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DurstewitzLabCan time series (TS) <a href="https://mathstodon.xyz/tags/FoundationModels" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#FoundationModels</a> (FM) like Chronos zero-shot generalize to unseen <a href="https://mathstodon.xyz/tags/DynamicalSystems" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#DynamicalSystems</a> (DS)? <a href="https://mathstodon.xyz/tags/AI" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#AI</a>No, they cannot!But *DynaMix* can, the first TS/DS foundation model based on principles of DS reconstruction, capturing the long-term evolution of out-of-domain DS: <a href="https://arxiv.org/pdf/2505.13192v1" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://arxiv.org/pdf/2505.13192v1</a>Unlike TS foundation models, DynaMix exhibits <a href="https://mathstodon.xyz/tags/ZeroShotLearning" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ZeroShotLearning</a> of long-term stats of unseen DS, incl. attractor geometry & power spectrum, w/o *any* re-training, just from a context signal. It does so with only 0.1% of the parameters of Chronos & 10x faster inference times than the closest competitor.It often even outperforms TS FMs on forecasting diverse empirical time series, like weather, traffic, or medical data, typically used to train TS FMs. This is surprising, cos DynaMix’ training corpus consists *solely* of simulated limit cycles & chaotic systems, no empirical data at all!And no, it’s neither based on Transformers nor Mamba – it’s a new type of mixture-of-experts architecture based on the recently introduced AL-RNN (<a href="https://proceedings.neurips.cc/paper_files/paper/2024/file/40cf27290cc2bd98a428b567ba25075c-Paper-Conference.pdf" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://proceedings.neurips.cc/paper_files/paper/2024/file/40cf27290cc2bd98a428b567ba25075c-Paper-Conference.pdf</a>), specifically trained for DS reconstruction.Remarkably, DynaMix not only generalizes zero-shot to novel DS, but it can even generalize to new initial conditions and regions of state space not covered by the in-context information.We dive a bit into the reasons why current time series FMs not trained for DS reconstruction fail, and conclude that a DS perspective on time series forecasting & models may help to advance the <a href="https://mathstodon.xyz/tags/TimeSeriesAnalysis" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#TimeSeriesAnalysis</a> field.

Eduardo Vera-ValdesIntroducing LongMemory.jl: A Julia Package for Long Memory Time Series Analysis 🖥️📚📈📊I am happy to announce that after several months of getting to understand the language better, I have finally published my first Julia registered package: LongMemory.jl. 🙂 This package is the result of my research on long memory time series analysis, which is a fascinating topic in econometrics and statistics. Long memory models are useful for capturing the persistence and dependence of many real-world phenomena, such as inflation, interest rates, volatility, network traffic, and environmental data.LongMemory.jl makes it easy to generate, estimate, and forecast long memory models in Julia. It supports various types of models, such as fractional differencing, cross-sectional aggregation, and stochastic duration shocks. It also provides functions for testing the presence of long memory, computing the Hurst exponent, and simulating long memory processes. The package is fully documented and includes classical data examples, such as the Nile River minima. 🌊The package can be installed easily from the Julia general registry. I have prepared a short video that shows how to install the package and generate long memory diagnostics plots for the Nile River minima dataset. The Nile River minima is a famous example of a long memory time series.I hope you find LongMemory.jl useful and practical. I welcome any feedback, suggestions, or contributions to improve the package. You can contact me or open an issue on GitHub. Thank you for your interest and feedback!<a href="https://mathstodon.xyz/tags/julialang" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#julialang</a> <a href="https://mathstodon.xyz/tags/programming" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#programming</a> <a href="https://mathstodon.xyz/tags/programmingjourney" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#programmingjourney</a> <a href="https://mathstodon.xyz/tags/longmemory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#longmemory</a> <a href="https://mathstodon.xyz/tags/timeseriesanalysis" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#timeseriesanalysis</a> <a href="https://mathstodon.xyz/tags/timeseries" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#timeseries</a> <a href="https://mathstodon.xyz/tags/econometrics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#econometrics</a> <a href="https://mathstodon.xyz/tags/statistics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#statistics</a> <a href="https://bird.makeup/users/julialanguage" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@julialanguage@bird.makeup</a> <a href="https://mastodon.social/@julialanguage" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@julialanguage@mastodon.social</a>

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