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.
Months of data used
Dynamically forecast months
Ljung-Box Q(24) p-value
01 / Fast scan
Case in 60 seconds
A quick scan of the case: what was happening, what needed to be solved, what I did, and what value is demonstrated.
Situation
SMany 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.
Task
TIndividual 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.
Action
A- 01Visualise the series and decide to work in logs.
- 02Apply seasonal and regular differencing.
- 03Identify candidate models with ACF/PACF.
- 04Estimate SARIMA alternatives in Stata.
Result
R- 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.
- Demonstrates ability to plan under temporal uncertainty.
- Transferable to demand, sales, traffic, operations, and business KPIs.
- 216 · Months of data used
02 / Context
Problem
This section explains the business or analytical challenge before going into technical detail.
02.1
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.
02.2
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.
03 / Method
Approach
Methods, tools, and workflow. This shows how I structured the analysis.
03.1
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.
03.2
Process
- 01Visualise the series and decide to work in logs.
- 02Apply seasonal and regular differencing.
- 03Identify candidate models with ACF/PACF.
- 04Estimate SARIMA alternatives in Stata.
- 05Select the model using AIC/BIC and residual diagnostics.
- 06Generate dynamic forecasts and 95% intervals.
04 / Decision
Evidence and impact
Outputs, findings, and implications translated into decisions or professional value.
04.1
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.
04.2
Business implications
- Demonstrates ability to plan under temporal uncertainty.
- Transferable to demand, sales, traffic, operations, and business KPIs.
05 / Close
Professional close
Limitations, next steps, and available assets. This keeps the case honest and actionable.
05.1
Limitations
- Academic context and environmental series.
- Does not include exogenous variables.
- Forecast quality depends on temporal stability and model assumptions.
05.2
What I would do next
- Compare with models using exogenous variables.
- Evaluate out-of-sample errors.
- Create a forecast dashboard and alerts.
05.3
Assets
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