Artificial Neural Network with Histogram Data Time Series Forecasting: A Least Squares Approach Based on Wasserstein Distance

This paper aims to predict the histogram time series, and we use the high-frequency data with 5-min to construct the Histogram data for each day. In this paper, we apply the Artificial Neural Network (ANN) to Autoregressive (AR) structure and introduce the AR—ANN model to forecast this histogram time series. However, the conventional approach to estimate this histogram time series may not give reliable forecasting. Thus, we deal with this type of data considering the approach of Irpino-Verde [8]. The Least squares-based Wasserstein distance is employed to measure the loss function of AR—ANN model for histogram-valued data. We apply our model to forecast the US. Stock returns and examine the performance of the model with other competing models, namely AR—ANN based Billard-Diday [3] and AR models, using the root of the mean square error. The empirical results demonstrate that the AR—ANN model based Irpino-Verde approach performs better than other models.