Diebold-Mariano Research Articles

Forecasting Orange Juice Futures: LSTM, ConvLSTM, and Traditional Models Across Trading Horizons

This study evaluated the forecasting accuracy of various models over 5-day and 10-day trading horizons to predict the prices of orange juice futures (OJ = F). The analysis included traditional models like Autoregressive Integrated Moving Average (ARIMA) and advanced neural network models such as Long Short-Term Memory (LSTM), Recurrent Neural Network (RNN), Backpropagation Neural Network (BPNN), Support Vector Regression (SVR), and Convolutional Long Short-Term Memory (ConvLSTM), incorporating factors like the Commodities Index and the S&P500 Index. We employed loss function metrics and various tests to assess model performance. The results indicated that for the 5-day horizon, the LSTM and ConvLSTM consistently outperformed the other models. LSTM achieved the lowest error rates and demonstrated superior capability in capturing temporal dependencies, especially in single-factor and S&P500 Index predictions. ConvLSTM also performed strongly, effectively modeling spatial and temporal data patterns. In the 10-day horizon, similar trends were observed. LSTM and ConvLSTM models had significantly lower errors and better alignment with actual values. The BPNN model performed well when all factors were included, and the SVR model maintained consistent accuracy, particularly for single-factor predictions. The Diebold–Mariano (DM) test indicated significant differences in forecasting accuracy, favoring advanced neural network models. In addition, incorporating multiple influencing factors further improved predictive performance, enhancing investment outcomes and reducing risk.

Potential formation mechanism and prediction of crude oil price based on underdetermined independent component analysis

In most crude oil price prediction, a few of them explored the potential formation mechanism of oil price. This study proposes a novel multi-scale integrated (MSI) learning paradigm to mine the potential formation mechanism of the crude oil price and predict the crude oil price. Firstly, we propose a novel underdetermined independent component analysis (UICA) model based on extreme-point symmetric mode decomposition (ESMD) and independent component analysis (ICA) to study the potential formation mechanism of crude oil price. Based on the representative independent components (ICs), we found and analyzed some factors affecting the crude oil price from high frequency to low frequency, as well as the potential formation mechanism of crude oil price, such as geopolitical implications, natural disasters, historical pricing data and copper futures price. Moreover, the ICs are predicted and generated the final forecasting result of crude oil price via radial basis function neural network (RBFNN). The experimental results based on the West Texas Intermediate (WTI) crude oil price, confirm that the proposed MSI model is superior to the existing prediction models in terms of statistical and error performance criteria and Diebold-Mariano (DM) test with the optimal D stat = 99.0220 , MAE = 0.0050 , RMSE = 0.0537 , MAPE = 0.0116 , ESD = 0.0007 , R 2 = 0.9960 .

Stock Price Forecasting using N-Beats Deep Learning Architecture

Stock prices present unique forecasting challenges due to factors such as market volatility, investor sentiment, and economic indicators, which contribute to significant fluctuations in time series data. This paper addresses these complexities by applying Deep Learning (DL) models to predict stock prices, with a particular focus on the S&P 500 index. Although DL models have shown remarkable success in fields like image processing and natural language processing, they require specialized architectures to effectively handle time series forecasting. This study examines the Neural Basis Expansion Analysis for Interpretable Time Series Forecasting (N-BEATS) model, a novel DL architecture specifically tailored for time series data, using S&P 500 stock price data. The performance of N-BEATS is benchmarked against three baseline models: Convolutional Neural Network (CNN), Long Short-Term Memory (LSTM), and Gated Recurrent Units (GRU). The evaluation metrics include Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE). Results indicate that the N-BEATS model consistently surpasses the other models in all metrics. Additionally, the Diebold-Mariano (DM) test further validates the superior predictive accuracy of the N-BEATS model compared to the alternatives. This research underscores the potential of the N-BEATS model to significantly improve stock price forecasting, offering valuable insights for investors, financial analysts, and other market participants.

Multi-step carbon emissions forecasting using an interpretable framework of new data preprocessing techniques and improved grey multivariable convolution model

As China stands at a critical juncture in its transition towards a low-carbon future, the precise prediction and analysis of provincial carbon emissions have emerged as paramount tasks. Focusing on forecasting in this intricate and vital domain, an updated grey multivariable convolution model is designed by employing the unified new-information-oriented accumulating generation operator (UNAGO) technique to process raw sequences. Equipped with UNAGO's hyper-parameters that enable the independent scaling effects and prioritize new information, the newly-designed model offers high flexibility and adaptability for handling complex provincial carbon emissions. Subsequently, four different restricted carbon emission sequences are utilized as case studies for validation purposes, and the new model's performance is scrutinized against five contrasting methods across three prediction forecasting horizons. Comparative experimental results reveal the new model's superior level of accuracy in predicting carbon emissions across four different provinces, with MAPE values of <4 % and 10 % in the in-sample and out-of-sample periods, respectively. Furthermore, rigorous evaluations with Diebold-Mariano (DM) and Probability Density Analysis (PDA) tests confirm the model's robust and general forecasting capabilities.

Wind Speed Forecasting Based on Phase Space Reconstruction and a Novel Optimization Algorithm

The wind power generation capacity is increasing rapidly every year. There needs to be a corresponding development in the management of wind power. Accurate wind speed forecasting is essential for a wind power management system. However, it is not easy to forecast wind speed precisely since wind speed time series data are usually nonlinear and fluctuant. This paper proposes a novel combined wind speed forecasting model that based on PSR (phase space reconstruction), NNCT (no negative constraint theory) and a novel GPSOGA (a hybrid optimization algorithm that combines global elite opposition-based learning strategy, particle swarm optimization and the genetic algorithm) optimization algorithm. SSA (singular spectrum analysis) is firstly applied to decompose the original wind speed time series into IMFs (intrinsic mode functions). Then, PSR is employed to reconstruct the intrinsic mode functions into input and output vectors of the forecasting model. A combined forecasting model is proposed that contains a CBP (cascade back propagation network), RNN (recurrent neural network), GRU (gated recurrent unit), and CNNRNN (convolutional neural network combined with recurrent neural network). The NNCT strategy is used to combine the output of the four predictors, and a new optimization algorithm is proposed to find the optimal combination parameters. In order to validate the performance of the proposed algorithm, we compare the forecasting results of the proposed algorithm with different models on four datasets. The experimental results demonstrate that the forecasting performance of the proposed algorithm is better than other comparison models in terms of different indicators. The DM (Diebold–Mariano) test, Akaike’s information criterion and the Nash–Sutcliffe efficiency coefficient confirm that the proposed algorithm outperforms the comparison models.

Energy fluctuation pattern recognition coupled with decomposition-integration: A novel ocean tidal energy forecasting system

Ocean tidal energy is a new energy source which is recognized and utilized earlier by human beings. For the complexity of tidal generation and the singleness of tidal prediction, this paper proposes a multi-factor forecasting system for ocean tidal energy based on energy fluctuation pattern recognition with confluent ReliefF-density-based spatial clustering of applications with noise (ReliefF-DBSCAN), improved symplectic geometric mode decomposition (ISGMD) and convolutional neural network−bidirectional long short-term memory (CNN-BiLSTM) with temporal pattern attention (TPA), named ReliefF-DBSCAN-ISGMD-TPA-CNN-BiLSTM. Precisely, ReliefF-DBSCAN can extract effective features and fluctuation patterns, and reduce the forecasting difficulty. ISGMD significantly improves the endpoint effect and false components of the decomposition results, and heightens the stability and correlation of each component. TPA-CNN-BiLSTM method have strong feature extraction ability, memory ability and recognition ability. In the evaluation stage, this study introduces some indicators such as root mean square error (RMSE) and Diebold Mariano (DM) test to evaluate the forecasting system comprehensively. To highlight the effect of the developed system, use actual data collected from Port SanLuis and Port Chicago as experimental data and compare with five contrastive models. The experimental result shows that the predicted value for the developed system is the closest to the real value, and the RMSE, mean absolute error (MAE) and goodness of fit (R2) of Port Chicago are 0.3152, 0.2900 and 0.9964, respectively, indicating that the prediction ability is better than all contrastive models. In addition, the result proves that the decomposition-integration system is beneficial to improve forecasting accuracy. This study can make a meaningful improvement and innovation for the forecasting of ocean tidal energy.

Ensemble empirical mode decomposition based deep learning models for forecasting river flow time series

River flow forecasting is important for flood prediction and effective utilization of water resources. This study proposed a comprehensive methodology that simultaneously enables the creation of multiple datasets and a comparison of multiple learning models for forecasting river flows. First, the data characteristics of the river flow time series were assessed based on its nature and pattern characteristics. Second, data decomposition was made for simplifying the complex data into decomposed modes. Ensemble Empirical Mode Decomposition (EEMD) was used for this purpose that provides intrinsic mode functions (IMFs). In addition, as benchmark, traditional time series decomposition was also applied over the complex data. Third, based on their data characteristics, the IMFs were combined into different components. These components along with the traditional time series decomposition create multiple datasets. Then, the components from the different datasets were forecasted using deep learning models, mainly BPNN (Back-Propagation Neural Network), CNN (Convoluted Neural Network) and LSTM (Long-Short Term Memory). Then, ensemble prediction was used to get the final output. For verification and benchmark purpose, we have also used statistical models like SARIMA over the datasets. A comprehensive evaluation and model comparisons were made using Diebold-Mariano (DM) test, k-fold cross validation and with the results of Prophet. In addition, the temporal convolution network (TCN) and the gated recurrent unit (GRU) were also modelled. Finally, all the DL modelling was performed for two data situations: with missing data deleted and missing data imputed. An empirical case study was done considering the average of daily time series data of Neeleswaram Hydrological Observation (HO) station over the Periyar river of South India for the period 2017–2021. The empirical assessment was made using several tests for all the different datasets and different learning models for further insights. Our results indicate that the deep learning-based models offer better predictions for complex time series in comparison to traditional statistical models. The DL models applied on the original time series data provided robust predictions with good performance such as low RMSE and high correlation values. However, the DL models’ performances are not enhanced through integration with time series decomposition and EEMD. Furthermore, the empirical results and the k-fold cross validation-based test indicate that all the DL models show equivalent performances. Interestingly, the DL models show superior performance over Prophet.

Constructing two-stream input matrices in a convolutional neural network for photovoltaic power prediction

To enhance the prediction accuracy of photovoltaic (PV) power and provide a more exact decision basis for power system management, an end-to-end reinforced two-stream convolutional neural network (RTS-CNN) is proposed. A temporal data converter is firstly devised to adaptively transform the input series into two different input matrices for improving the representational ability of the input data. One matrix is obtained through the tensor dimension adjustment, while the other uses Fast Fourier Transform (FFT) to acquire periodic information to reconstruct the shape of raw data. Next, to fully extract features from these two input matrices, the RTS-CNN model selects the powerful ConvNeXt block as the foundational building block of the encoder. Subsequently, the PV power prediction is realized using a decoder augmented with the Convolutional Block Attention Module (CBAM). Finally, for better performance and learning speed, the model is trained using the Second-order Clipped Stochastic Optimization (Sophia). Three sets of comparative experiments are conducted on the dataset obtained from the Desert Knowledge Australia Solar Centre (DKASC), and the model performance is further validated using the Diebold-Mariano (DM) test and external validation. The experimental results show that the proposed RTS-CNN model has outstanding performance in predicting PV power under different temporal resolutions and seasonal conditions. In the spring season, with time intervals of 15 min, 30 min, and 1 h, the RTS-CNN model achieves root mean square errors (RMSE) of 0.5113, 0.5984, and 0.7801, respectively.

Deep Learning Wind Power Prediction Model Based on Attention Mechanism-Based Convolutional Neural Network and Gated Recurrent Unit Neural Network

Accurate prediction of wind power is crucial for the efficient operation and risk management of wind farms. This paper introduces a deep learning model for wind power prediction that integrates an Attention mechanism with a convolutional neural network (CNN) and a gated recurrent unit (GRU) neural network. Addressing the randomness, intermittency, volatility and uncertainty of wind speed, we first apply swarm decomposition (SWD) to preprocess the original wind power data into subsequences. Subsequently, the CNN extracts spatial features, and the GRU identifies temporal correlations. The Attention mechanism enhances feature significance, further optimizing prediction accuracy. Complex error sequences generated by the CNN–GRU–Attention (CGA) model are corrected using the autoregressive integrated moving average (ARIMA). We evaluated the model’s performance using three wind power datasets against 16 other models, employing six evaluation indices (MSE, RMSE, MAPE, Theil’s [Formula: see text], TIC and SPL) and the Diebold–Mariano (DM) test and model confidence set (MCS) for model testing. Our results demonstrate the proposed model’s superior accuracy and efficiency in predicting wind power.

Non-parametric quantile regression-based modelling of additive effects to solar irradiation in Southern Africa

Modelling of solar irradiation is paramount to renewable energy management. This warrants the inclusion of additive effects to predict solar irradiation. Modelling of additive effects to solar irradiation can improve the forecasting accuracy of prediction frameworks. To help develop the frameworks, this current study modelled the additive effects using non-parametric quantile regression (QR). The approach applies quantile splines to approximate non-parametric components when finding the best relationships between covariates and the response variable. However, some additive effects are perceived as linear. Thus, the study included the partial linearly additive quantile regression model (PLAQR) in the quest to find how best the additive effects can be modelled. As a result, a comparative investigation on the forecasting performances of the PLAQR, an additive quantile regression (AQR) model and the new quantile generalised additive model (QGAM) using out-of-sample and probabilistic forecasting metric evaluations was done. Forecasted density plots, Murphy diagrams and results from the Diebold–Mariano (DM) hypothesis test were also analysed. The density plot, the curves on the Murphy diagram and most metric scores computed for the QGAM were slightly better than for the PLAQR and AQR models. That is, even though the DM test indicates that the PLAQR and AQR models are less accurate than the QGAM, we could not conclude an outright greater forecasting performance of the QGAM than the PLAQR or AQR models. However, in situations of probabilistic forecasting metric preferences, each model can be prioritised to be applied to the metric where it performed slightly the best. The three models performed differently in different locations, but the location was not a significant factor in their performances. In contrast, forecasting horizon and sample size influenced model performance differently in the three additive models. The performance variations also depended on the metric being evaluated. Therefore, the study has established the best forecasting horizons and sample sizes for the different metrics. It was finally concluded that a 20% forecasting horizon and a minimum sample size of 10000 data points are ideal when modelling additive effects of solar irradiation using non-parametric QR.

Hidden Markov guided Deep Learning models for forecasting highly volatile agricultural commodity prices

Predicting agricultural commodity prices accurately is of utmost importance due to various factors such as perishability, seasonality, production uncertainty etc. Moreover, the substantial volatility that may be exhibited in time series further adds to the complexity and constitutes a significant challenge. In this paper, a Hidden Markov (HM) guided Deep Learning (DL) models has been developed on nonlinear and nonstationary price data of agricultural commodities for forecasting by considering technical indicators viz., Moving Average (MA), Bollinger Bands (BB), Moving Average Convergence Divergence (MACD), Exponential MA (EMA) and Fast Fourier Transformation (FFT). HM Models (HMMs) can effectively handle the sequential dependencies and hidden states, while DL approach can learn complex patterns and relationships within the price series and thus the drawback of lack of generalization capability in the DL model has been overcome by HMM. In this study, the Potato price data of the Champadanga district of West Bengal, India has been utilized to assess the performance of the proposed technique. HMM has been combined with six baseline DL models viz., Recurrent Neural Networks (RNN), Convolutional Neural Networks (CNN), Long Short-Term Memory (LSTM), Gated Recurrent Units (GRU), Bidirectional LSTM (BiLSTM) and Bidirectional GRU (BiGRU) for forecast modeling. Performance evaluation metrics viz., Root Mean Squared Error (RMSE), Mean Absolute Percentage Error (MAPE), Mean Absolute Error (MAE) and the insightful Diebold–Mariano (DM) test revealed that Hidden Markov hybridized with DL models surpassed baseline DL models in forecasting accuracy for 1-week, 4-week, 8-week and 12-week ahead DL predictions. The proposed approach holds significant promise for enhancing the precision of agricultural commodity price forecasting with far-reaching implications for various stakeholders such as farmers and planners.

Can real-time investor sentiment help predict the high-frequency stock returns? Evidence from a mixed-frequency-rolling decomposition forecasting method

This research examines the predictive effect of real-time investor sentiment on high-frequency stock returns. Utilizing text sentiment analysis, we extract investor sentiment with a half-hour frequency from the stock message board. The RR-MIDAS method is used to model half-hourly sentiment and three-minute stock returns, and economic analysis reveals that investor sentiment significantly affects the stock returns during seven high-frequency periods, and the influence gradually weakens. Subsequently, we propose the “MF-EEMD-ML” prediction system, which introduces a rolling decomposition algorithm into the RR-MIDAS framework for predicting high-frequency trend items combined with real-time forum sentiment. The results, using rolling EMD decomposition for comparison, show that the “MF-EEMD-ML” system achieves a maximum reduction of 19.18 % in MAE, 19.08 % in RMSE, 11.71 % in SMAPE, and a maximum improvement of 16.66 % in DS. Additionally, the outcomes of the Diebold-Mariano (DM) tests also demonstrate that the “MF-EEMD-ML” prediction system significantly outperforms both the “MF-EMD-ML” system and the LR model.

A novel crude oil price forecasting model using decomposition and deep learning networks

Crude oil prices are susceptible to a variety of elements, including military, political, financial, and diplomatic forces, resulting in price fluctuations that are random, abrupt, and chaotic. Based on the chaotic nature of crude oil price series, this paper proposes a model for predicting crude oil prices that incorporates variational modal decomposition algorithm (VMD), phase space reconstruction technique (PSR), convolutional neural network (CNN), and bidirectional long and short-term memory network (BiLSTM). Specifically, the noises in the original data are removed using VMD. Next, the crude oil price is reconstructed using PSR. Then the reconstructed and denoised phase space is fed into the CNN-BiLSTM model for multi-step predictions. The empirical results show that the proposed model achieves the lowest MAPEs as 0.662%, 2.283%, 3.829%, and 4.44% and the lowest MSEs as 0.335, 3.942, 10.047 and 13.681. The Diebold Mariano (DM) test also demonstrates the proposed model’s superiority in the domain of crude oil price forecasting.

Crude oil volatility index forecasting: New evidence based on positive and negative jumps from Chinese stock market

This article investigates the crude oil volatility index (OVX) forecasting from the perspective of cross-market asymmetric effects of Chinese stock market jumps. We calculate six kinds of positive and negative jumps based on the high-frequency data of stock returns which are used to represent the asymmetric shocks of stock markets. Principal component analysis (PCA) and momentum of predictability (MoP) strategy are employed separately to synthesize the information of asymmetric jumps. Our empirical results find that considering the positive and negative jumps in Chinese stock market helps to improve the forecasting ability of OVX, especially under the MoP strategy. The out-of-sample model confidence set (MCS) tests and Diebold-Mariano (DM) tests, the evaluation of economic significance and the robustness tests further verify our results.

A deep learning interpretable model for river dissolved oxygen multi-step and interval prediction based on multi-source data fusion

Water bodies experiencing excessively low dissolved oxygen (DO) concentrations cannot sustain aquatic life and disrupt ecosystem balance, whereas overly high concentrations induce eutrophication, deteriorating the water environment's health. DO monitoring and safeguarding have perennially been paramount for global environmental protection authorities. Precise DO prediction is vital for water resource protection. Due to the non-linearity, complexity, and periodicity of DO data sequence, this study introduces a predictive model integrating multi-source data fusion, mode decomposition, improved sparrow search algorithm (SSA), attention (AT) mechanism, and gated recurrent unit (GRU). Initially, the original sequence undergoes decomposition via variational mode decomposition (VMD), with the resultant decomposed sub-sequences being trained and predicted using the GRU. The final predictive outcomes are derived by summing the predictions of each sub-sequence. This study substantiates the proposed model's efficacy by contrasting single models, various decomposition strategies, and combined models utilizing diverse methods. For the testing sets of two datasets, the Nash-Sutcliffe efficiency (NSE) coefficient, and the proportion of acceptable predictive values of the proposed model are 0.980, 100% and 0.987, 100%, respectively, outperforming other benchmark models. Additionally, the Diebold Mariano (DM) test, valley, multi-step ahead, interval predictions, and interpretability are employed to compare and analyze the model results. DM test results reveal that at a 1% significance level, the predictions from the models proposed in this study surpass those of other benchmark models. Through various approaches and perspectives' comparison and analysis, it is further demonstrated that the model developed herein displays exceptional prediction accuracy and can be effectively deployed across diverse watersheds.

Dengue incidence forecasting model in Magalang, Pampanga using time series analysis

This study aimed to provide an Auto-Regressive Integrated Moving Average (ARIMA) model that can predict dengue incidence in Magalang, Pampanga based on the past dengue incidences & climate variables from 2016 to 2019 and identify significant predictor/predictors among the climate variables. Weekly dengue incidence and climatological data from January 2016 to December 2019 were gathered and considered as the dependent and independent variables, respectively. Then, the Expert Modeler in IBM SPSS 22 automatically selected and estimated the best fitting ARIMA model for one dependent variable series. The created model was then used to forecast dengue incidence for the 52-week period of 2020, employing quarterly, semi-annual, and annual forecasting. A one-way ANOVA was conducted to evaluate differences among the four groups, followed by a post hoc Scheffe test to determine which groups differed from each other. Additionally, the Diebold-Mariano (DM) test was utilized to validate the forecasting performance of the ARIMA model. The non-seasonal ARIMA (0,1,6) model, with the sum of rainfall as the sole predictor from seven candidate predictors, was identified as the best fit. Model fit statistics indicated a stationary R-squared value of 0.739. The Ljung-Box statistics test value of 0.344, deemed not significant, confirmed correct model specification. One-way ANOVA analysis revealed a significant difference among the four groups, with an F value of 34.37 and a p-value approaching zero. Post hoc Scheffe tests further indicated a significant difference between the observed dataset and both semi-annual and annual forecasting, with p-values of 0.014 and approaching zero, respectively. However, no significant difference was observed between the observed dataset and quarterly forecasting, with a p-value of 0.281. Moreover, DM test statistics revealed that quarterly forecasting outperformed both annual and semi-annual forecasting. This suggests that the non-seasonal ARIMA (0,1,6) model, with the sum of rainfall as a predictor, effectively predicts future dengue incidences using quarterly forecasting.

Time Series Forecasting for Energy Production in Stand-Alone and Tracking Photovoltaic Systems Based on Historical Measurement Data

This article presents a time series analysis for predicting energy production in photovoltaic (PV) power plant systems, namely fixed and solar-tracking ones, which were located in the north-east of Poland. The purpose of one-day forecasts is to determine the effectiveness of preventive actions and manage power systems effectively. The impact of climate variables affecting the production of electricity in the photovoltaic systems was analyzed. Forecasting models based on traditional machine learning (ML) techniques and multi-layer perceptron (MLP) neural networks were created without using solar irradiance as an input feature to the model. In addition, a few metrics were selected to determine the quality of the forecasts. The preparation of the dataset for constructing the forecasting models was discussed, and some ways for improving the metrics were given. Furthermore, comparative analyses were performed, which showed that the MLP neural networks used in the regression problem provided better results than the MLP classifier models. The Diebold–Mariano (DM) test was applied in this study to distinguish the significant differences in the forecasting accuracy between the individual models. Compared to KNN (k-nearest neighbors) or ARIMA models, the best results were obtained for the simple linear regression, MLPRegressor, and CatBoostRegressor models in each of the investigated photovoltaic systems. The R-squared value for the MLPRegressor model was around 0.6, and it exceeded 0.8 when the dataset was split and separated into months.

Predicting Indian electricity exchange‐traded market prices: SARIMA and MLP approach

AbstractThis research investigates the short‐term (ST) forecasting performance of the daily prices of the Indian exchange‐traded day‐ahead (DAM) market, divided into 13 bid areas, each consisting of states with varied fundamentals. Forecasts are built employing SARIMA (seasonal autoregressive integrated moving average) and MLP (multilayer perceptron) methods. Moreover, the robustness and performance of the model is compared using the lowest error and the Diebold–Mariano (DM) test statistic values. The results indicates that the SARIMA model has high prediction accuracy with error values ranging from 1% to 5% with Southern region having the highest error of 4.53% and Northern having the least error of 1.27%. However, validation by the DM test suggests no statistical significant difference between the two models. The power generators, distribution companies, traders, policymakers, strategists and managers could use the findings for effective power management through proper planning.

A new hybrid prediction model of COVID-19 daily new case data

With the emergence of new mutant corona virus disease 2019 (COVID-19) strains such as Delta and Omicron, the number of infected people in various countries has reached a new high. Accurate prediction of the number of infected people is of far-reaching sig Nificance to epidemiological prevention in all countries of the world. In order to improve the prediction accuracy of COVID-19 daily new case data, a new hybrid prediction model of COVID-19 is proposed, which consists of four modules: decomposition, complexity judgment, prediction and error correction. Firstly, singular spectrum decomposition is used to decompose the COVID-19 data into singular spectrum components (SSC). Secondly, the complexity judgment is innovatively divided into high-complexity SSC and low-complexity SSC by neural network estimation time entropy. Thirdly, an improved LSSVM by GODLIKE optimization algorithm, named GLSSVM, is proposed to improve its prediction accuracy. Then, each low-complexity SSC is predicted by ARIMA, and each high-complexity SSC is predicted by GLSSVM, and the prediction error of each high-complexity SSC is predicted by GLSSVM. Finally, the predicted results are combined and reconstructed. Simulation experiments in Japan, Germany and Russia show that the proposed model has the highest prediction accuracy and the lowest prediction error. Diebold Mariano (DM) test is introduced to evaluate the model comprehensively. Taking Japan as an example, compared with ARIMA prediction model, the RMSE, average error and MAPE of the proposed model are reduced by 93.17%, 91.42% and 81.20% respectively.

Application of ARIMA, and hybrid ARIMA Models in predicting and forecasting tuberculosis incidences among children in Homa Bay and Turkana Counties, Kenya.

Tuberculosis (TB) infections among children (below 15 years) is a growing concern, particularly in resource-limited settings. However, the TB burden among children is relatively unknown in Kenya where two-thirds of estimated TB cases are undiagnosed annually. Very few studies have used Autoregressive Integrated Moving Average (ARIMA), and hybrid ARIMA models to model infectious diseases globally. We applied ARIMA, and hybrid ARIMA models to predict and forecast TB incidences among children in Homa Bay and Turkana Counties in Kenya. The ARIMA, and hybrid models were used to predict and forecast monthly TB cases reported in the Treatment Information from Basic Unit (TIBU) system by health facilities in Homa Bay and Turkana Counties between 2012 and 2021. The best parsimonious ARIMA model that minimizes errors was selected based on a rolling window cross-validation procedure. The hybrid ARIMA-ANN model produced better predictive and forecast accuracy compared to the Seasonal ARIMA (0,0,1,1,0,1,12) model. Furthermore, using the Diebold-Mariano (DM) test, the predictive accuracy of ARIMA-ANN versus ARIMA (0,0,1,1,0,1,12) model were significantly different, p<0.001, respectively. The forecasts showed a TB incidence of 175 TB cases per 100,000 (161 to 188 TB incidences per 100,000 population) children in Homa Bay and Turkana Counties in 2022. The hybrid (ARIMA-ANN) model produces better predictive and forecast accuracy compared to the single ARIMA model. The findings show evidence that the incidence of TB among children below 15 years in Homa Bay and Turkana Counties is significantly under-reported and is potentially higher than the national average.