Time Series Models

By now we have a strong foundational understanding of various concepts essential for time series analysis. The rest of the course will focus on the following:

  1. A theoretical understanding of the important time series models (White Noise, AutoRegressive (AR), Moving Average (MA), ARMA.
  2. The ARIMA model and how various time series processes can be explained by ARIMA.
  3. Simulating and estimating these time series models in R.
  4. Box-Jenkins (B-J) methodology for time series forecasting.
  5. A comprehensive case study for time series analysis in R (With code and plots).

Time Series Models

The objective of the following text is to provide a theoretical understanding of the time series models. It can be a bit complex to grasp, however, as we move to practical implementation in the next lessons, things will start to make more sense.

White Noise

White Noise is the simplest example of a stationary process and is also the foundation of the other models we will discuss. A white noise process is a random process of random variables that are uncorrelated, have mean zero, and a finite variance. In other words, a series is called white noise if it is purely random in nature. Random noise is donated by εt

Plots of white noise series exhibit a very erratic, jumpy, unpredictable behavior. Since the εt are uncorrelated, previous values do not help us to forecast future values. White noise series themselves are quite uninteresting from a forecasting standpoint (they are not linearly forecastable), but they form the building blocks for more general models.

Simple Time Series Models

A simple trend model can be expressed as follows:

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