gen_rw: Generate a Random Walk without Drift

In SMAC-Group/simts: Time Series Analysis Tools

Generate a Random Walk without Drift

Description

Generates a random walk without drift.

Usage

gen_rw(N, sigma2 = 1)

Arguments

N	An integer for signal length.
sigma2	A double that contains process variance.

Value

grw A vec containing the random walk without drift.

Process Definition

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.

Generation Algorithm

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.

SMAC-Group/simts documentation built on Sept. 4, 2023, 5:25 a.m.