autoregressive models

How Do Autoregressive Models Work?

Mathematically, an AR model of order p (AR(p)) can be written as:
\[ X_t = c + \sum_{i=1}^{p} \phi_i X_{t-i} + \epsilon_t \]
where:
- \( X_t \) is the value at time t.
- \( c \) is a constant.
- \( \phi_i \) are the coefficients.
- \( \epsilon_t \) is the error term.
In the context of epidemiological data, \( X_t \) could represent the number of new cases at time t, and the model would use past values of new cases to predict future values.

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