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Forecasting · Time Series · Business PlanningIndividual academic project

Seasonal ARIMA Forecasting of Ozone Concentration

Monthly forecasting model using Box-Jenkins methodology, SARIMA, residual diagnostics, and 12-month dynamic forecasting in Stata.

Type

Individual academic project

Area

Forecasting · Time Series · Business Planning

Tools

Stata · .do script

Techniques

Box-Jenkins · SARIMA · ACF / PACF · AIC / BIC · Ljung-Box · Dynamic forecast

Output

SARIMA model + 12-month forecast

Value

Individual project where I modelled a monthly ozone-concentration series using Stata, Box-Jenkins methodology, and SARIMA to generate forecasts with residual diagnostics and uncertainty intervals.

216

Months of data used

12

Dynamically forecast months

0,7486

Ljung-Box Q(24) p-value

Executive summary

Applied forecasting case where the value lies in following a full process: preparing the series, identifying temporal structure, comparing models, validating residuals, and presenting forecasts with uncertainty.

Business context

Many business decisions depend on anticipating demand, activity, traffic, sales, or operational indicators. This case uses an environmental series as an academic context, but the logic is transferable to KPI, demand, or commercial-activity planning.

My role

Individual academic project. I prepared the series, ran the Box-Jenkins workflow, compared SARIMA models in Stata, validated residuals, and generated dynamic forecasts with intervals.

Data & methods

  • Monthly ozone-concentration series, 1980m1–1997m12.
  • Log transformation and regular/seasonal differencing.
  • Identification through ACF and PACF.
  • Model comparison using AIC/BIC.
  • Diagnostics with Ljung-Box, sktest, Q-Q, P-P, and histograms.
  • Dynamic forecast for 1998 and back-transform with lognormal correction.

Process

  1. 01Visualise the series and decide to work in logs.
  2. 02Apply seasonal and regular differencing.
  3. 03Identify candidate models with ACF/PACF.
  4. 04Estimate SARIMA alternatives in Stata.
  5. 05Select the model using AIC/BIC and residual diagnostics.
  6. 06Generate dynamic forecasts and 95% intervals.

Key findings

  • The selected model was ARIMA(1,1,1) x (0,1,1)[12] without constant.
  • The model achieved the best AIC/BIC among compared alternatives.
  • Ljung-Box tests did not reject white-noise residuals.
  • The final output includes a 12-month dynamic forecast with prediction intervals.

Business implications

  • Demonstrates ability to plan under temporal uncertainty.
  • Transferable to demand, sales, traffic, operations, and business KPIs.

Limitations

  • Academic context and environmental series.
  • Does not include exogenous variables.
  • Forecast quality depends on temporal stability and model assumptions.

What I would do next

  • Compare with models using exogenous variables.
  • Evaluate out-of-sample errors.
  • Create a forecast dashboard and alerts.

Assets

View summaryComing soonSummary can be expanded if needed.View notebookComing soonStata .do script available for a reproducible version.

Suggested visuals

Original and transformed time series.

ACF/PACF.

Forecast fan chart.

Residual diagnostics grid.

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