FInite Memory Random Walks

A model in which effects of recent shocks persist for a specified finite window, allowing temporary dependence and streaks.

A finite-memory random process can let a recent sequence of shocks affect the current value while older shocks drop out. A simple illustrative construction is V(t) = X(t) + X(t−1) + X(t−2): each new value adds a fresh shock and removes the oldest one. Adjacent values overlap, so streaks can arise without a permanently superior performer.

This finite-window construction is closely related to a moving-average process. It should not be confused with the claim that a Markov process has no historical influence: an ordinary random walk can summarize accumulated shocks in its current position. Nor does a finite window justify ignoring old information in actual markets, organizations, or personal history. The length and form of dependence need evidence.

When to use it

Useful for understanding toy competition models and evaluating a proposed finite-window description of a process.

How it can help

Compare short-lived contributions with persistent effects and inspect the consequences of overlapping observations.