Friday, January 25, 2008

Time Series Analysis

Time series is a sequence of measurement collected on time. The analysis of experimental data that have been observed at different points in time leads to new and unique problems in statistical modeling and inference. The obvious correlation introduced by the sampling of adjacent time points can severely restrict the applicability of the many conventional statistical methods that traditionally depend on the assumption that the adjacent observations are independent and identically distributed. The systematic approach by which one goes about answering the mathematical and statistical questions posed by these time correlations is commonly referred to as Time Series Analysis.

The utility of time series analysis can be well documented by producing a partial listing of the diverse fields in which important time series problems may arise. For example, many familiar time series arise in the field of economics, where we are continually exposed to daily stock market quotations or to monthly unemployment figures. Social scientists and demographers are interested in following population series such as birthrates or school enrollments. An epidemiologist might be interested in the number of influenza cases observed over time. In medicine, diastolic and systolic blood pressure measurements traced over time for various individuals could be useful for evaluating drugs used in treating hypertension. Encephalographic recordings of brain wave patterns might be used to classify individuals into disease categories or even into intelligence groupings.

The first step in any time series investigation must always be a careful scrutiny of the recorded data plotted over time. This suggests the method of analysis as well as the summary statistics that will be of use in summarizing the information in the data.

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