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Practical Data Science Cookbook, Second Edition

You're reading from   Practical Data Science Cookbook, Second Edition Data pre-processing, analysis and visualization using R and Python

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Product type Paperback
Published in Jun 2017
Publisher Packt
ISBN-13 9781787129627
Length 434 pages
Edition 2nd Edition
Languages
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Authors (5):
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Anthony Ojeda Anthony Ojeda
Author Profile Icon Anthony Ojeda
Anthony Ojeda
Prabhanjan Narayanachar Tattar Prabhanjan Narayanachar Tattar
Author Profile Icon Prabhanjan Narayanachar Tattar
Prabhanjan Narayanachar Tattar
ABHIJIT DASGUPTA ABHIJIT DASGUPTA
Author Profile Icon ABHIJIT DASGUPTA
ABHIJIT DASGUPTA
Sean P Murphy Sean P Murphy
Author Profile Icon Sean P Murphy
Sean P Murphy
Bhushan Purushottam Joshi Bhushan Purushottam Joshi
Author Profile Icon Bhushan Purushottam Joshi
Bhushan Purushottam Joshi
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Table of Contents (12) Chapters Close

Preface 1. Preparing Your Data Science Environment FREE CHAPTER 2. Driving Visual Analysis with Automobile Data with R 3. Creating Application-Oriented Analyses Using Tax Data and Python 4. Modeling Stock Market Data 5. Visually Exploring Employment Data 6. Driving Visual Analyses with Automobile Data 7. Working with Social Graphs 8. Recommending Movies at Scale (Python) 9. Harvesting and Geolocating Twitter Data (Python) 10. Forecasting New Zealand Overseas Visitors 11. German Credit Data Analysis

ARIMA models


In the previous section, we saw the random walk and the role of ACF and PACF functions. The random walk may be seen as a series that depends on past observations as well as past errors. It is thus possible to visualize time series as functions of past observations, errors, or both. In general, given the time series Yt, 1 < t < T and the error process εt, 1 < t < T a linear process is defined as:

The terms 

are the coefficients of linear processes. Now, suppose that we are interested in a model where Y t depends on the past p observations:

The preceding model is well known as the autoregressive model of order p and it is denoted by AR(p). It is important to note here that the AR coefficients 

are not unrestricted and we simply note that their absolute values need to be less than 1 if the time series is assumed to be stationary. Next, we define the moving average model of order q, abbreviated as MA(q), as:

The parameters of the MA(q) model are

. It is indeed possible...

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