Holt-Winters Model Research Articles

Time Series Forecasting Using Holt-Winters Exponential Smoothing: Application to Abaca Fiber Data

This study utilized the data on abaca fiber production and used Holt-Winters model to forecast the abaca fiber production since the studied variable is characterized by a fairly strong intensity of seasonality. For the construction of forecasts, additive and multiplicative models were used. The most accurate forecasts were selected on the basis of Mean Square Error, Root Mean Square Error, Mean Absolute Percentage Error, and Mean Absolute Scaled Error. It was found that the multiplicative method had a higher accuracy, hence it was utilized to forecast the production for the next three years. According to the findings, the anticipated fiber production for 2021-2023 showed an increase up to the second quarter, but then declining afterwards.

A combination model for evaluating deformation regional characteristics of arch dams using time series clustering and residual correction

Deformation monitoring models developed for the relationship between influencing factors and deformation are widely used in dam structural health monitoring. Because of the integrity of the arch dam, every part of the dam is interrelated and interactive. The regional characteristics of arch dam deformation have not been fully considered in the current arch dam monitoring model. The main purpose of this paper is to develop and verify a combination model for arch dam deformation considering regional characteristics. The arch dam measuring points are first clustered according to the similarity indicator of Bilateral Slope-based Distance and Dynamic Time Warping algorithm (BSD-DTW) between their measured deformation time series. Then the BSD-DTW clustering-based panel data model is established for each clustered zone to reflect the similarities and differences of deformation laws in different regions. Considering intra-regional differences in measuring point deformation, the Holt-Winters model is utilized to identify the potential features contained in panel data model's residual series. Finally, a combination model is constructed by superimposing the predicted value of the Holt-Winters model on the predicted value of the BSD-DTW clustering-based panel data model. The engineering example demonstrates that the BSD-DTW clustering method is a more reasonable method for arch dam regional zoning, and the combination model with residual correction can fully explore the deformation regional characteristics of each measuring point and has higher prediction accuracy, making it an effective analysis method for structural deformation of arch dams.

Holt-Winters Forecast on Seasonal Time Series Crop Insurance Data with Structural Outliers (2000-2018) Using Ms Excel

Time series data on the number of farmers enrolled in different crop insurance schemes such as NAIS, MNAIS and PMFBY in the state of Tamil Nadu, India was analysed for its seasonality, outliers and forecast. The data was found to be seasonal and exponentially increasing. Seasonality is innate as the crop insurance itself was registered separately for two seasons (Kharif and Rabi). Multiplicative Holt-Winters Model should be applied in order to do short range forecast for an exponentially increasing dataset. The model was run in Ms-Excel in order to understand the basics of times series forecasting. Minimum MSE value was the criteria used to find the better fitting smoothing values. The residual of the model was examined for the fit of the model. Residual mean value was close to zero. Residuals are tested for autocorrelation with Durbin-Watson test and Runs test. Histogram of residuals implies a normal distribution. Presence of outliers are detected using 3IQR method and the identified outliers are part of the structure of data and need not be removed. However, alternate models of Holt-Winters itself which are robust to work with outliers are reviewed and RHW model of Gelpers et al. [1] was suggested.

ПРОГНОЗИРОВАНИЕ И УПРАВЛЕНИЕ ЭЛЕКТРОПОТРЕБЛЕНИЕМ СООБЩЕСТВА МИКРОСЕТЕЙ С ПРИМЕНЕНИЕМ ИСКУССТВЕННОГО ИНТЕЛЛЕКТА

A characteristic feature of the modern electric power industry in recent decades is the sharp increase in electricity consumption. This can be explained by technological, social, economic, and other reasons. Therefore, the forecasting of electricity consumption is important for many processes, including the planned operation of genera¬ting equipment and managing and optimizing the operating modes of energy systems. It is also a significant aspect in the opera-tion of industrial enterprises, since breaches can result in fines. One of the urgent tasks in the electricity market today is the forecasting of electricity consumption for a certain period. The article presents a description of a microgrid model with a built-in block for predicting power consumption, as well as intelligent load control for several objects at the same time, including those with distributed generation. Decisions are made the previous day, in order to forme stra¬tegies or the generation profile and control of power receivers. This timing is dictated by the information available to the intelli-gent system. This information includes forecast of demand and electricity prices of the centralized energy system for every hour of the next day. The process of switching at peak time to additional sources of electricity, distribution over microgrids is also described. The forecast was implemented using the Holt-Winters model from the statsmodels library (Python 3). The model uses the ideas of exponential smoothing, but is more complex and can be applied to series containing trend and seasonality. The trained model predicts with 95.21% accuracy.

Malaria time series in the extra-Amazon region of Brazil: epidemiological scenario and a two-year prediction model

BackgroundIn Brazil, malaria is caused mainly by the Plasmodium vivax and Plasmodium falciparum species. Its transmission occurs in endemic and non-endemic areas. Malaria geography in Brazil has retracted and is now concentrated in the North region. The Brazilian Amazon region accounts for 99% of Brazil's cases. Brazil’s extra-Amazon region has a high frequency of imported cases and in 2019 presented a mortality rate 123 times higher than the Amazon region. Extra-Amazon cases present risks of reintroduction. This study aims to characterize the epidemiological scenario for malaria in the extra-Amazon region of Brazil from 2011 to 2020 with a two-year forecast.MethodsTime-series study with description of malaria cases and deaths registered in Brazilian extra-Amazon region from 2011 to 2020. Public data from the Notifiable Diseases Information System (Sinan) and the Mortality Information System (SIM) were used. Descriptive analysis, incidence, and notification rates were calculated. Flow charts analysed the flux between Places of Probable Infection (PI) and places of notification. The prediction model utilized a multiplicative Holt-winters model for trend and seasonality components.ResultsA total of 6849 cases were registered. Cases were predominantly white males with 9 to 11 years of education, mostly between 30 and 39 years old. Imported cases accounted for 78.9% of cases. Most frequent occupations for imported cases are related to travelling and tourism activities. Among autochthonous cases, there is a higher frequency of agriculture and domestic economic activities. In the period there were 118 deaths due to malaria, of which 34.7% were caused by P. falciparum infections and 48.3% were not specified. The most intense flows of imported cases are from Amazonas and Rondônia to São Paulo, Rio de Janeiro, and Paraná. The prediction estimates around 611 cases for each of the following two years.ConclusionThe time series allows a vast epidemiological visualization with a short-term prediction analysis that supports public health planning. Government actions need to be better directed in the extra-Amazon region so the objective of eliminating malaria in Brazil is achieved. Carrying out quality assessments for information systems and qualifying personnel is advisable. Malaria outside the Amazon region is mainly due to imported cases and delay in diagnosis is associated with a higher fatality rate. Better strategies to diagnose and treat suspected cases can lead to lower risk of deaths and local outbreaks that will be important for achieving malaria elimination in Brazil.

Stock Indices Forecasting: A Comparison of Holt-Winters Seasonality and Dynamic Harmonic Regression

This research aims to investigate the performance of various time-series forecasting approaches in predicting stock indices in Indonesia. This research compared the performance of additive Holt-Winters seasonality, multiplicative Holt-Winters seasonality, and Dynamic Harmonic regression. The stock indices being forecast are SRI-KEHATI, LQ45, and IHSG. Forecasting SRI-KEHATI index is the novelty in this research. SRI-KEHATI index contains all the companies that comply with the requirements regarding sustainability and concerns for the environmental impact of the companies operations. Decompositions of SRI-KEHATI, LQ45, and IHSG reveal that the trend and seasonality components are all existent within all indices. The results showed that Holt-Winters models are superior to Dynamic Harmonic Regression. Multiplicative Holt-Winters seasonality forecast best for SRI-KEHATI and LQ45. Additive Holt-Winters excelled at predicting IHSG. Although Dynamic Harmonic Regression had less accuracy, its performance was still very outstanding since its mean average percentage errors never exceeded 8%. The result signifies the excellence of the Holt-Winters model for predicting stock indices and also shows that Dynamic Harmonic Regression also scores high in accuracy. Both models validate the time variance notion of the stock market proposed by Boudreaux (1995). The practical benefit for Investors is that this research enables investors to forecast the stock indices in the future and make adjustments in their trading strategy thereof.

An Integrated Method for Locating Logistic Centers in a Rural Area

Transport has long been considered a concern for rural residents around the world. Rural express logistics, one of the transport topics, is associated with rural residents’ convenience as well as e-commerce development. As key nodes in the network, logistic centers need to be properly located to improve the delivery efficiency. This paper provides an integrated method for locating logistic centers which is of strong feasibility: on one hand, the proposed method seeks to maximize coverage of express service; on the other hand, considerations are given to operational profitability of the centers, ensuring overall viability for the plan. Specifically, the Holt–Winters model is used for demand prediction. Total predicted demand is then allocated to each town according to population, gross regional product, and some other indicators. A maximal covering model is applied to select logistic centers based on demand under different service radius and numbers of logistic centers. Revenue evaluation is then conducted for the selected logistic centers to evaluate their future operating conditions. The proposed method is applied in rural areas in Lhasa, China. Numerical analysis suggested that 12 of the selected 22 logistic centers could make a profit by 2025. Finally, policy recommendations are given for the development of rural logistic systems.

Has Covid-19 increased gender inequalities in professional advancement? Cross-country evidence on productivity differences between male and female software developers

Objective: This article analyzed gender differences in professional advancement following the outbreak of the Covid-19 pandemic based on data from open-source software developers in 37 countries.
 Background: Men and women may have been affected differently from the social distancing measures implemented to contain the Covid-19 pandemic. Given that men and women tend to work in different jobs and that they have been unequally involved in childcare duties, school and workplace closings may have impacted men’s and women’s professional lives unequally.
 Method: We analyzed original data from the world’s largest social coding community, GitHub. We first estimated a Holt-Winters forecast model to compare the predicted and the observed average weekly productivity of a random sample of male and female developers (N=177,480) during the first lockdown period in 2020. To explain the cross-country variation in the gendered effects of the Covid-19 pandemic on software developers’ productivity, we estimated two-way fixed effects models with different lockdown measures as predictors – school and workplace closures, in particular.
 Results: In most countries, both male and female developers were, on average, more productive than predicted, and productivity increased for both genders with increasing lockdown stringency. When examining the effects of the most relevant types of lockdown measures separately, we found that stay-at-home restrictions increased both men’s and women’s productivity and that workplace closures also increased the number of weekly contributions on average – but for women, only when schools were open.
 Conclusion: Having found gender differences in the effect of workplace closures contingent on school and daycare closures within a population that is relatively young and unlikely to have children (software developers), we conclude that the Covid-19 pandemic may indeed have contributed to increased gender inequalities in professional advancement.

Application of a Novel Optimized Fractional Grey Holt-Winters Model in Energy Forecasting

It is of great significance to be able to accurately predict the time series of energy data. In this paper, based on the seasonal and nonlinear characteristics of monthly and quarterly energy time series, a new optimized fractional grey Holt–Winters model (NOFGHW) is proposed to improve the identification of the model by integrating the processing methods of the two characteristics. The model consists of three parts. Firstly, a new fractional periodic accumulation operator is proposed, which preserves the periodic fluctuation of data after accumulation. Secondly, the new operator is introduced into the Holt–Winters model to describe the seasonality of the sequence. Finally, the LBFGS algorithm is used to optimize the parameters of the model, which can deal with nonlinear characteristics in the sequence. Furthermore, in order to verify the superiority of the model in energy prediction, the new model is applied to two cases with different seasonal, different cycle, and different energy types, namely monthly crude oil production and quarterly industrial electricity consumption. The experimental results show that the new model can be used to predict monthly and quarterly energy time series, which is better than the OGHW, SNGBM, SARIMA, LSSVR, and BPNN models. Based on this, the new model demonstrates reliability in energy prediction.

A novel time series data clustering approach for wind speed forecasting

Wind energy plays an essential role in the generation process of sustainable energy, with a bright future. Therefore, predicting wind speed fluctuations and their output power plays a crucial role in electric power generation. The integration of wind power is based on the accuracy of wind speed and power prediction model. In this paper, a clustering algorithm is proposed based on the length of the trendlet components. After spotting the different clusters, one suitable cluster is selected for modeling using the panda’s correlation method. This paper uses specific ARIMA, Naive Forecast, and Holt Winter models to forecast the selected cluster. Here three hybrid models, namely, C-ARIMA, C-NAIVE Forecast, and C-Holt-Winter, are proposed for wind speed forecasting. The performances of the proposed models are evaluated using the mean absolute error (MAE) and root mean squared error (RMSE). The experiment outcomes show that the cluster-based forecasting technique (Hybrid models) improved performance compared with un-clustered forecasting techniques.

Forecasting of Jakarta Islamic Index (JII) returns using Holt-Winters family models

Purpose: This research aims to forecast JII returns by employing various Holt-Winters models. The models used in this research are Holt-Winters seasonality, Holt-Winters damped method, and Holt-Winters with maximum likelihood approach. Holt-Winters model is capable of recognizing and modeling trends and seasonality. Therefore, it is suitable for forecasting purposes.Methodology: Three models are employed in this research. The first one is Holt-Winters seasonality, also known as triple exponential smoothing. This model analyzes the level, trend, and seasonality components in the return series. The second model is the Holt-Winters damped method that uses smoothing parameters to lower the overstatement effect that usually occurs within Holt-Winters seasonality. The third model is Holt-Winters with Maximum Likelihood. Holt-Winters seasonality estimates parameters by choosing the least-squares. At the same time, Holt-Winters with Maximum Likelihood uses maximum likelihood to fit in the series with certain distributions and generate forecasts by determining distributions with the most likelihood.Findings: The result showed that Holt-Winters seasonality forecasts better than the other methods. The model could recognize the seasonal pattern and trend of the JII returns. It has the lowest Root Mean Squared Error (RMSE) as the parameter for forecast accuracy. Holt-Winters damped method has accuracy right below Holt-Winters seasonality. It can also map the pattern and trend of the returns. Holt-Winters with Maximum likelihood predicts less accurately. However, it can recognize the random walk inclination of the return, although it failed to generate the seasonal pattern and trend of the JII returns.Originality: This research attempted to apply Holt-Winters models to predict JII returns. Most research concerning the Islamic stock index focuses on volatility and forecast based on the level of volatility. Therefore, this research can fill in the gaps in the literature in which forecast of Islamic stock index can be conducted by modeling the seasonality and trend using Holt-Winters models.Practical implications: Investors always try to find the best generating investment return. Investors concerned with the shariah rules will always find lawful investment tools such as Islamic stocks or the Islamic stock index. Returns of the Islamic stock index can be forecast by using the Holt-Winters model. Therefore, investors might know the pattern of returns generated by investing in Islamic stocks.

METHODS FOR FORECASTING DEMAND IN REPAIRING AN AIRLINE’S REPAIRABLE LINE REPLACEABLE UNIT PARTS

Scattered failure frequency, variable and complex influencing factors, and a low accuracy in predicting inventory demand are characteristics of line replaceable unit (LRU) parts. Some high-priced repairable LRU (HR-LRU) parts have a considerable impact on the cost of aircraft spare parts.This study presents procedures to identify the optimal model for forecasting the demand for HR-LRU parts. First, a traditional prediction model, seven single measurement models, and four combined models were selected and used to predict failure data. Subsequently, evaluating indexes were selected for assessment to obtain the optimal model. Finally, we compared the actual and predicted values to verify the conclusions drawn during the previous evaluation step. The results indicated that, among the single models, the negative binomial regression model and the Holt-Winters model were most suitable for HR-LRU parts. The SSE (sum of squares error) and MAE (mean absolute error) of the negative binomial regression were the lowest at 118.4114 and 1.97352 respectively, and the Holt-Winters model’s MAE was the lowest at 1. 13270. The IOWA operator prediction model and the error reciprocal variable weight combination method produced predictions closest to the actual values among the combined models. In addition to constructing a set of processes to prediction, we also discuss the fit of different methods, the reasons for the change in the guaranteed rate, and the reasons for the occurrence of special years. We also compare the similarities and differences between this article and other papers.

An Intelligent Forecasting Model for Disease Prediction Using Stack Ensembling Approach

This research work proposes a new stack-based generalization ensemble model to forecast the number of incidences of conjunctivitis disease. In addition to forecasting the occurrences of conjunctivitis incidences, the proposed model also improves performance by using the ensemble model. Weekly rate of acute Conjunctivitis per 1000 for Hong Kong is collected for the duration of the first week of January 2010 to the last week of December 2019. Pre-processing techniques such as imputation of missing values and logarithmic transformation are applied to pre-process the data sets. A stacked generalization ensemble model based on Auto-ARIMA (Autoregressive Integrated Moving Average), NNAR (Neural Network Autoregression), ETS (Exponential Smoothing), HW (Holt Winter) is proposed and applied on the dataset. Predictive analysis is conducted on the collected dataset of conjunctivitis disease, and further compared for different performance measures. The result shows that the RMSE (Root Mean Square Error), MAE (Mean Absolute Error), MAPE (Mean Absolute Percentage Error), ACF1 (Auto Correlation Function) of the proposed ensemble is decreased significantly. Considering the RMSE, for instance, error values are reduced by 39.23%, 9.13%, 20.42%, and 17.13% in comparison to Auto-ARIMA, NAR, ETS, and HW model respectively. This research concludes that the accuracy of the forecasting of diseases can be significantly increased by applying the proposed stack generalization ensemble model as it minimizes the prediction error and hence provides better prediction trends as compared to Auto-ARIMA, NAR, ETS, and HW model applied discretely

A COMPARATIVE ANALYSIS OF HOLTS-WINTERS’ AND NEURAL NETWORK PREDICTION MODELS ON ANNUAL BLOEMFONTEIN’S PRECIPITATION: RISK AVERSION

Neural Networks are a series of algorithms that mimic the human brain’s operation to recognise various relationships amongst vast amounts of data. These algorithms are better in predictive analytics than linear regression models due to the use of the hidden layers of neutrons. Failure to accurately predict precipitation pattern may lead major risks agriculture and other heavy water-using economic sectors. The present study’s aim was to aid water resources management sector with accurate annual predicted precipitation values for informed decision making. Prior to predictions, data quality controls were conducted, where outliers in the dataset were detected, removed and replaced by expectation maximum algorithm aided by SPSS computer software. Holt-Winter and Neural Network models were comparatively deployed in the predictions of the annual precipitation in the study area. Evident from these results is that NN provided more accurate results in prediction than HW where MSE and MAE for NN were relatively smaller. It can therefore be concluded that NN produces relatively more accurate results than linear models. The study therefore recommends that researchers in meteorology, agrometeorology, water resources management sectors deploy NN for forecasting climate variables for better informed decision making for protection and mitigation of climaterelated risks.

Benchmarking GHG Emissions Forecasting Models for Global Climate Policy

Climate change and pollution fighting have become prominent global concerns in the twenty-first century. In this context, accurate estimates for polluting emissions and their evolution are critical for robust policy-making processes and ultimately for solving stringent global climate challenges. As such, the primary objective of this study is to produce more accurate forecasts of greenhouse gas (GHG) emissions. This in turn contributes to the timely evaluation of the progress achieved towards meeting global climate goals set by international agendas and also acts as an early-warning system. We forecast the evolution of GHG emissions in 12 top polluting economies by using data for the 1970–2018 period and employing six econometric and machine-learning models (the exponential smoothing state-space model (ETS), the Holt–Winters model (HW), the TBATS model, the ARIMA model, the structural time series model (STS), and the neural network autoregression model (NNAR)), along with a naive model. A battery of robustness checks is performed. Results confirm a priori expectations and consistently indicate that the neural network autoregression model (NNAR) presents the best out-of-sample forecasting performance for GHG emissions at different forecasting horizons by reporting the lowest average RMSE (root mean square error) and MASE (mean absolute scaled error) within the array of predictive models. Predictions made by the NNAR model for the year 2030 indicate that total GHG emissions are projected to increase by 3.67% on average among the world’s 12 most polluting countries until 2030. Only four top polluters will record decreases in total GHG emissions values in the coming decades (i.e., Canada, the Russian Federation, the US, and China), although their emission levels will remain in the upper decile. Emission increases in a handful of developing economies will see significant growth rates (a 22.75% increase in GHG total emissions in Brazil, a 15.75% increase in Indonesia, and 7.45% in India) that are expected to offset the modest decreases in GHG emissions projected for the four countries. Our findings, therefore, suggest that the world’s top polluters cannot meet assumed pollution reduction targets in the form of NDCs under the Paris agreement. Results thus highlight the necessity for more impactful policies and measures to bring the set targets within reach.

A new hybrid method for predicting univariate and multivariate time series based on pattern forecasting

Time series forecasting has become indispensable for multiple applications and industrial processes. Currently, a large number of algorithms have been developed to forecast time series, all of which are suitable depending on the characteristics and patterns to be inferred in each case. In this work, a new algorithm is proposed to predict both univariate and multivariate time series based on a combination of clustering, classification and forecasting techniques. The main goal of the proposed algorithm is first to group windows of time series values with similar patterns by applying a clustering process. Then, a specific forecasting model for each pattern is built and training is only conducted with the time windows corresponding to that pattern. The new algorithm has been designed using a flexible framework that allows the model to be generated using any combination of approaches within multiple machine learning techniques. To evaluate the model, several experiments are carried out using different configurations of the clustering, classification and forecasting methods that the model consists of. The results are analyzed and compared to classical prediction models, such as autoregressive, integrated, moving average and Holt-Winters models, to very recent forecasting methods, including deep, long short-term memory neural networks, and to well-known methods in the literature, such as k nearest neighbors, classification and regression trees, as well as random forest.

Multiple forecasting approach: a prediction of CO2 emission from the paddy crop in India.

This paper compares four prediction methods, namely random forest regressor (RFR), SARIMAX, Holt-Winters (H-W), and the support vector regression (SVR), to forecast the total CO2 emission from the paddy crop in India. The major objective of this study is to compare these four models and suggest an effective model for the prediction of total CO2 emission. Data from 1961 to 2018 has been categorised into two parts: training and test data. The study forecasts total CO2 emission from paddy crops in India from 2019 to 2025. A comparison of mean absolute percentage error (MAPE) and the mean square error (MSE) highlights the differences in accuracy among the four models. The mean absolute percentage eror (MAPE) and the mean square error (MSE) for the four methods are RFR (MAPE: 5.67; MSE: 549,900.02), SARIMAX (MAPE: 1.67; MSE:70,422.35), H-W (MAPE:0.75; MSE:16,648.58), and SVR (MAPE: 0.91; MSE: 17,832.4). The values of MAPE and MSE with the Holt-Winters (H-W) and the support vector regression (SVR) are relatively low as compared to SARIMAX and RFR. Based on these results, it can be inferred that H-W and SVR were found suitable models to forecast the total CO2 emission from paddy crops. Holt-Winters model predicted 14,364.97 for the year 2025, and SVR predicted 13,696.67 for the year 2025. The decision-maker can use these predictions to build a suitable policy for the future. This approach can be contrasted with other forecasting methods, such as the neural network, and train the model to achieve better forecast accuracy.

Forecasting e-waste recovery scale driven by seasonal data characteristics: A decomposition-ensemble approach.

Forecasting the scale of e-waste recycling is the basis for the government to formulate the development plan of circular economy and relevant subsidy policies and enterprises to evaluate resource recovery and optimise production capacity. In this article, the CH-X12 /STL-X framework for e-waste recycling scale prediction is proposed based on the idea of 'decomposition-integration', considering that the seasonal data characteristics of quarterly e-waste recycling scale data may lead to large forecasting errors and inconsistent forecasting results of a traditional single model. First, the seasonal data characteristics of the time series of e-waste recovery scale are identified based on Canova-Hansen (CH) test, and then the time series suitable for seasonal decomposition is extracted with X12 or seasonal-trend decomposition procedure based on loess (STL) model for seasonal components. Then, the Holt-Winters model was used to predict the seasonal component, and the support vector regression (SVR) model was used to predict the other components. Finally, the linear sum of the prediction results of each component is used to obtain the final prediction result. The empirical results show that the proposed CH-X12/STL-X forecasting framework can better meet the modelling requirements for time-series forecasting driven by different seasonal data characteristics and has better and more stable forecasting performance than traditional single models (Holt-Winters model, seasonal autoregressive integrated moving average model and SVR model).

The Inflation Forecasting of Major Cities In East Kalimantan: A Comparison Of Holt-Winters And SARIMA Model

This research aims to compare the performance of Holt Winters and Seasonal Autoregressive Integrate Moving Average (SARIMA) models in predicting inflation in Balikpapan and Samarinda, two biggest cities in East Kalimantan province. The importance of East Kalimantan province cannot be overstated since it has been declared as the venue for the capital of Indonesia. Hence, inflation prediction of the two cities will give valuable insights about the economic nature of the province for the country’s new capital. The data used in this study extended from January 2015 to September 2021. The data were divided into training and test data. The training data were used to model the time series equation using Holt winters and SARIMA models. Later, the models derived from training data were employed to produce forecasts. The forecasts were compared to the actual inflation data to determine the appropriate model for forecasting. Test data were from January 2015 to December 2020 and test data extended from January 2021 to September 2021. The result showed that Holt-Winters performed better than SARIMA in prediction inflation. The Root Mean Squared Error (RMSE) values are lower for Holt-Winters Exponential Smoothing for both cities. It also predicts better timing of cyclicality than SARIMA model.

Prediction of NDVI using the Holt-Winters model in high and low vegetation regions: A case study of East Africa

The Normalized Difference Vegetation Index (NDVI) indicates vegetation condition and is a vital index in monitoring and forecasting vegetation. Forecasting vegetation aids in decision making and land resource management. The objective of this study was to build a pixel-wise NDVI time series modelled using the Holt-Winters model. Moderate resolution NDVI data at 16 - days temporal resolution and 250 m spatial resolution was obtained from MOD13Q1 of the Moderate Resolution Imaging Spectroradiometer (MODIS) Terra Vegetation Indices from 2000 to 2019. The model was tested and its performance evaluated in a low and high vegetation regions in East Africa. The results showed that the model performed better in the high vegetation region than in the low vegetation region for 600 ✕ 600 pixels, achieving a mean absolute error (MAE) of 0.0679 and a root mean squared error (RMSE) of 0.084. 6 months mean NDVI forecast spatial maps were also generated to identify regions of potential vegetation deficit. The maps showed that the low vegetation region is predicted to experience moderate to light vegetation deficit while the high vegetation region is predicted to experience moderate to extremely high vegetation condition. Forecast error measures was computed to validate the forecast results. Our results show the suitability of using the Holt-Winters model in monitoring and forecasting NDVI using univariate data and may be used as a foundation for future studies interested in pixel-wise prediction of NDVI. The forecast maps may be useful to guide planners and decision makers to formulate mitigation plans and reduce the impacts of vegetation degradation at the local and regional level.