Random walk

Summary

• A started AR(1) process \(Y_t=δ+θY_{t-1}+ε_t\) is called a random walk if \(δ=0\) and \(θ=1\) ,

\[Y_t=Y_{t-1}+ε_t\]

• A started AR(1) process \(Y_t=δ+θY_{t-1}+ε_t\) is called a random walk with drift if \(δ≠0\) and \(θ=1\)
• A random walk is not stationary . For example, with \(y_0=0\) we have \(Var\left( y_t \right)=tσ^2\) .