Price series in speculative markets show a common set of statistical properties, termed ‘stylised facts’. While some facts support simple efficient markets composed of homogenous rational agents (e.g., the absence of autocorrelation in price increments), others do not (e.g., heavy-tailed distributions of price changes and volatility clustering) (Campbell et al., 1997; Fama, 1970; Mandelbrot, 1966; Mandelbrot, 1963; Cont, 2001). Collectively, these facts have been explained by either more complex markets or markets of heterogeneous agents (Cont 2007; Giardina & Bouchaud, 2003; Hommes, 2006; Barberis & Thaler, 2005), with asset-market experiments validating the latter approach (Hommes 2011; Kirchler & Huber, 2009). However, it is unknown whether markets are necessary to produce these features. Here we show that within-individual variability alone is sufficient to produce many of the stylised facts. In a series of experiments, we increasingly simplified a price prediction task by first removing external information, then removing any interaction between participants. Finally, we removed any resemblance to an asset market by asking participants to simply reproduce temporal intervals. All three experiments produced the main stylised facts. The robustness of the results across tasks suggests a common cognitive-level mechanism underlies these patterns, and we identify a candidate that is a general-purpose approximation to rational behavior. We recommend a stronger focus on individual psychology in macroeconomic theory, and particularly within-individual variability. Combining these insights with existing economic mechanisms could help explain price changes in speculative markets.