Generates a random walk without drift.
gen_rw(N, sigma2 = 1)grw A vec containing the random walk without drift.
An integer for signal length.
A double that contains process variance.
Random Walk (RW) with parameter \(\gamma^2 \in {\rm I\!R}^{+}\). This process is defined as: $${X_t} = \sum\limits_{t = 1}^T {\gamma {Z_t}} $$ and is often called Rate Random Walk in the engineering literature.
To generate we first obtain the standard deviation from the variance by taking a square root. Then, we sample \(N\) times from a \(N(0,\sigma^2)\) distribution. Lastly, we take the cumulative sum over the vector.