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THE FEUTEX TOOLKIT

AR(1) Conditional Forecast

Project a stationary autoregressive series and its innovation variance over a horizon.

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01 Your input
02 Your result
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FormulaForecast = mu+phi**h*(last-mu); Forecast Variance = sigma**2*(1-phi**(2*h))/(1-phi**2)
Sources and model references

Made for real tasks

  • Project a stationary autoregressive series and its innovation variance over a horizon.
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Worked example

Inputs

Last observed value
12 number
Long-run mean
10 number
AR coefficient
0.7 number
Innovation standard deviation
2 number
Forecast horizon
5 count

Expected results

Forecast
10.33614 number
Forecast Variance
7.62158804 number

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

  1. Enter last observed value, long-run mean, ar coefficient, innovation standard deviation, forecast horizon.
  2. Use the displayed units and confirm the model assumptions.
  3. Calculate and compare the outputs against your input scenario.

Try this example

{
  "last": 12,
  "mu": 10,
  "phi": 0.7,
  "sigma": 2,
  "h": 5
}

Accuracy and scope

Stationary AR(1) with known parameters and independent innovations. Parameter estimation uncertainty is excluded.

Is my data uploaded?

This tool runs locally in your browser. Input and output are not sent to a processing server. Copy or download your result before leaving the page.