Impact of Uncertainty in the Input Variables and Model Parameters on Predictions of a Long Short Term Memory (LSTM) Based Sales Forecasting Model

Abstract

A Long Short Term Memory (LSTM) based sales model has been developed to forecast the global sales of hotel business of Travel Boutique Online Holidays (TBO Holidays). The LSTM model is a multivariate model; input to the model includes several independent variables in addition to a dependent variable, viz., sales from the previous step. One of the input variables, “number of active bookers per day”, is estimated for the same day as sales. This need for estimation requires the development of another LSTM model to predict the number of active bookers per day. The number of active bookers is variable, so the predicted is used as an input to the sales forecasting model. The use of a predicted variable as an input variable to another model increases the chance of uncertainty entering the system. This paper discusses the quantum of variability observed in sales predictions for various uncertainties or noise due to the estimation of the number of active bookers. For the purposes of this study, different noise distributions such as normalized, uniform, and logistic distributions are used, among others. Analyses of predictions demonstrate that the addition of uncertainty to the number of active bookers via dropouts as well as to the lagged sales variables leads to model predictions that are close to the observations. The least squared error between observations and predictions is higher for uncertainties modeled using other distributions (without dropouts) with the worst predictions being for Gumbel noise distribution. Gaussian noise added directly to the weights matrix yields the best results (minimum prediction errors). One possibility of this uncertainty could be that the global minimum of the least squared objective function with respect to the model weight matrix is not reached, and therefore, model parameters are not optimal. The two LSTM models used in series are also used to study the impact of corona virus on global sales. By introducing a new variable called the corona virus impact variable, the LSTM models can predict corona-affected sales within five percent (5%) of the actuals. The research discussed in the paper finds LSTM models to be effective tools that can be used in the travel industry as they are able to successfully model the trends in sales. These tools can be reliably used to simulate various hypothetical scenarios also.

Keywords

• sales forecasting
• uncertainty analysis
• LSTM
• corona
• RNN
• neural network