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y = randn(100)

#Fit Model
output = StateSpaceLearning.fit_model(y; estimation_input = estimation_input, estimation_function = estimation_function_min_sq)</code></pre><p>By following these steps, you can customize and extend the StateSpaceLearning framework to suit a variety of state space models and estimation procedures.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../manual/">« StateSpaceLearning</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Monday 26 August 2024 20:32">Monday 26 August 2024</span>. Using Julia version 1.0.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
output = StateSpaceLearning.fit_model(y; estimation_input = estimation_input, estimation_function = estimation_function_min_sq)</code></pre><p>By following these steps, you can customize and extend the StateSpaceLearning framework to suit a variety of state space models and estimation procedures.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../manual/">« StateSpaceLearning</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Monday 16 September 2024 21:46">Monday 16 September 2024</span>. Using Julia version 1.0.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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<h3 style="color: black;">Star us on GitHub!</h3>
<a class="github-button" href="https://github.com/LAMPSPUC/StateSpaceLearning.jl" data-icon="octicon-star" data-size="large" data-show-count="true" aria-label="Star LAMPSPUC/StateSpaceLearning.jl on GitHub" style="margin:auto">Star</a>
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</div><h1 id="StateSpaceLearning.jl-Documentation"><a class="docs-heading-anchor" href="#StateSpaceLearning.jl-Documentation">StateSpaceLearning.jl Documentation</a><a id="StateSpaceLearning.jl-Documentation-1"></a><a class="docs-heading-anchor-permalink" href="#StateSpaceLearning.jl-Documentation" title="Permalink"></a></h1><p>StateSpaceLearning.jl is a package for modeling and forecasting time series in a high-dimension regression framework.</p><h2 id="Installation"><a class="docs-heading-anchor" href="#Installation">Installation</a><a id="Installation-1"></a><a class="docs-heading-anchor-permalink" href="#Installation" title="Permalink"></a></h2><p>This package is registered so you can simply <code>add</code> it using Julia&#39;s <code>Pkg</code> manager:</p><pre><code class="language-julia hljs">pkg.add(&quot;StateSpaceLearning&quot;)</code></pre><h2 id="Citing-StateSpaceLearning.jl"><a class="docs-heading-anchor" href="#Citing-StateSpaceLearning.jl">Citing StateSpaceLearning.jl</a><a id="Citing-StateSpaceLearning.jl-1"></a><a class="docs-heading-anchor-permalink" href="#Citing-StateSpaceLearning.jl" title="Permalink"></a></h2><p>If you use StateSpaceLearning.jl in your work, we kindly ask you to cite the following preprint (<a href=".">pdf</a>):</p><p>@misc{ramos2024timeseriesanalysisstate, title={Time Series Analysis by State Space Learning}, author={André Ramos and Davi Valladão and Alexandre Street}, year={2024}, eprint={2408.09120}, archivePrefix={arXiv}, primaryClass={stat.ML}, url={https://arxiv.org/abs/2408.09120}, }</p></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="manual/">StateSpaceLearning »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Monday 26 August 2024 20:32">Monday 26 August 2024</span>. Using Julia version 1.0.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
</div><h1 id="StateSpaceLearning.jl-Documentation"><a class="docs-heading-anchor" href="#StateSpaceLearning.jl-Documentation">StateSpaceLearning.jl Documentation</a><a id="StateSpaceLearning.jl-Documentation-1"></a><a class="docs-heading-anchor-permalink" href="#StateSpaceLearning.jl-Documentation" title="Permalink"></a></h1><p>StateSpaceLearning.jl is a package for modeling and forecasting time series in a high-dimension regression framework.</p><h2 id="Installation"><a class="docs-heading-anchor" href="#Installation">Installation</a><a id="Installation-1"></a><a class="docs-heading-anchor-permalink" href="#Installation" title="Permalink"></a></h2><p>This package is registered so you can simply <code>add</code> it using Julia&#39;s <code>Pkg</code> manager:</p><pre><code class="language-julia hljs">pkg.add(&quot;StateSpaceLearning&quot;)</code></pre><h2 id="Citing-StateSpaceLearning.jl"><a class="docs-heading-anchor" href="#Citing-StateSpaceLearning.jl">Citing StateSpaceLearning.jl</a><a id="Citing-StateSpaceLearning.jl-1"></a><a class="docs-heading-anchor-permalink" href="#Citing-StateSpaceLearning.jl" title="Permalink"></a></h2><p>If you use StateSpaceLearning.jl in your work, we kindly ask you to cite the following preprint (<a href=".">pdf</a>):</p><p>@misc{ramos2024timeseriesanalysisstate, title={Time Series Analysis by State Space Learning}, author={André Ramos and Davi Valladão and Alexandre Street}, year={2024}, eprint={2408.09120}, archivePrefix={arXiv}, primaryClass={stat.ML}, url={https://arxiv.org/abs/2408.09120}, }</p></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="manual/">StateSpaceLearning »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Monday 16 September 2024 21:46">Monday 16 September 2024</span>. Using Julia version 1.0.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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&quot;sigma2_ζ&quot; =&gt;residuals_variances[&quot;ζ&quot;],
&quot;sigma2_ω&quot; =&gt;residuals_variances[&quot;ω&quot;]))
fit!(model)</code></pre><h2 id="Paper-Results-Reproducibility"><a class="docs-heading-anchor" href="#Paper-Results-Reproducibility">Paper Results Reproducibility</a><a id="Paper-Results-Reproducibility-1"></a><a class="docs-heading-anchor-permalink" href="#Paper-Results-Reproducibility" title="Permalink"></a></h2><p>The paper has two experiments (results for the M4 competition and a simulation study). To reproduce each experiment follow the instructions below:</p><h3 id="M4-Experiment"><a class="docs-heading-anchor" href="#M4-Experiment">M4 Experiment</a><a id="M4-Experiment-1"></a><a class="docs-heading-anchor-permalink" href="#M4-Experiment" title="Permalink"></a></h3><p>To reproduce M4 paper results you can clone the repository and run the following commands on terminal:</p><pre><code class="language-shell hljs">julia paper_tests/m4_test/m4_test.jl
python paper_tests/m4_test/m4_test.py</code></pre><p>The results for SSL model in terms of MASE and sMAPE for all 48000 series will be stored in folder &quot;paper_tests/m4_test/results_SSL&quot;. The average results of MASE, sMAPE and OWA will be saved in file &quot;paper_tests/m4_test/metric_results/SSL_METRICS_RESULTS.csv&quot;.</p><p>The results for SS model in terms of MASE and sMAPE for all 48000 series will be stored in folder &quot;paper_tests/m4_test/results_SS&quot;. The average results of MASE, sMAPE and OWA will be saved in file &quot;paper_tests/m4_test/metric_results/SS_METRICS_RESULTS.csv&quot;.</p><h3 id="Simulation-Experiment"><a class="docs-heading-anchor" href="#Simulation-Experiment">Simulation Experiment</a><a id="Simulation-Experiment-1"></a><a class="docs-heading-anchor-permalink" href="#Simulation-Experiment" title="Permalink"></a></h3><p>To reproduce the simulation results you can clone the repository and run the following commands on terminal:</p><pre><code class="language-shell hljs">julia paper_tests/simulation_test/simulation.jl 0</code></pre><p>As this test takes a long time, you may want to run it in parallel, for that you can change the last argument to be number of workers to use in the parallelization:</p><pre><code class="language-shell hljs">julia paper_tests/simulation_test/simulation.jl 3</code></pre><p>The results will be saved in two separated files: &quot;paper_tests/simulation_test/results_metrics/metrics_confusion_matrix.csv&quot; and &quot;paper_tests/simulation_test/results_metrics/metrics_bias_mse.csv&quot;</p><h2 id="Contributing"><a class="docs-heading-anchor" href="#Contributing">Contributing</a><a id="Contributing-1"></a><a class="docs-heading-anchor-permalink" href="#Contributing" title="Permalink"></a></h2><ul><li>PRs such as adding new models and fixing bugs are very welcome!</li><li>For nontrivial changes, you&#39;ll probably want to first discuss the changes via issue.</li></ul></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Home</a><a class="docs-footer-nextpage" href="../adapting_package/">Add New Models »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Monday 26 August 2024 20:32">Monday 26 August 2024</span>. Using Julia version 1.0.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
python paper_tests/m4_test/m4_test.py</code></pre><p>The results for SSL model in terms of MASE and sMAPE for all 48000 series will be stored in folder &quot;paper_tests/m4_test/results_SSL&quot;. The average results of MASE, sMAPE and OWA will be saved in file &quot;paper_tests/m4_test/metric_results/SSL_METRICS_RESULTS.csv&quot;.</p><p>The results for SS model in terms of MASE and sMAPE for all 48000 series will be stored in folder &quot;paper_tests/m4_test/results_SS&quot;. The average results of MASE, sMAPE and OWA will be saved in file &quot;paper_tests/m4_test/metric_results/SS_METRICS_RESULTS.csv&quot;.</p><h3 id="Simulation-Experiment"><a class="docs-heading-anchor" href="#Simulation-Experiment">Simulation Experiment</a><a id="Simulation-Experiment-1"></a><a class="docs-heading-anchor-permalink" href="#Simulation-Experiment" title="Permalink"></a></h3><p>To reproduce the simulation results you can clone the repository and run the following commands on terminal:</p><pre><code class="language-shell hljs">julia paper_tests/simulation_test/simulation.jl 0</code></pre><p>As this test takes a long time, you may want to run it in parallel, for that you can change the last argument to be number of workers to use in the parallelization:</p><pre><code class="language-shell hljs">julia paper_tests/simulation_test/simulation.jl 3</code></pre><p>The results will be saved in two separated files: &quot;paper_tests/simulation_test/results_metrics/metrics_confusion_matrix.csv&quot; and &quot;paper_tests/simulation_test/results_metrics/metrics_bias_mse.csv&quot;</p><h2 id="Contributing"><a class="docs-heading-anchor" href="#Contributing">Contributing</a><a id="Contributing-1"></a><a class="docs-heading-anchor-permalink" href="#Contributing" title="Permalink"></a></h2><ul><li>PRs such as adding new models and fixing bugs are very welcome!</li><li>For nontrivial changes, you&#39;ll probably want to first discuss the changes via issue.</li></ul></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Home</a><a class="docs-footer-nextpage" href="../adapting_package/">Add New Models »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Monday 16 September 2024 21:46">Monday 16 September 2024</span>. Using Julia version 1.0.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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