This chapter discusses statistical procedures that can be used to explore historical or diachronic data. First, specific features of diachronic studies are outlined and techniques that provide effective visualizations of diachronic change are introduced. Second, the chapter focuses on the statistical comparison of two time periods using a procedure called bootstrapping. Next, the diachronic application of the cluster analysis (introduced in chapter 5) is discussed. A specific type of the cluster technique (neighbouring cluster analysis), which takes into account the diachronic ordering of data, is introduced. Finally, the chapter presents a method for statistical identification of peaks and troughs in diachronic data and an extension called Meaning Fluctuation Analysis (MFA). The Peaks and Troughs technique applies a non-linear regression model to the data to identify extreme points in time (outliers), where a dramatic change in discourse occurred. MFA, traces the development of collocates of a word of interest over time; using the peaks and troughs technique it identifies points where a major change in the use of a word took place.