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7 - Modeling Trends

Published online by Cambridge University Press:  05 June 2012

Edward W. Frees
Affiliation:
University of Wisconsin, Madison
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Summary

Chapter Preview. This chapter begins our study of time series data by introducing techniques to account for major patterns, or trends, in data that evolve over time. The focus is on how regression techniques developed in earlier chapters can be used to model trends. Further, new techniques, such differencing data, allow us to naturally introduce a random walk, an important model of efficient financial markets.

Introduction

Time Series and Stochastic Processes

Business firms are not defined by physical structures such as the solid stone bank building that symbolizes financial security. Nor are businesses defined by spacealien invader toys that they manufacture for children. Businesses comprise several complex, interrelated processes. A process is a series of actions or operations that lead to a particular end.

Processes not only are the building blocks of businesses but also provide the foundations for our everyday lives. We may go to work or school every day, practice martial arts, or study statistics. These are regular sequences of activities that define us. In this text, our interest is in modeling stochastic processes, defined as ordered collections of random variables that quantify a process of interest.

Some processes evolve over time, such as daily trips to work or school, or the quarterly earnings of a firm. We use the term longitudinal data for measurements of a process that evolves over time.

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Publisher: Cambridge University Press
Print publication year: 2009

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  • Modeling Trends
  • Edward W. Frees, University of Wisconsin, Madison
  • Book: Regression Modeling with Actuarial and Financial Applications
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511814372.008
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  • Modeling Trends
  • Edward W. Frees, University of Wisconsin, Madison
  • Book: Regression Modeling with Actuarial and Financial Applications
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511814372.008
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Modeling Trends
  • Edward W. Frees, University of Wisconsin, Madison
  • Book: Regression Modeling with Actuarial and Financial Applications
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511814372.008
Available formats
×