ARIMA Forecast Calculator

Model time series with practical ARIMA controls and diagnostics. Compare forecasts, residuals, and confidence bands. Turn raw observations into reliable planning signals for decisions.

Calculator Inputs

Use numeric values only. Example: 120, 128, 133, 140
Provide the same count as your series if you want custom labels.
Choose how many future periods to predict.
Provide at least p values.
Provide at least q values.

Example Data Table

This sample series shows steadily rising monthly demand and works well for testing ARIMA settings and forecast exports.

Month Observed Value
Jan120
Feb128
Mar133
Apr140
May149
Jun158
Jul166
Aug172
Sep181
Oct190
Nov198
Dec207

Formula Used

1) Differencing
First difference:
y′t = yt − yt−1
Repeating the operation d times removes trend and stabilizes the working series.
2) ARIMA relationship on the differenced series
zt = c + φ1zt−1 + φ2zt−2 + ... + φpzt−p + et + θ1et−1 + θ2et−2 + ... + θqet−q
Here, z is the differenced series, c is the constant, φ values are AR coefficients, and θ values are MA coefficients.
3) Recursive forecast
The calculator predicts each next differenced value from the fitted AR and MA terms, then reverses differencing to return forecasts on the original scale.
4) Approximate confidence interval
Forecast ± z × RMSE × √h
Where z comes from the selected confidence level, RMSE is the training error, and h is the forecast step.

Automatic mode uses conditional least squares for a fast transparent estimate. It is useful for planning and learning, while full production modeling may need deeper diagnostics.

How to Use This Calculator

  1. Paste historical observations into the data box using commas or new lines.
  2. Add matching labels if you want named points on the graph.
  3. Choose AR order p, differencing order d, and MA order q.
  4. Select automatic estimation or enter your own constant and coefficients.
  5. Set the forecast horizon and confidence level.
  6. Click Generate Forecast to show results above the form.
  7. Review diagnostics, coefficients, the forecast table, and the Plotly graph.
  8. Use the CSV or PDF buttons to export the forecast output.

FAQs

1) What does ARIMA mean?

ARIMA stands for AutoRegressive Integrated Moving Average. It models a series by combining past values, differencing, and past errors to produce forecasts.

2) What do p, d, and q control?

The value p sets autoregressive lags, d sets how many times the series is differenced, and q sets moving average error lags.

3) When should I increase d?

Increase d when the original series has obvious trend and the model struggles with stability. Too much differencing can also distort useful structure.

4) What does automatic mode do?

Automatic mode estimates the constant and coefficients with conditional least squares on the differenced series, giving a quick practical model without outside libraries.

5) Can I enter my own coefficients?

Yes. Manual mode lets you enter the constant, AR terms, and MA terms directly, which is useful for classroom examples and scenario testing.

6) Are the confidence intervals exact?

They are approximate. This page scales training RMSE by the forecast step and confidence z score, so results are useful but not identical to full statistical software.

7) What kind of data works best?

ARIMA works best with ordered numeric observations collected over equal time intervals, such as monthly demand, weekly traffic, or daily counts.

8) Why are my forecasts flat or unstable?

That usually means the chosen orders are not suitable, the series is too short, or the coefficients need adjustment. Try simpler settings first.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.