From 959b8a670d5025f10a318d99e2b6ff69982eafd6 Mon Sep 17 00:00:00 2001
From: Berend Bouvy <b.n.bouvy@student.tudelft.nl>
Date: Fri, 29 Nov 2024 10:33:17 +0100
Subject: [PATCH] forecast update
---
book/time_series/forecasting.md | 5 ++++-
1 file changed, 4 insertions(+), 1 deletion(-)
diff --git a/book/time_series/forecasting.md b/book/time_series/forecasting.md
index 595c8c6f..a8c83417 100644
--- a/book/time_series/forecasting.md
+++ b/book/time_series/forecasting.md
@@ -24,8 +24,11 @@ In summary, given a time series $Y=\mathrm{Ax}+\epsilon$, the workflow is as fol
3. Predict the signal-of-interest: $\hat{Y}_{signal}=\mathrm{A}_p\hat{X}$, where $\mathrm{A}_p$ is the design matrix describing the functional relationship between the future values $Y_p$ and $\mathrm{x}$.
-4. Predict the noise $\hat{\epsilon}_p$ based on the AR model.
+4. Predict the noise $\hat{\epsilon}_p$ based on the AR model. $\hat{\epsilon}_p = \Sigma_{Y_pY}\Sigma_Y^{-1}\hat{\epsilon}$, where $\Sigma_{Y_pY}$ is the covariance matrix between the future values $Y_p$ and the observed values $Y$.
5. Predict future values of the time series: $\hat{Y}_p=\mathrm{A}_p\hat{X}+\hat{\epsilon}_p$.
+```(note)
+This procedure is a general approach to forecasting time series data. It resembles the process of stochastic inter- and extrapolation, which is used in many fields of science and engineering.
+```
--
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