This tutorial introduces white noise and random walk.

#### 1 White Noise

##### 1.1 Motivation

When we fit mathematical models to time series data, if the model captured most of the *deterministic* features of the time series, the *residual error series* should appear to be a realization of *independent* random variable from some probability distribution. Due to this criteria of judging how good a model is in fitting given data, it seems natural to build models up from a model of independent randon variation, known as *discrete white noise*.