Predictive Modeling

Purpose

Two forecasting tools: exponential smoothing on a synthetic seasonal series, and an absorbing Markov chain that gives the probability of conversion.

Variables

• y_tobserved value at time t
• ŷ_tforecast for time t
• αweight of the latest observation
• N, Bfundamental matrix and absorption probabilities

Assumptions

• The series is synthetic: trend, a 12-period season and noise, from the seed.
• Smoothing has no seasonal term on purpose, to show where it falls short.
• Chain probabilities are illustrative; rows must sum to 1, and the remainder goes to Exit.

Model

Data this would need in practice

• A real time series with enough history to cover a full season.
• Real navigation or collection logs, with consent, to estimate transitions.
• A holdout period to measure forecast error.

Interpretation

A high α follows the data but amplifies noise; a low α lags. The best α minimizes the error. Because the series is seasonal, smoothing alone stays well above the noise level: the model is incomplete, and the lab shows it. In the chain, B gives the probability of ending in conversion from each starting state.

Limitations

• One-step error on synthetic data says nothing about real data.
• The Markov assumption ignores history.
• Probabilities here are not measured.