# Time Series Methods and Business Intelligent Tools for Budget Planning--Case Study
## 2 Methods of Quantitative and Value Strategic Planning of Budget
### Forecasting Methods
#### 2.1.1 Exponential Smoothing  
The Holt-Winters method, which is often referred to as exponential smoothing for time series with a trend and seasonality, is a widely used and simple forecasting technique. Its main objective is to predict future values based on historical data, considering two main model variations: additive and multiplicative [21]. This method is based on the iterative analysis of two basic components of a time series: the trend and the seasonality of the series. * Trend refers to long-term changes in the level of a time series. In the Holt-Winters model, the evolution of the trend is modeled by means of progressive smoothing, which is the estimation of the changes in the level over time. In the case of a linear trend, the additive approach is used. The multiplicative model is used when the trend shows an exponential rise or fall. * Seasonality refers to cyclical patterns that occur in the data at regular intervals, such as monthly or quarterly. The Holt-Winters model takes this into account by using exponential smoothing for seasonal periods. When seasonal fluctuations are constant over time, an additive model is used. When the amplitude of the seasonal fluctuations changes proportionally to the level of the time series, a multiplicative model is preferred. In paper [22], the authors analyzed the prediction of electricity consumption in office buildings using different forecasting methods such as the Holt-Winters model, ARIMA/SARIMA and neural networks. The purpose of this study was to compare the effectiveness of classical statistical methods with modern approaches based on artificial intelligence. The results show that relatively simple methods, such as exponential smoothing or ARIMA/SARIMA, significantly outperform more advanced neural network-based methods. This finding suggests that when analyzing data of a specific nature, simple statistical models may be more effective and practical than complex AI. The obtained results can be used to determine the expected costs of electricity consumption in the budget of enterprises with a large number of office properties of different types. The paper [23] presents the development of an innovative hybrid model that is dedicated to the very short-term forecasting of the electricity consumption of Chinese households. The model integrates the HW technique, which is used to analyze the linear part, with the ELM net, which is used to analyze the nonlinear part. The input data were pre-processed using a moving average filter, and the prediction was performed in two stages: the linear components were analyzed using HW, while the nonlinear components were analyzed using ELM. The results of the investigation showed that the hybrid HW and ELM model outperforms other methods in terms of both accuracy and efficiency, especially for limited training datasets, and confirms its potential as an effective tool to predict electricity consumption. Thus, it can be useful in estimating household budgets that take into account the necessity of electricity consumption of household appliances. Paper [24] uses data from 2012 to 2022 to predict rainfall in the Abiansemal area, where agriculture is highly dependent on weather. The analysis included a comparison between additive and multiplicative models. The results showed the higher efficiency of the multiplicative model in the context of rainfall forecasting. However, both model configurations had high error values. This indicates a limited prediction accuracy, especially under variable weather conditions. Despite these limitations, the authors consider the multiplicative model to be a more adequate tool for the prediction of future rainfall trends while at the same time suggesting the need for further improvement of the methodology. The article [25] uses Holt-Winters exponential smoothing to forecast the demand for an antibiotic used to treat COVID-19. It considers the impact of the pandemic on the increase in demand in March 2020 and analyzes consumption of the drug from 2017 to 2020.