Seasonal Decomposition Algorithm

Overview: The Seasonal Decomposition algorithm in SQL Server Analysis Services is a powerful tool for understanding and forecasting time-series data by breaking it down into its core components: trend, seasonality, and residual (random) elements.

Understanding Time Series Components

Time-series data often exhibits patterns that repeat over specific intervals. Identifying these patterns is crucial for accurate forecasting and business analysis. The Seasonal Decomposition algorithm helps isolate these patterns:

  • Trend: The long-term movement or direction of the data. This could be an upward or downward slope over an extended period.
  • Seasonality: The repeating pattern of fluctuations within a fixed period (e.g., daily, weekly, monthly, yearly). This component captures cyclical behavior.
  • Residual: The remaining variation in the data after the trend and seasonal components have been removed. This often represents random fluctuations or unpredictable events.

How it Works

The algorithm employs a moving average or other smoothing techniques to estimate the trend component. Once the trend is identified, it's used to isolate the seasonal effect. For additive models, seasonality is directly subtracted from the data. For multiplicative models, it's divided out.

The core process can be generalized as follows:

  1. Detrending: Estimate and remove the trend component from the original time series.
  2. Seasonality Estimation: Analyze the detrended data to identify recurring seasonal patterns. This often involves averaging values across corresponding periods (e.g., averaging all January values).
  3. Deseasonalizing: Remove the seasonal component from the original data (using addition or multiplication, depending on the model).
  4. Residual Calculation: The remaining data after removing trend and seasonality is the residual component.

Key Parameters

When building a time-series mining model with seasonal decomposition, you can configure several parameters:

Parameter Description Default
MODELING_NAME The name of the model. Automatic generation
DESCRIPTION A description for the model. Empty
SEASONALITY Specifies the expected seasonal period. Can be 'AUTO', a specific integer (e.g., 12 for monthly data with yearly seasonality), or a list of periods. 'AUTO'
SEASONAL_EXPLAIN_THRESHOLD A threshold to determine if a detected seasonal component is significant enough to be included. 0.5
SPLIT_POINT The point at which to split the time series into training and testing sets for model evaluation. 0.7 (70% for training)
METHOD The method used for decomposition. Options typically include 'ADDITIVE' and 'MULTIPLICATIVE'. 'ADDITIVE'

Usage Example (DMX)

Here's a conceptual example of how you might create a time-series model using DMX (Data Mining Extensions) that leverages seasonal decomposition:

CREATE MINING MODEL [SalesForecastingModel]
FROM
    SalesData
PREDICTION Amount, OrderDate
USING
    Microsoft_Time_Series(
        TIME_SERIES_COLUMNS = "OrderDate",
        REGRESSOR_COLUMNS = "Amount",
        SEASONALITY = "12", // Assuming monthly data with yearly seasonality
        METHOD = "MULTIPLICATIVE",
        SPLIT_POINT = 0.7,
        SEASONAL_EXPLAIN_THRESHOLD = 0.6
    );

Benefits of Seasonal Decomposition

  • Improved Forecast Accuracy: By accounting for predictable seasonal patterns, forecasts become more reliable.
  • Deeper Insight: Understand the underlying drivers of your data by separating cyclical influences from long-term trends and random noise.
  • Better Business Decisions: Make informed decisions about inventory, staffing, marketing campaigns, and resource allocation based on clearer data patterns.
  • Anomaly Detection: Residual analysis can help identify unusual events that deviate from expected patterns.

Related Algorithms and Concepts