The Warmest Day of Any Week Tends to Occur on the First or Last Day of That Week

Abstract

The author analyzed daily maximum temperature data collected at the San Francisco International Airport from 1949 to 1994. For each week, he computed the day of the week on which the weekly maximum temperature falls. He found that the warmest day of the week is more likely to occur on the first (or last) day of the week than a day in the middle of the week. This conclusion does not depend on which day is designated as the first day of the week. The same phenomenon is observed when the data is detrended. The author argues that this surprising phenomenon results from positive temporal correlation in the daily maximum temperature data. He shows that the same phenomenon occurs for two stochastic time series models: a positively correlated Gaussian AR(1) process and a random walk. For the AR(1) process, results are obtained by Monte Carlo simulation experiments. For the random walk, an analytical formula (from the literature) is given.