Chapter 10: On the Analysis of Time Series with Nonstationary Increments
Joseph L. McCauley, Kevin E. Bassler and Gemunu H. Gunaratne* 10.1 Introduction The finance and physics literature contains many papers claiming scaling via Hurst exponents on the one hand, and fat tail scaling on the other. We can identify as the ‘central dogma of econophysics’ the widespread expectations of Hurst exponent scaling and fat-tailed distributions. Some dynamical models that have been postulated or (much better) inferred from empirical data are Markovian, others are not. That is, there are very strongly contradictory claims in the literature about the underlying market dynamics, although various ‘stylized facts’ have been widely accepted. The inference of Markov dynamics (diffusive dynamics with no memory) from empirical data would seem to be a reasonable approximation to reality because normal financial markets are very hard to beat, while a Markovian market would be imposssible to beat. That is, we expect finance markets to be Markovian to lowest order. But what exactly do we mean by ‘lowest order’, and why is the Markov approximation not a ‘stylized fact’? We’ve recently constructed a new theoretical analysis (McCauley, Bassler and Gunaratne, 2008) based on our recent foreign exchange (FX) data analysis (Bassler, McCauley and Gunaratne, 2008) that defines below precisely what ‘lowest order’ means. We will explain that the ‘central dogma of econophysics’, Hurst exponent scaling and fat tails, fails to be realized in FX markets. We will exhibit explicitly why most existing data analyses are wrong: most data analyses make a single wrong assumption that generates both a Hurst exponent...
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