## 1 Introduction
Out of all machine learning and statistical methods that can be used for financial time series forecasting highlighted by the authors in [2; 3], the choice of using ARIMA depends on the fact that it is well suited for the data types we have collected and allows working with exogenous variables, which consist of further data we can feed to the model. A lot of the data we have extracted related to the Amazon products' prices over a wide interval time exhibit consistent pattern over time with a minimum amount of outliers. Basically, the first thing we have analysed has been the stationarity of the data and we have noticed that most of the prices of a given product remain at a fairly constant level over time. This happens for a lot of products. There are also cases of non stationarity time series in our data and this is where we had to perform some preprocessing steps. Our method can be applied to any kind of product as long as we provide the price and the related date. ARIMA also works well in presence of several missing daily tuples (price, date) among its inputs and that is also one more reason we chose it (as we had missing data for certain products in certain interval times). Of course, the higher the number of entries per each product, the more precise the forecast step will be. Similar studies using ARIMA for price forecasting have been done in [4; 5; 6; 7; 8; 9; 10; 11]. Other works focused on the forecasting of e-commerce prices have been proposed in [12] where authors proposed LSTM neural networks to obtain better prediction performances in daily phone prices in one particular marketplace, amazon.fr. In one further work [13], researchers adopted a Stochastic Differential Equations (SDE) approach to describe a plausible course of the online auction price. The proposed model has several practical implications. First, an SDE model enables one to individually model an online auction price curve in which the price dynamics can be determined by its own parameters. Second, this approach facilitates the price prediction of an online auction, which can help improving auction strategies. Besides, several articles have used Google Trends to improve the forecasts of different phenomena [14; 15]. We have trained the ARIMA model with 90% of the data we collected and predicted the prices of the remaining data. We had to fine-estimate the ARIMA parameters \((p,q,d)\) and performed the forecast with a low Mean Absolute Percentage Error Score. ARIMA depends on different inputs such as ACF (AutoCorrelation Function) and PACF (Partial AutoCorrelation Function) and, on the basis of the time series theory [16], it works well if the process is stationary. For this reason, when it is non-stationary we introduce a preprocessing step. It should be observed that several studies in literature proved that many machine learning models are able to get the same performance of ARIMA (i.e., in terms of forecasting performance) when they involved a large number of time series [17; 18]. We have chosen to exploit ARIMA models instead of other machine learning ones for the following reasons: (i) differently from many machine learning approaches, they provide good forecasting performance when a small/big number of data (i.e., time series) is employed; (ii) in terms of short-run forecasting those models are relatively more robust and efficient than more complex ones [19]; (iii) the strictly statistical method used by ARIMA only requires the prior data of a time series in order to generalize the forecast, then it is able to increase its forecasting accuracy by involving a minimum number of parameters [20]. More in detail, the scientific contribution of this paper is the following:  
* First, this is the first work analyzing the correlation of Google Trends and products reviews information with Amazon products' prices, using huge amount of real world data.