This paper deals with the theoretical development of some aspects of the trend removal problem. The objective is to show the difference between the two most popular trend removal methods: first differences and linear least squares regression. On the one hand, we show that if first differences are used to eliminate a linear trend, the series of residuals would be stationary but would not be white noises as they contain a first lag autocorrelation of -0.50. Furthermore, the spectral density function (SDF) of these residuals relative to that of a white noise series would be exaggerated at the high frequency portion and attenuated at the low frequency portion. On the other hand, we show that the regression residuals from the linear detrending of a random walk series would contain large positive autocorrelations in the first few lags. Relative to that of white noises, the SDF of the regression residuals would be exaggerated at the low frequency portion and attenuated at the high frequency portion.

Using transactions data, the behavior of returns and characteristics of trades at the micro level is examined. A minute‐by‐minute market return series is formed and tested for normality and autocorrelation. Evidence of differences in return distributions is found among overnight trades, trades during the first 30 minutes following the market opening, trades at the close, and trades during the remainder of the day. The latter distribution is found to be normal. Unusually high returns and standard deviations of returns are found at the beginning and the end of the trading day. When the beginning‐and end‐of‐the‐day effects are omitted, autocorrelation in the market return series is reduced substantially. A number of patterns in trading are reported.

Using transactions data, the behavior of returns and characteristics of trades at the micro level is examined. A minute-by-minute market return series is formed and tested for normality and autocorrelation. Evidence of differences in return distributions is found among overnight trades, trades during the first 30 minutes following the market opening, trades at the close, and trades during the remainder of the day. The latter distribution is found to be normal. Unusually high returns and standard deviations of returns are found at the beginning and the end of the trading day. When the beginning-and end-of-the-day effects are omitted, autocorrelation in the market return series is reduced substantially. A number of patterns in trading are reported.