo> <mn>2.1</mn> </mrow> </math></EquationSource> </InlineEquation>), and the <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$\Delta \textrm{PE}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Δ</mi> <mtext>PE</mtext> </mrow> </math></EquationSource> </InlineEquation> is positive for post-2022 (up to 1.7, reducing with window length). These results indicate that global shocks induce short-term structural reorganizations in migration dynamics, temporarily increasing irregularity before returning to a stable, persistent trend.</p>

A fractal analysis of Australian migration trends

期刊论文
发表日期：

2026年1月20日

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Mridul Patel,
G. Verma,
A. Eberhard,
A. Rao

摘要

This study examines the long-term dynamics of Australia’s net overseas migration (NOM) from Sept-04 to Sept-24 and reveals a persistent time series structure, with a Hurst exponent of $H = 0.814$ $H = 0.814$ , indicating long-range correlations. Box-dimensional analysis shows that inclusion of major global crises elevates structural complexity: the full period yields a box dimension of 1.663, compared to 1.367 when both the Global Financial Crisis (GFC) and COVID-19 periods are excluded. Sliding-window permutation entropy (PE) (window sizes 8–20 quarters) reveals a window-invariant trough in 2020–2021 aligned with pandemic border closures, followed by a post-2022 rebound that is strong at short horizons yet stabilizes below pre-2019 complexity at longer horizons. Event-aligned magnitudes confirm this pattern: The $\Delta \textrm{PE}$ $Δ PE$ for GFC is positive (standardized effects 0.7–1.5), the $\Delta \textrm{PE}$ $Δ PE$ for COVID-19 is negative (standardized effects down to $-2.1$ $- 2.1$ ), and the $\Delta \textrm{PE}$ $Δ PE$ is positive for post-2022 (up to 1.7, reducing with window length). These results indicate that global shocks induce short-term structural reorganizations in migration dynamics, temporarily increasing irregularity before returning to a stable, persistent trend.