A comparative analysis of time series models for forecasting recovered and deceased COVID-19 cases in India

Forecasting daily admissions to an emergency department considering single and multiple seasonal patterns

The coronavirus disease (COVID-19) is a severe, ongoing, novel pandemic that emerged in Wuhan, China, in December 2019. As of January 21, 2021, the virus had infected approximately 100 million people, causing over 2 million deaths. This article analyzed several time series forecasting methods to predict the spread of COVID-19 during the pandemic’s second wave in Italy (the period after October 13, 2020). The autoregressive moving average (ARIMA) model, innovations state space models for exponential smoothing (ETS), the neural network autoregression (NNAR) model, the trigonometric exponential smoothing state space model with Box–Cox transformation, ARMA errors, and trend and seasonal components (TBATS), and all of their feasible hybrid combinations were employed to forecast the number of patients hospitalized with mild symptoms and the number of patients hospitalized in the intensive care units (ICU). The data for the period February 21, 2020–October 13, 2020 were extracted from the website of the Italian Ministry of Health (www.salute.gov.it). The results showed that (i) hybrid models were better at capturing the linear, nonlinear, and seasonal pandemic patterns, significantly outperforming the respective single models for both time series, and (ii) the numbers of COVID-19-related hospitalizations of patients with mild symptoms and in the ICU were projected to increase rapidly from October 2020 to mid-November 2020. According to the estimations, the necessary ordinary and intensive care beds were expected to double in 10 days and to triple in approximately 20 days. These predictions were consistent with the observed trend, demonstrating that hybrid models may facilitate public health authorities’ decision-making, especially in the short-term.

Effective planning and optimization of rail transport operations depends on effective and reliable forecasting of demand. The results of transport performance forecasts usually differ from measured values because the mathematical models used are inadequate. In response to this applicative need, we report the results of a study whose goal was to develop, on the basis of historical data, an effective mathematical model of rail passenger transport performance that would allow to make reliable forecasts of future demand for this service. Several models dedicated to this type of empirical data were proposed and selection criteria were established. The models used in the study are: the seasonal naive model, the Exponential Smoothing (ETS) model, the exponential smoothing state space model with Box–Cox transformation, ARMA errors, trigonometric trend and seasonal components (TBATS) model, and the AutoRegressive Integrated Moving Average (ARIMA) model. The proposed time series identification and forecasting methods are dedicated to the processing of time series data with trend and seasonality. Then, the best model was identified and its accuracy and effectiveness were assessed. It was noticed that investigated time series is characterized by strong seasonality and an upward trend. This information is important for planning a development strategy for rail passenger transport, because it shows that additional investments and engagement in the development of both transport infrastructure and superstructure are required to meet the existing demand. Finally, a forecast of transport performance in sequential periods of time was presented. Such forecast may significantly improve the system of scheduling train journeys and determining the level of demand for rolling stock depending on the season and the annual rise in passenger numbers, increasing the effectiveness of management of rail transport.

Short-term solar irradiance forecasting using exponential smoothing state space model

Demand forecasting plays a key role in supply chain planning, management and its sustainable development, but it is a challenging process as demand depends on numerous, often unidentified or unknown factors that are seasonal in nature. Another problem is limited availability of information. Specifically, companies lacking modern IT systems are constrained to rely on historical sales observation as their sole source of information. This paper employs and contrasts a selection of mathematical models for short-term demand forecasting for products whose sales are characterized by high seasonal variations and a development trend. The aim of this publication is to demonstrate that even when only limited empirical data is available, while other factors influencing demand are unknown, it is possible to identify a time series that describes the sales of a product characterized by strong seasonal fluctuations and a trend, using selected mathematical methods. This study uses the seasonal ARIMA (autoregressive integrated moving average) model, ARIMA with Fourier terms model, ETS (exponential smoothing) model, and TBATS (Trigonometric Exponential Smoothing State Space Model with Box–Cox transformation, ARMA errors, Trend and Seasonal component). The models are presented as an alternative to popular machine learning models, which are more complicated to interpret, while their effectiveness is often similar. The selected methods were presented using a case study. The results obtained were compared and the best solution was identified, while emphasizing that each of the methods used could improve demand forecasting in the supply chain.

It is well known that accurate forecasts of mortality rates are essential to various demographic research like population projection, and the pricing of insurance products such as pensions and annuities. Recent studies suggest that mortality rates of multivariate ages are usually not leading indicators in mortality forecasting. Therefore, multivariate stochastic mortality models including the classic Lee–Carter may not necessarily lead to more accurate forecasts, compared with sophisticated univariate counterparties like the exponential smoothing state space (ETS) model. Despite its improved forecasting accuracy, the original ETS model cannot ensure the age-coherence of forecast mortality rates. By introducing an effective penalty scheme, we propose a penalized ETS model to significantly overcome this problem, with discussions on related technical issues including the reduction of parameter dimensionality and the selection of tuning parameter. Empirical results based on mortality rates of the Australian males and females suggest that the proposed model consistently outperforms the Lee–Carter and original ETS models. Robust conclusions are drawn when various forecasting scenarios are considered. Long-term forecasting analyses up to 2050 comparing the three models are further performed. To illustrate its usefulness in practice, an application to price fixed-term annuities with the penalized ETS model is demonstrated.

The choice of a suitable forecasting method carries noteworthy significance for organisations in adequately accomplishing their business targets. The selection of forecasting method becomes more sophisticated when there is a significant impact of seasonality on the business of an organisation. To deal with the situation of selecting the most relevant forecasting method for seasonal data, this paper proposes a framework using analytical hierarchy process (AHP) to rank various forecasting techniques for long time series. Accuracy measures namely Theil's U, mean absolute error (MAE), root mean square error (RMSE) and mean absolute percentage error (MAPE) are used as AHP criteria for performance measurement of various univariate time series methods such as naïve + season level trend (SLT), error, trend, seasonal (ETS), seasonal autoregressive moving average (SARIMA), exponential smoothing state space model with Box-Cox transformation (BATS) and trigonometric exponential smoothing state space model with Box-Cox transformation (TBATS) for seasonal data. The proposed framework is validated through real-time data provided by a public sector company in India. Ranking obtained from the developed AHP framework suggests that SARIMA is ranked top amongst all the techniques for short-term forecasting of seasonal data.

The choice of a suitable forecasting method carries noteworthy significance for organisations in adequately accomplishing their business targets. The selection of forecasting method becomes more sophisticated when there is a significant impact of seasonality on the business of an organisation. To deal with the situation of selecting the most relevant forecasting method for seasonal data, this paper proposes a framework using analytical hierarchy process (AHP) to rank various forecasting techniques for long time series. Accuracy measures namely Theil's U, mean absolute error (MAE), root mean square error (RMSE) and mean absolute percentage error (MAPE) are used as AHP criteria for performance measurement of various univariate time series methods such as naive + season level trend (SLT), error, trend, seasonal (ETS), seasonal autoregressive moving average (SARIMA), exponential smoothing state space model with Box-Cox transformation (BATS) and trigonometric exponential smoothing state space model with Box-Cox transformation (TBATS) for seasonal data. The proposed framework is validated through real-time data provided by a public sector company in India. Ranking obtained from the developed AHP framework suggests that SARIMA is ranked top amongst all the techniques for short-term forecasting of seasonal data.

Objective: Smart city projects are still in their initial research stages in Oman. This paper aims to prove the effectiveness of smart cities by using Data Mining Techniques (DMT) to predict energy consumption in Oman. Methods: Data collected from thirteen residential and eight industrial meters are used for electricity consumption forecast. Detailed data analysis is carried out using K-means clustering and time-series forecasting in R. Energy consumption data is modeled using average, naive, seasonal naive, Seasonal decomposition of Time Series by Loess (STL) +Random Walk with Drift (RWD), Exponential smoothing state space model with Box-Cox transformation, ARMA errors, Trend and Seasonal component (TBATS) and Autoregressive Integrated Moving Average (ARIMA) models. Findings: Even though the dataset isn’t characterized by seasons or trends, Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE) error measures suggest that electricity consumption for residential sector is more accurately forecasted using TBATS model. Energy consumption for small, medium and large scale industries, on the other hand are more accurately predicted by TBATS, Average and STL + RWD models respectively. Applications: The obtained results confirm the efficiency in forecasting energy consumption in Oman using time series models in order to initiate smart city implementation. Keywords: Data Mining, Energy Consumption, Smart City, Clustering, Time-Series Forecasting, R

Combined TBATS and SVM model of minimum and maximum air temperatures applied to wheat yield prediction at different locations in Europe

Hemorrhagic fever with renal syndrome (HFRS), one of the main public health concerns in mainland China, is a group of clinically similar diseases caused by hantaviruses. Statistical approaches have always been leveraged to forecast the future incidence rates of certain infectious diseases to effectively control their prevalence and outbreak potential. Compared to the use of one base model, model stacking can often produce better forecasting results. In this study, we fitted the monthly reported cases of HFRS in mainland China with a model stacking approach and compared its forecasting performance with those of five base models. We fitted the monthly reported cases of HFRS ranging from January 2004 to June 2019 in mainland China with an autoregressive integrated moving average (ARIMA) model; the Holt-Winter (HW) method, seasonal decomposition of the time series by LOESS (STL); a neural network autoregressive (NNAR) model; and an exponential smoothing state space model with a Box-Cox transformation; ARMA errors; and trend and seasonal components (TBATS), and we combined the forecasting results with the inverse rank approach. The forecasting performance was estimated based on several accuracy criteria for model prediction, including the mean absolute percentage error (MAPE), root-mean-squared error (RMSE) and mean absolute error (MAE). There was a slight downward trend and obvious seasonal periodicity inherent in the time series data for HFRS in mainland China. The model stacking method was selected as the best approach with the best performance in terms of both fitting (RMSE 128.19, MAE 85.63, MAPE 8.18) and prediction (RMSE 151.86, MAE 118.28, MAPE 13.16). The results showed that model stacking by using the optimal mean forecasting weight of the five abovementioned models achieved the best performance in terms of predicting HFRS one year into the future. This study has corroborated the conclusion that model stacking is an easy way to enhance prediction accuracy when modeling HFRS.

ObjectiveHemorrhagic fever with renal syndrome (HFRS), one of the main public health concerns in mainland China, is a group of clinically similar diseases caused by hantaviruses. Statistical approaches have always been leveraged to forecast the future incidence rates of certain infectious diseases to effectively control their prevalence and outbreak potential. Compared to the use of one base model, model stacking can often produce better forecasting results. In this study, we fitted the monthly reported cases of HFRS in mainland China with a model stacking approach and compared its forecasting performance with those of five base models.MethodWe fitted the monthly reported cases of HFRS ranging from January 2004 to June 2019 in mainland China with an autoregressive integrated moving average (ARIMA) model; the Holt-Winter (HW) method, seasonal decomposition of the time series by LOESS (STL); a neural network autoregressive (NNAR) model; and an exponential smoothing state space model with a Box-Cox transformation; ARMA errors; and trend and seasonal components (TBATS), and we combined the forecasting results with the inverse rank approach. The forecasting performance was estimated based on several accuracy criteria for model prediction, including the mean absolute percentage error (MAPE), root-mean-squared error (RMSE) and mean absolute error (MAE).ResultThere was a slight downward trend and obvious seasonal periodicity inherent in the time series data for HFRS in mainland China. The model stacking method was selected as the best approach with the best performance in terms of both fitting (RMSE 128.19, MAE 85.63, MAPE 8.18) and prediction (RMSE 151.86, MAE 118.28, MAPE 13.16).ConclusionThe results showed that model stacking by using the optimal mean forecasting weight of the five abovementioned models achieved the best performance in terms of predicting HFRS one year into the future. This study has corroborated the conclusion that model stacking is an easy way to enhance prediction accuracy when modeling HFRS.

Forecasting electricity demand through time series is a tool used by transmission system operators to establish future operating conditions. The accuracy of these forecasts is essential for the precise development of activity. However, the accuracy of the forecasts is enormously subject to the calendar effect. The multiple seasonal Holt–Winters models are widely used due to the great precision and simplicity that they offer. Usually, these models relate this calendar effect to external variables that contribute to modification of their forecasts a posteriori. In this work, a new point of view is presented, where the calendar effect constitutes a built-in part of the Holt–Winters model. In particular, the proposed model incorporates discrete-interval moving seasonalities. Moreover, a clear example of the application of this methodology to situations that are difficult to treat, such as the days of Easter, is presented. The results show that the proposed model performs well, outperforming the regular Holt–Winters model and other methods such as artificial neural networks and Exponential Smoothing State Space Model with Box-Cox Transformation, ARMA Errors, Trend and Seasonal Components (TBATS) methods.

Condensed water vapor in the atmosphere is observed as precipitation whenever moist air rises sufficiently enough to produce saturation, condensation, and the growth of precipitation particles. It is hard to measure the amount and concentration of total precipitation over time due to the changes in the amount of precipitation and the variability of climate. As a result of these, the modelling and forecasting of precipitation amount is challenging. For this reason, this study compares forecasting performances of different methods on monthly precipitation series with covariates including the temperature, relative humidity, and cloudiness of Muğla region, Turkey. To accomplish this, the performance of multiple linear regression, the state space model (SSM) via Kalman Filter, a hybrid model integrating the logistic regression and SSM models, the seasonal autoregressive integrated moving average (SARIMA), exponential smoothing with state space model (ETS), exponential smoothing state space model with Box-Cox transformation-ARMA errors-trend and seasonal components (TBATS), feed-forward neural network (NNETAR) and Prophet models are all compared. This comparison has yet to be undertaken in the literature. The empirical findings overwhelmingly support the SSM when modelling and forecasting the monthly total precipitation amount of the Muğla region, encouraging the time-varying coefficients extensions of the precipitation model.

Short-term electricity load demand forecast is a vital requirements for power systems. This research considers the combination of exponential smoothing for double seasonal patterns and neural network model. The linear version of Holt-Winter method is extended to accommodate a second seasonal component. In this work, the Fourier with time varying coefficient is presented as a means of seasonal extraction. The methodological contribution of this paper is to demonstrate how these methods can be adapted to model the time series data with multiple seasonal pattern, correlated non stationary error and nonlinearity components together. The proposed hybrid model is started by implementing exponential smoothing state space model to obtain the level, trend, seasonal and irregular components and then use them as inputs of neural network. Forecasts of future values are then can be obtained by using the hybrid model. The forecast performance was characterized by root mean square error and mean absolute percentage error. The proposed hybrid model is applied to two real load series that are energy consumption in Bawen substation and in Java-Bali area. Comparing with other existing models, results show that the proposed hybrid model generate the most accurate forecast