IFAC PapersOnLine 52-25 (2019) 208–213 ScienceDirect Available online at www.sciencedirect.com 2405-8963 © 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Peer review under responsibility of International Federation of Automatic Control. 10.1016/j.ifacol.2019.12.474 © 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. 1. INTRODUCTION The idea that nature repeats itself in creating new shapes and structures on larger scales has been expanding to a growing number of fields. In economics and finance, it led to the early insight about the Elliott Wave in the Dow- Jones Index in the 1930s, and to Mandelbrot’s discovery in the 1960s of the self-similar distributions of cotton prices over days and decades. In our time it helped formulate some of the natural laws that biological life, business organizations, and modern cities have in common (West, 2017). While the neural network community acknowledges that, “The social network is a fractal extension of our brain networks” (Apolloni, 2013), little is known about how that scaling up actually happens. A recent hypothesis about “social / socioeconomic fractality” posits that cognitive- emotional interactions active on the time scale of hundreds of milliseconds to seconds in the brain, repeat themselves on the scales of days, months, and years in the life of social communities and entire societies (Mengov, 2015a, 2016). Ideas for its testing were proposed by us in a previous TECIS publication (Mengov, 2015b). It is likely that individual primitive emotion projects onto cooperative behaviour and may be observed in a number of domains, including financial markets. There, a kind of collective mind – or super-agent – is believed to exist (Sornette, 2003) and constantly oscillate between opti- mism and pessimism creating the market sentiment of “bulls” and “bears”. Behavioural finance is the research field studying those phenomena for nearly four decades now. In our time, it employs big data analysis to assess emotional content in social media comments and blogs on financial issues, and has some success in stock price forecasting (Chen, 2017; Tu et al., 2018; Nuzula, 2019). Yet, its level of modelling and theorizing remains phe- nomenological with no serious attempts at mechanistic explanation. The present paper is an effort to analyze financial data with a theory, originating in mathematical neuroscience. It makes sense to start the investigation from the primi- tive emotions because they are well understood by psy- chologists who have developed elaborate mathematical models about them. In particular, in our study we use the Grossberg–Schmajuk dipole, a neural circuit described by a system of ordinary nonlinear differential equations that capture opponent emotions, emotional memory, and reflex conditioning (Grossberg and Schmajuk, 1987). An important feature of the model is that it shows how a biological organism’s mood oscillates in real time. We postulate that the individual emotions of fear and hope project onto collective emotion of the market mood, which, in turn is expressed in the price fluctuations in a financial market. More specifically, we take the highest and lowest traded prices of a stock in a day and relate them to the peaks of positive and negative emotions generated by the Grossberg–Schmajuk dipole. We calibrate a neural circuit with sample financial data and let it forecast future financial data. Then we compare the model’s achievements with those of the standard econometric tools. Should the Keywords: Computational neuroscience, gated dipole, financial forecasting, econometric modelling Abstract: Collective behaviour sums up the emotional and rational actions of many individuals. In the financial markets, the economic agents’ aggregate activity leads to price fluctuations driven by hope and fear, optimism and pessimism. While the market mood mechanism is unknown, a number of hypotheses exist including the suggestion that the mind’s complex cognitive processes scale up to the domain of socioeconomic activity. Here we show how a neurocomputational model for primitive individual emotion and memory can predict the highest and lowest daily prices of NASDAQ-traded companies. The model, known as the Grossberg–Schmajuk recurrent gated dipole, beats some state-of-the-art econometric tools for emotion–influenced financial data. This finding comprises an indirect evidence for the existence of a fractal projection from individual to collective cognition. * Department of Industiral Organization and Management, Sofia University St. Kliment Ohridski, Sofia, Bulgaria (e-mail: g.mengov@feb.uni-sofia.bg). ** Technology and Innovation Group, SAP (e-mail: iliyan.nenov@sap.com). *** Department of Psychology, Sofia University St. Kliment Ohridski, Sofia, Bulgaria, (e-mail: zinovieva@phls.uni-sofia.bg) George Mengov * Iliyan Nenov ** Irina Zinovieva *** A Model for Collective Emotion Forecasts Financial Data