Book Image

Mathematica Data Analysis

By : Sergiy Suchok
Book Image

Mathematica Data Analysis

By: Sergiy Suchok

Overview of this book

There are many algorithms for data analysis and it’s not always possible to quickly choose the best one for each case. Implementation of the algorithms takes a lot of time. With the help of Mathematica, you can quickly get a result from the use of a particular method, because this system contains almost all the known algorithms for data analysis. If you are not a programmer but you need to analyze data, this book will show you the capabilities of Mathematica when just few strings of intelligible code help to solve huge tasks from statistical issues to pattern recognition. If you're a programmer, with the help of this book, you will learn how to use the library of algorithms implemented in Mathematica in your programs, as well as how to write algorithm testing procedure. With each chapter, you'll be more immersed in the special world of Mathematica. Along with intuitive queries for data processing, we will highlight the nuances and features of this system, allowing you to build effective analysis systems. With the help of this book, you will learn how to optimize the computations by combining your libraries with the Mathematica kernel.
Table of Contents (15 chapters)
Mathematica Data Analysis
Credits
About the Author
About the Reviewer
www.PacktPub.com
Preface
Index

Tests on stationarity, invertibility, and autocorrelation


When we deal with observed data, we are usually interested in a few things:

  • Are we observing a certain constant that simply has some random noisy data? In this case, we check for stationarity (the mean value of the sample does not depend on time).

  • Will the process characteristics repeat again after a certain time (invertible processes)?

  • Is the observation data dependent on the previous data? Is the seasonality possible (process autocorrelation)?

Let's consider each of these tests in practice.

Checking for stationarity

Here we'll check whether the process is weakly stationary. A random process, proc, is weakly stationary if its mean function is independent of time and its covariance function is independent of time translation. This check is done using the WeakStationarity function with the random process as its only parameter:

Invertibility check

A time series process is invertible if it can be written as an autoregressive time series, possibly...