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# Practical Time Series Analysis: Prediction with Statistics and Machine Learning

## Book Preface

This book is intended for both veteran and new data analysts seeking an overview of modern time series analysis. Time series data and the analysis of such data are rapidly growing in new importance due to a number of massive producers of such data, such as the internet of things, the digitalization of health care, and the rise of smart cities. In the next decade (and beyond), the quantity and quality of time series data will grow rapidly.

As continuous monitoring and data collection grows increasingly common, the need for competent time series analysis with both traditional statistical methods and innovative machine learning techniques will continue to grow. This book will provide you with a background in a broad range of time series techniques useful for analyzing and predicting human behavior, scientific phenomena, and industrial pipelines.

Let’s start from scratch. What is time series analysis? Time series analysis is the endeavor of extracting meaningful summary and statistical information from points arranged in chronological order. This is done to diagnose past behavior as well as to predict future behavior. In this book we will use a variety of approaches, ranging from hundred-year-old statistical models to newly developed neural network architectures.

None of these techniques we will study has developed in a vacuum or out of purely theoretical interest. Innovations in time series analysis result from new ways of collecting, recording, and visualizing data. Those connections is what we will think about in this chapter.

# Time series in diverse applications

Time series analysis includes questions of causality: how did the past influence the future? Often such problems, and their solutions, go unlabeled as time series problems. That’s generally a good thing, as it means thinkers from a variety of disciplines have contributed novel ways of thinking about time series data sets.

Here we briefly survey a few historical examples of time series data and analysis popping up in a variety of contexts.

## Medicine as a Time Series Problem

### Population health

Medicine got a surprisingly slow start to thinking about the mathematics of predicting the future, despite the fact that prognoses are an essential part of medical practice. This was the case for many reasons. For starters, statistics and a probabilistic way of thinking about the world are recent phenomena. Also, most doctors practiced in isolation, without easy professional communications and without formal record-keeping infrastructure for patient or population health measures. Even if they had been statistical thinkers, there wasn’t much data available for them.

For this reason, it is not too surprising that one of the early mathematical innovations related to population health came not from a physician but from someone who might have been more accustomed to record keeping and large numbers, namely a merchant. The innovator was John Graunt, and he was a 17th century London haberdasher.

Graunt undertook a study of the death records that had been kept in London parishes since the early 1500s. In doing so, Graunt originated the discipline of demography. In 1662, he published Natural and Political Observations . . . Made upon the Bills of Mortality

In this book, he presented the first life tables. This may be more familiar to you as what are commonly referred to as actuarial tables. These give the probability that a person of a given age will die before her next birthday, and Graunt was the first person known to have formulated and published these life tables, in the process becoming one of the first people to apply statistics to a question related to medicine and human health. His life tables looked something like the sample below, which is taken from some course notes1 in a statistics course.