<p>Topological data analysis (TDA) is increasingly acknowledged within financial markets for its capacity to manage complexity and discern nuanced patterns and structures. It has been applied effectively to uncover intricate relationships and capture non-linear dependencies inherent in market data. This manuscript presents a groundbreaking study that delves into integrating features derived from TDA to improve the performance of forecasting models for univariate time series prediction. The research specifically examines whether incorporating features extracted from TDA-such as entropy, amplitude, and the number of points obtained from persistent diagrams can provide valuable supplementary information to the baseline forecasting model. Thus, the aim is to determine if these TDA-derived features can boost forecasting accuracy by offering additional insights that existing models might overlook. The <Emphasis FontCategory="NonProportional">N-BEATS</Emphasis> model serves as the baseline forecasting model due to its robust generalization capabilities and flexibility in incorporating additional features into the model. The proposed methodology is compared against a univariate <Emphasis FontCategory="NonProportional">N-BEATS</Emphasis> model without additional features and other strategies incorporating supplementary features such as temporal decomposition and time delay embeddings. The evaluation includes forecasting for six cryptocurrencies across four distinct time scenarios and four traditional financial instruments across two scenarios each, resulting in 32 datasets. The results obtained were promising, as the proposed method, <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="521_2024_10787_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="97" /> </InlineMediaObject> <EquationSource Format="TEX">$\texttt {N-BEATS}_\mathrm {+TDA}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="monospace">N</mi> <mo>-</mo> <msub> <mi mathvariant="monospace">BEATS</mi> <mrow> <mo>+</mo> <mi mathvariant="normal">TDA</mi> </mrow> </msub> </mrow> </math></EquationSource> </InlineEquation>, achieved the best results in mean performance and mean ranking for the three metrics considered (MAPE, MAE, and RMSE). Significant differences were observed with the rest of the proposed methods using a significance level of <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="521_2024_10787_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="63" /> </InlineMediaObject> <EquationSource Format="TEX">$\alpha = 0.10$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.10</mn> </mrow> </math></EquationSource> </InlineEquation>, highlighting the effectiveness of integrating TDA features to enhance forecasting models.</p>

Enhancing financial time series forecasting through topological data analysis

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2025年1月17日

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Luiz Carlos de Jesus Jr.,
Francisco Fernández-Navarro,
Mariano Carbonero-Ruz

摘要

Topological data analysis (TDA) is increasingly acknowledged within financial markets for its capacity to manage complexity and discern nuanced patterns and structures. It has been applied effectively to uncover intricate relationships and capture non-linear dependencies inherent in market data. This manuscript presents a groundbreaking study that delves into integrating features derived from TDA to improve the performance of forecasting models for univariate time series prediction. The research specifically examines whether incorporating features extracted from TDA-such as entropy, amplitude, and the number of points obtained from persistent diagrams can provide valuable supplementary information to the baseline forecasting model. Thus, the aim is to determine if these TDA-derived features can boost forecasting accuracy by offering additional insights that existing models might overlook. The N-BEATS model serves as the baseline forecasting model due to its robust generalization capabilities and flexibility in incorporating additional features into the model. The proposed methodology is compared against a univariate N-BEATS model without additional features and other strategies incorporating supplementary features such as temporal decomposition and time delay embeddings. The evaluation includes forecasting for six cryptocurrencies across four distinct time scenarios and four traditional financial instruments across two scenarios each, resulting in 32 datasets. The results obtained were promising, as the proposed method, $\texttt {N-BEATS}_\mathrm {+TDA}$ $N - {BEATS}_{+ TDA}$ , achieved the best results in mean performance and mean ranking for the three metrics considered (MAPE, MAE, and RMSE). Significant differences were observed with the rest of the proposed methods using a significance level of $\alpha = 0.10$ $α = 0.10$ , highlighting the effectiveness of integrating TDA features to enhance forecasting models.