INAR1

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INAR1(α, dist, add_noise)

First-Order Integer Numerated AutoRegressive Process.

The INAR(1) model for a time series \(X_t\) is defined by: \(X_t = \alpha \circ X_{t-1} + \epsilon_t\) where:

• \[ \alpha \circ X_{t-1} \]

  is a thinning operator (e.g., binomial thinning).

• \[ \epsilon_t \]

  is an independent sequence of random variables (the innovation).

Fields

• α::Float64: The autoregressive parameter (thinning probability). Must be in \((0, 1)\).
• dist::DiscreteUnivariateDistribution: The distribution of the innovation term \(\epsilon_t\).
• add_noise::Bool: Flag indicating whether a small amount of uniform noise should be added to the process (usually for simulating continuous-like observations from a discrete process).