A multiscale theory for the dynamical evolution of sentiment in novels

Recent work in literary sentiment analysis has suggested that shifts in emotional valence may serve as a reliable proxy for plot movement in novels. The raw sentiment time series of a novel can now be extracted using a variety of different methods, and after extraction, filtering is commonly used to smooth the irregular sentiment time series. Using an adaptive filter, which is among the most effective in determining trends of a signal, reducing noise, and performing fractal and multifractal analysis, we show that the energy of the smoothed sentiment signals decays with the smoothing parameter as a power-law, characterized by a Hurst parameter H of 1/2 <; H <; 1, which signifies long-range correlations. We further show that a smoothed sentiment arc corresponds to the sentiment of fast playing mode or sentiment retained in one's memory, and that for a novel to be both captivating and rich, H has to be larger than 1/2 but cannot be too close to 1.