Add time series decomposition post for 2022

Author: DiogoRibeiro7

_posts/2022-10-15-time_series_decomposition.md

@@ -0,0 +1,52 @@
+---
+author_profile: false
+categories:
+- Data Science
+- Time Series
+classes: wide
+date: '2022-10-15'
+excerpt: Learn how time series decomposition reveals trend, seasonality, and residual components for clearer forecasting insights.
+header:
+  image: /assets/images/data_science_12.jpg
+  og_image: /assets/images/data_science_12.jpg
+  overlay_image: /assets/images/data_science_12.jpg
+  show_overlay_excerpt: false
+  teaser: /assets/images/data_science_12.jpg
+  twitter_image: /assets/images/data_science_12.jpg
+keywords:
+- Time series
+- Trend
+- Seasonality
+- Forecasting
+- Decomposition
+seo_description: Discover how to separate trend and seasonal patterns from a time series using additive or multiplicative decomposition.
+seo_title: 'Time Series Decomposition Made Simple'
+seo_type: article
+summary: This article explains how decomposing a time series helps isolate long-term trends and recurring seasonal effects so you can model data more effectively.
+tags:
+- Time series
+- Forecasting
+- Data analysis
+- Python
+title: 'Time Series Decomposition: Separating Trend and Seasonality'
+---
+
+Time series data often combine several underlying components: a long-term **trend**, repeating **seasonal** patterns, and random **residual** noise. By decomposing a series into these pieces, you can better understand its behavior and build more accurate forecasts.
+
+## Additive vs. Multiplicative Models
+
+In an **additive** model, the components simply add together:
+
+$$ y_t = T_t + S_t + R_t $$
+
+where $T_t$ is the trend, $S_t$ is the seasonal component, and $R_t$ represents the residuals. A **multiplicative** model instead multiplies these terms:
+
+$$ y_t = T_t \times S_t \times R_t $$
+
+Choose the form that best fits the scale of seasonal fluctuations in your data.
+
+## Extracting the Components
+
+Python libraries like `statsmodels` or `pandas` offer built-in functions to perform decomposition. Once the trend and seasonality are isolated, you can analyze them separately or remove them before applying forecasting models such as ARIMA.
+
+Understanding each component allows you to explain past observations and produce more transparent predictions for future values.