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    Comparison of ARIMA, holt-winters, and LSTM forecasting models using kullback information measure
    (Maltepe Üniversitesi, 2019) Batra, Luckshay; Taneje, H.C.
    Various forecasting models such as the Autoregressive Integrated Moving Average (ARIMA) and HoltWinters that aren’t just widely accepted but also exceptionally good predictors of the time series. Recently, Artificial Neural Networks (ANNs) have been widely studied and utilized in the prediction of time series, and their flexible non-linear modeling capacity is the key advantage of deep learning. Long Short Term Memory (LSTM), in particular has been used in the prediction of time-series in financial sector. The objective of this study is to examine and compare different forecasting models in terms of performance on a time series that is considered difficult to predict. This article’s core contribution is to contrast the performance of ARIMA, Holt-Winters and a recurrent neural network LSTM with reference to minimization obtained in the Kullback measure of relative information in prediction. The results shows that LSTM network performs well on monthly data from the NIFTY 50 stock index, a real-life time series forecast in comparison with traditional models like ARIMA and Holt-winters.
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    Entropy as a measure of implied volatility in options market
    (Maltepe Üniversitesi, 2019) Taneja, H.C.; Batra, Luckshay
    Volatility estimation is critical for several reasons for stakeholders in stock markets and the concept of Shannon entropy originated in the communication system has been extensively applied in finance. There are several well-known traditional techniques in the literature to measure stock market volatility, in this communication, we focus on comparing two popular techniques, the standard deviation and implied volatility with a methodology based on information entropy. In our study, the empirical analysis is conducted so as to find some relationship between the three different approaches: implied volatility, historical volatility and entropy and all three give a similar kind of sense, maybe not of the same scale but all of them follow the same trend. This paper focuses on the behavior of Indian markets between 2001-2017 for comparative analysis. We have also tried to model implied volatility as a linear combination of historical volatility and entropy and found that the model was heavily dependent on the values of entropy. Calculating implied volatility evolves numerical complexities and replacing it with entropy simplifies the problem. We have used Shannon entropy; using generalised entropies (i.e., entropy with additional parameters) may give better approximations.