Predicting fluctuations in Tehran Stock Exchange indices through a Harmonic Quantum Oscillator model

Fluctuation Forecasting has always been one of the most important issues in financial markets and has attracted the attention of many academic researchers and activists and investors in financial and Capital markets in the past few decades. In the present study, the fluctuation of Total index and Dividend and Price index of the Tehran Stock Exchange were predicted using a harmonic quantum oscillator model. Monthly data of logarithmic return of total index and Dividend and Price index were collected and calculated in the period of April 2012 to March 2021 as a time series. In terms of purpose, this research is applied and in terms of its nature, it is part of descriptive-analytical studies. In order to implement the harmonic quantum oscillator model, the probability density function and the Fokker -Plank function were used and the prediction results were also compared with the random geometric Brownian motion model. In total, six hypotheses were examined based on the ratio of the Mean Absolute Percentage Error. The results of the hypotheses showed that in the total index of the stock exchange, the Harmonic Quantum Oscillator model for short-term (24 months), medium-term (48 to 72 months) and long-term (96 to 120 months) time periods compared to the geometric Brownian motion model. It has higher accuracy in predicting fluctuations. However, in the Dividend and Price index, this efficiency was observed only during short-term periods of 24 months and medium-term periods of 48 to 72 months, and for the long-term period of 96 to 120 months, the Harmonic Quantum Oscillator model cannot be considered a suitable approach for predicting fluctuations.