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Practical Time Series Analysis by Dr. PKS Prakash, Dr. Avishek Pal

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Introduction to time series smoothing

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:

xt = f(xi) + εt for i=1,2,3, ... t-1

Here, xt is observations and εt is white noise. The f(xi) denotes the functional form; an example of a constant as a functional form is as follows:

xt = μ + εt

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 ...

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