Decomposing Time Series: Trend, Seasonality, and Residuals
Decomposing Time Series: Trend, Seasonality, and Residuals
A time series is a sequence of data points collected or recorded at successive points in time, usually at uniform intervals. To analyze and understand a time series, it’s often helpful to break it down into three main components:
1. Trend
Definition: The trend component represents the long-term progression or movement in the data.
What it shows: Whether the data is generally increasing, decreasing, or remaining constant over time.
Example: In sales data, a steady increase in sales over several years indicates an upward trend.
2. Seasonality
Definition: Seasonality refers to repeating patterns or cycles in the data that occur at regular intervals (daily, weekly, monthly, yearly, etc.).
What it shows: Periodic fluctuations caused by seasonal factors like holidays, weather, or other recurring events.
Example: Ice cream sales might peak every summer and drop every winter, showing seasonal variation.
3. Residuals (or Noise)
Definition: Residuals are the leftover part of the data after removing trend and seasonality.
What it shows: Random, irregular fluctuations or noise in the data that can’t be explained by the trend or seasonality.
Example: Sudden spikes in sales due to one-time promotions or unexpected events.
Why Decompose a Time Series?
Understanding patterns: Separating the components helps to better understand the underlying behavior.
Forecasting: Makes it easier to predict future values by modeling trend and seasonality separately.
Anomaly detection: Helps identify unusual deviations or outliers in the residual component.
How is Decomposition Done?
Common methods include:
Additive Model:
When the components combine as:
Observed
=
Trend
+
Seasonality
+
Residual
Observed=Trend+Seasonality+Residual
Used when the magnitude of seasonal fluctuations doesn’t depend on the level of the series.
Multiplicative Model:
When the components combine as:
Observed
=
Trend
×
Seasonality
×
Residual
Observed=Trend×Seasonality×Residual
Used when seasonal effects change proportionally with the level of the series.
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