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About

Time-series analysis relies heavily on isolating seasonal variations from underlying trends. Retailers, supply chain managers, and financial analysts use seasonality indices to smooth data and predict future peaks. Ignoring these cyclic patterns often leads to stockouts during high demand or excess inventory during off-seasons. This tool decomposes raw data using the Ratio-to-Moving-Average method.

The process involves calculating a Centered Moving Average (CMA) to strip away noise and seasonality. By comparing actual values to this smoothed baseline, we derive specific indices for each period. A value above 1.0 indicates a high season, while a value below 1.0 suggests a slowdown. Accurate decomposition is mathematically rigorous but essential for precise forecasting.

time-series forecasting seasonality moving-average data-analysis

Formulas

The calculation utilizes a Centered Moving Average (CMA) to smooth the time series. For a 12-month cycle, the CMA at time t is derived from the average of two consecutive 12-month moving averages.

{
MAt = 6i=-5 yt+i12CMAt = MAt + MAt+12

The Seasonal Index (SI) for a specific month is the average of the ratios of Actual to CMA for that month across all available years.

Reference Data

PeriodRaw DataMA (12-Period)Centered MASeas. Irreg.Seas. Index
Month 1120NULLNULLNULL0.85
Month 2135NULLNULLNULL0.92
Month 7200150.4151.21.321.30
Month 8110152.1153.00.720.75

Frequently Asked Questions

A simple 12-month average aligns with the period between the 6th and 7th month, causing a phase shift. Centering averages two consecutive moving averages to align the smoothed value exactly with the 7th month, ensuring temporal accuracy in the index calculation.
A minimum of 24 periods (2 full years) is necessary to calculate the first set of Centered Moving Averages. However, 36 to 48 months provides a more robust index by mitigating the impact of one-off anomalies.
An index of 1.25 means the demand or value in that specific period is typically 25% higher than the average monthly trend. Conversely, an index of 0.80 implies activity is 20% below the average.