# Demand Forecasting Model for Airline Flights Based on Historical Passenger Flow Data
## 3 Results  
The modeling results present the distribution of demand for the airline's turnaround flight direction for each hour of the forecast period from 2025 to 2029. Consequently, two flight directions were considered, with demand determined independently: from A to B and in the reverse direction from B to A. The inputs to the model comprised historical passenger demand data for the A-B and B-A routes, together with historical time slot data, including dates and times of departure for all flights to and from each destination over the specified historical period. The data for developing the forecasting model were obtained from the airline's booking system and collected independently for each route under consideration from 2019 to the first half of 2024. Historical data on the final demand for a flight were equated to the number of tickets sold for each flight on the selected route, with demand calculated as the absolute number of passengers who completed the flight. In order to consider the influence of macroeconomic variables on the distribution of forecast demand, data on GRP, median per capita income, and population for departure and arrival points between 2014 and 2024 were collected. The data were sourced from publications by the Federal State Statistics Service, where each macroeconomic indicator was represented as an annual aggregate value over the 2014-2024 period.  
During the model development process, data preprocessing was carried out, including the stages of data collection and cleaning, unification of data formats, extraction of seasonal components at specific levels of seasonality, and determination of rules to account for the geographical specifics of flight routes. Initially, historical passenger demand data for routes A-B and B-A were combined into a single dataset, where each instance described the demand for a specific time slot, including the flight date and time. Outliers and anomalies in the historical data were then removed, specifically excluding records of flights with non-representative passenger demand values (significant deviations from the median demand  
Figure 2: Interrelationship between historical and forecast demand, taking into account the upper-level calibration.  
for a specific period). Missing values for time intervals were filled using linear interpolation or simulation based on the original time intervals. Economic indicators (regional GDP, income, and population) were normalized and synchronized with the historical demand data over time.  
When forming training and testing datasets, data from 2014 to 2023 were used for training the model, while data from 2024 were reserved for testing. To account for the specifics of the routes, data for A-B and B-A were processed independently to eliminate mutual influence and ensure accurate demand modeling for each direction.  
The results of the forecast demand estimation for the direction of flights from point A to point B from 2025 to 2029 are presented in the graph (see Figure 3).  
The results of the forecast demand estimate for the direction of flights from B to A from 2025 to 2029 are illustrated in the accompanying graph (see Figure 4).  
Figure 4: Distribution of passenger demand forecast for B–A direction.  
Figure 3: Distribution of passenger demand forecast for A–B direction.  
Table 2 shows the results of the RMSE, MAE, and MAPE forecast accuracy evaluation metrics for two directions: A-B and B-A. The RMSE and MAE metrics represent the mean model prediction error in units of the variable of interest, whereas the MAPE metric expresses the mean absolute error in percentage terms. The metrics were employed to assess the predictive capacity of the developed model by contrasting the actual demand metrics for 2023 with the model's predicted values for that year, based on training on historical data from 2019 to 2022.