Time series data is composed of signals and noise, where signals capture intrinsic dynamics of the process; however, noise represents the unmodeled component of a signal. The intrinsic dynamics of a time series signal can be as simple as the mean of the process or it can be a complex functional form within observations, as represented here:

*x*for

_{t}= f(x_{i}) + ε_{t}*i=1,2,3, ... t-1*

Here, *x _{t}* is observations and ε

_{t}is white noise. The

*f*(x

_{i}) denotes the functional form; an example of a constant as a functional form is as follows:

x

_{t}= μ + ε_{t}Here, the constant value **μ** in the preceding equation acts as a drift parameter, as shown in the following figure:

Figure 3.1: Example of time series with drift parameter ...