ARIMA Forecasting Calculator
Fit ARIMA models online. ACF, PACF, residual diagnostics and forecast plot with intervals.
When to use it
Use to fit a Box-Jenkins ARIMA(p, d, q) model to a non-seasonal univariate time series for short-horizon forecasting. The recommended workflow: identify d via ADF or KPSS, select p and q from ACF and PACF of the differenced series, fit, then check residual ACF for white noise (Ljung-Box).
When NOT to use it
Do not use for series with strong seasonality without seasonal terms; use SARIMA instead. Do not use for very short series (under about 50 observations). Do not use for series with structural breaks unaddressed; remove the break first. For multivariate or causal forecasting, prefer VAR or regression with ARIMA errors.
What you get
Estimated AR and MA coefficients with their SEs and z-tests; residual SD; AIC and BIC for model selection; ACF and PACF of the residuals; Ljung-Box test of residual white noise at multiple lags; multi-step forecast with prediction intervals.
How to interpret the output
Coefficients absolute-value much greater than 2 SE are statistically significant. Lower AIC across candidate (p, d, q) is preferred but parsimony matters; do not over-fit. Residual ACF should be inside the white-noise bands and Ljung-Box should not reject; otherwise the model is mis-specified. Forecast intervals widen with horizon; do not over-trust long horizons.
Common pitfalls
- Skipping the residual diagnostics; ARIMA can fit but residuals can still be autocorrelated.
- Choosing p and q without first looking at ACF and PACF.
- Forgetting that d differencing is destructive; do not over-difference.
- Reporting only point forecasts without intervals.
Try it in StatVeda
The ARIMA(p, d, q) - Box-Jenkins engine runs entirely in the browser. No signup, no install, no data sent to a server. Paste your data, hit Run, copy the output.
Open ARIMA(p, d, q) - Box-JenkinsReferences
- Box, G. E. P., Jenkins, G. M., Reinsel, G. C. and Ljung, G. M. (2015). Time Series Analysis: Forecasting and Control, 5th edition. John Wiley and Sons, Hoboken.
- Hyndman, R. J. and Athanasopoulos, G. (2021). Forecasting: Principles and Practice, 3rd edition. OTexts, Melbourne.