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Mean-reverting process

As explained in Build a Robo-Advisor with Python (From Scratch)

A mean-reverting process is a stochastic process whose values tend to move back toward a long-run average.

A mean-reverting process models inflation as deviations that gradually move toward a long-run average while receiving random shocks. Its discrete form is an AR(1) model: inf_t = c + φ inf_(t−1) + ε_t, with μ = c/(1−φ). section 5.7

Inflation simulation parameters

One simulation uses an initial inflation rate of 3.5%, φ = 0.6695, c = 0.0116, and residual standard deviation σ_inf = 0.02132.

How Build a Robo-Advisor with Python (From Scratch) covers it

How deep it goes
Defines the AR(1) formulation, estimates parameters by regression, and simulates paths, but does not develop deeper stochastic-process theory.
Examples
Uses CPIAUCNS observations, annual inflation rates, regression residuals, and simulated wealth paths.
What it assumes
Assumes Python data handling, lagged observations, ordinary least squares, and normally distributed random shocks.
What you can do after
Build inflation paths from estimated parameters and incorporate them into Monte Carlo wealth simulations.
How it connects
Connects stochastic processes, AR(1) models, linear regression, inflation risk, and Monte Carlo simulation.
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