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AR(1) Effective Sample Size

Approximate the information loss in a mean estimate from positive first-order serial correlation.

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FormulaEffective Sample = max(1,n*(1-rho)/(1+rho)); Se Inflation = sqrt((1+rho)/(1-rho))
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  • Approximate the information loss in a mean estimate from positive first-order serial correlation.
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Worked example

Inputs

Observed sample count
100 count
Lag-one correlation
0.5 correlation

Expected results

Effective Sample
33.33333333 observations
Se Inflation
1.732050808 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 observed sample count, lag-one correlation.
  2. Use the displayed units and confirm the model assumptions.
  3. Calculate and compare the outputs against your input scenario.

Try this example

{
  "n": 100,
  "rho": 0.5
}

Accuracy and scope

Large-sample stationary AR(1) approximation; effective sample is capped below at one. Not valid for arbitrary dependence or a unit root.

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.