Time Series Forecasting with Seasonal Decomposition and ARIMA

Data processing

We select a periodic time series covering the past 7 days with hourly points (7×24 points) and prepare it for analysis.

Split dataset

We use the first six days as the training set and the seventh day as the test set.

Smoothing

To remove spikes, we compute the difference between consecutive points, discard outliers, and fill them with the average of neighboring values; this yields a smoother series.

Seasonal decomposition

Using statsmodels.tsa.seasonal_decompose we separate the series into observed, trend, seasonal, and residual components (additive model). The two‑sided option affects edge values.

The first plot shows the original data (observed), followed by trend, seasonal, and residual plots.

Prediction

We forecast the trend component with an ARIMA model, selecting parameters p, d, q via AIC/BIC criteria, then add back the seasonal component to obtain the final forecast.

After fitting the model, predictions are generated and visualized, showing that the periodic characteristics are well captured.

Evaluation

Using the seventh day as test data, the forecast is evaluated with RMSE, which is below 5, indicating satisfactory performance.

Summary

The article presented a workflow for forecasting periodic time series, including data smoothing, seasonal decomposition, ARIMA trend prediction, and evaluation, and hints at future posts on periodicity detection methods.