📈 Seasonality

Seasonality#

Regular, calendar-linked cycles in a time series.

Important

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What it is#

Seasonality is a pattern in a time series that repeats at fixed, regular intervals — driven by seasonal factors such as the time of year, the month, the day of the week or the hour of the day. Unlike a trend (a long-term rise or fall), seasonality is periodic, recurring with a fixed frequency. In a decomposition, a series splits into trend, seasonal and residual parts, \(y_t = T_t + S_t + \varepsilon_t\), with \(S_t\) the seasonal component.

Examples#

Retail sales spike every December, ice-cream demand rises each summer, website traffic dips every weekend, and electricity load peaks on hot afternoons. In each case the same shape returns on a predictable cycle.

Detecting it#

Seasonality shows up as a repeating shape in a line plot, and is confirmed with seasonal subseries or decomposition plots and with the autocorrelation function (ACF), which spikes at the seasonal lag — for example lag 12 for monthly data with yearly seasonality.

Handling it in models#

Several tools absorb it: seasonal differencing removes it, SARIMA adds seasonal \((P, D, Q)_m\) terms, Prophet fits it with a Fourier series, and simpler models use seasonal dummy variables. Getting seasonality right is essential for accurate forecasting — ignoring it leaves systematic, repeating errors in the residuals.

Theme: Signal Processing & Time Series · All terminology

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Mind map — connected ideas

ARIMA (AutoRegressive Integrated Moving Average) · Prophet — Time Series Forecasting by Facebook (Meta) · Time Series · Seasonal Lag · Signal Processing · Temporal autocorrelation (Serial Correlation)

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More in Signal Processing & Time Series

ARIMA (AutoRegressive Integrated Moving Average) · Bayesian Time Series · Forecast Error · Forecasting Benchmarks · Forecasting Competitions · Log-Space · Low-pass Filtering · LSTM — Long Short-Term Memory Networks · M-Competitions (Makridakis Competitions) · Naïve Baseline Forecast · Prophet — Time Series Forecasting by Facebook (Meta) · Seasonal Lag · Signal Processing · Simple Baseline Methods