Autocorrelation

Sources

What is the best predictor of a student's 11th-grade academic performance? His or her 10th-grade grade point average. What is the best predictor of this year's crude divorce rate? Usually last year's divorce rate. The old slogan “Birds of a feather flock together” describes a college classroom in which students are about the same age, at the same academic stage, and often in the same disciplinary major. That slogan also describes many residential city blocks, where adult inhabitants have comparable incomes and perhaps even similar marital and parental status. When examining the spread of a disease, such as the H1N1 influenza, researchers often use epidemiological maps showing concentric circles around the initial outbreak locations.

All these are examples of correlated observations, that is, autocorrelation, in which two individuals from a classroom or neighborhood cluster, cases from a time series of measures, or proximity to a contagious event resemble each other more than two cases drawn from the total population of elements by means of a simple random sample. Correlated observations occur for several reasons:

• Repeated, comparable measures are taken on the same individuals over time, such as many pretest and posttest experimental measures or panel surveys, which reinterview the same individual. Because people remember their prior responses or behaviors, because many behaviors are habitual, and because many traits or talents stay relatively constant over time, these repeated measures become correlated for the same person.
• Time-series measures also apply to larger units, such as birth, divorce, or labor force participation rates in countries or achievement grades in a county school system. Observations on the same variable are repeated on the same unit at some periodic interval (e.g., annual rate of felony crimes). The units transcend the individual, and the periodicity of measurement is usually regular. A lag describes a measure of the same variable on the same unit at an earlier time, frequently one period removed (often called t − 1).
• Spatial correlation occurs in cluster samples (e.g., classrooms or neighborhoods): Physically adjacent elements have a higher chance of entering the sample than do other elements. These adjacent elements are typically more similar to already sampled cases than are elements from a simple random sample of the same size.
• A variation of spatial correlation occurs with contagion effects, such as crime incidence (burglars ignore city limits in plundering wealthy neighborhoods) or an outbreak of disease.
• Multiple (repeated) measures administered to the same individual at approximately the same time (e.g., a lengthy survey questionnaire with many Likert-type items in agree-disagree format).

Autocorrelation Terms

The terms positive or negative autocorrelation often apply to time-series data. Societal inertia can inflate the correlation of observed measures across time. The social forces creating trends such as falling marriage rates or rising gross domestic product often carry over from one period into the next. When trends continue over time (e.g., a student's grades), positive predictions can be made from one period to the next, hence the term positive autocorrelation.

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