Seasonal Decomposition of Market Time Series into Trend, Seasonality, and Residuals

Summary

The article introduces seasonal decomposition as a way to separate a time series into trend, seasonal, and residual components. It outlines additive and multiplicative forms: trend is estimated with a moving average centered to align with the original series; seasonal values are estimated from detrended observations grouped by position in each cycle; and residuals capture what remains after the components are removed or factored out. The method is illustrated with synthetic data containing a linear trend, a repeating cycle, and random noise, and the article discusses implementing the calculations in MQL5.

The stated uses include inspecting recurring patterns, isolating trends, and preparing data for forecasting. The author suggests seasonal forecasting methods when a clear seasonal pattern exists, while irregular or weak seasonality may call for other approaches. The synthetic example demonstrates the construction, not forecasting skill on live markets. Multiplicative decomposition also requires positive values, and the article does not establish that stock prices have stable seasonal structure or that decomposition improves trading results.

Key ideas

• Seasonal decomposition represents a time series with trend, seasonal, and residual components.
• A moving average over the seasonal period estimates trend, with padding used to align the result to the original series.
• Seasonal patterns are estimated by averaging detrended observations at corresponding positions in repeated cycles.
• Additive decomposition uses differences, while multiplicative decomposition uses ratios and requires positive values.
• The synthetic example illustrates the method but does not demonstrate market forecasting or trading performance.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.