Hybrid Autoregressive Integrated Moving Average Research Articles

Comparative Studies of Hybrid ARIMA and Artificial Neural Network (ANN) Techniques for Predicting Exchange Rate in Pakistan

For predicting time series data the ARIMA and ANN provides a good technique in the field of research. Time series data often contain both linear and nonlinear patterns. Therefore, neither ARIMA nor neural networks can be adequate in modeling and predicting time series data. When applying the linear models, most existing studies seem to use the same specification for estimation and forecasting, but the dynamic impact of the concerned variables is ignored. In this study combined the ARIMA and Artificial neural network model by adopting both an equal weighted approach and profit weighted approach to capture both th linear and nonlinear components of the exchange rate, and also developed a hybrid techniques by using models of artificial neural network (ANN) and autoregressive integrated moving average (ARIMA) and their performance were compared to ANN and Hybrid ARIMA models. The Hybrid models are used for forecasting the future exchange rate for dollar, the exports and imports of data The findings showed that combining both ARIMA and ANN models reap the advantage of linear and nonlinear modeling. The capability of the two models are analyzed based on standard statistical measures such as, mean absolute error (MAE), root mean square error (RMSE), and mean squared error (MSE). Models effectiveness The effectiveness of the models are analyzed for the foreign exchange rate, imports and exports of the data and concluded that hybrid techniques provided the best forecasting results.

Frequency prediction of a post-disturbance power system using a hybrid ARIMA and DBN model

The online prediction of power system dynamic frequency helps to guide the choice of control measures quickly and accurately after a disturbance, and this then ensures the reliable and stable operations of a power system. However, the prediction performance of the traditional single model is not accurate enough, and the prediction method cannot reflect the dynamic mechanism of the power system. To address these challenges, based on the analysis of the mechanism of the dynamic operation of a power system, a dynamic frequency online prediction method using the autoregressive integrated moving average (ARIMA) model and the deep belief network (DBN) is proposed in this paper. First, according to the mechanism of the dynamic operation of a power system, the dynamic frequency can be regarded as having two stages after the disturbance occurs. In the first stage, the frequency changes monotonously in the short term, which is predicted by the ARIMA model. Furthermore, the second stage is an oscillation phase with changing amplitude, which is predicted by the DBN. The calibration process is used to combine the two predicted results. Second, the three metrics including the frequency nadir (fnadir), the quasi-steady state frequency (fss), and the frequency curve obtained through the prediction are analyzed to measure the accuracy of the prediction results. Finally, to verify the accuracy of the proposed model, the IEEE 10-generator 39-bus benchmark system is used for verification.

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.

Global Solar Radiation Forecasting Based on Hybrid Model with Combinations of Meteorological Parameters: Morocco Case Study

The adequate modeling and estimation of solar radiation plays a vital role in designing solar energy applications. In fact, unnecessary environmental changes result in several problems with the components of solar photovoltaic and affects the energy generation network. Various computational algorithms have been developed over the past decades to improve the efficiency of predicting solar radiation with various input characteristics. This research provides five approaches for forecasting daily global solar radiation (GSR) in two Moroccan cities, Tetouan and Tangier. In this regard, autoregressive integrated moving average (ARIMA), autoregressive moving average (ARMA), feed forward back propagation neural networks (FFBP), hybrid ARIMA-FFBP, and hybrid ARMA-FFBP were selected to compare and forecast the daily global solar radiation with different combinations of meteorological parameters. In addition, the performance in three approaches has been calculated in terms of the statistical metric correlation coefficient (R2), root means square error (RMSE), stand deviation (σ), the slope of best fit (SBF), legate’s coefficient of efficiency (LCE), and Wilmott’s index of agreement (WIA). The best model is selected by using the computed statistical metric, which is present, and the optimal value. The R2 of the forecasted ARIMA, ARMA, FFBP, hybrid ARIMA-FFBP, and ARMA-FFBP models is varying between 0.9472% and 0.9931%. The range value of SPE is varying between 0.8435 and 0.9296. The range value of LCE is 0.8954 and 0.9696 and the range value of WIA is 0.9491 and 0.9945. The outcomes show that the hybrid ARIMA–FFBP and hybrid ARMA–FFBP techniques are more effective than other approaches due to the improved correlation coefficient (R2).

Analysis and Forecasting of Rice Production Behavior in Bangladesh

This research looks at how numerous factors, including the price of rice, area, improved seed distribution, areas irrigated by different improved methods, and fertilizer, influence rice production in Bangladesh. This study employed the autoregressive distributed lag (ARDL) model to investigate the short-run and long-run effects of each exogenous variable on rice production. In this research work, auto regressive integrated moving average (ARIMA) and hybrid ARIMA-(general autoregressive conditional heteroskedastic) GRACH were used to forecast rice production in Bangladesh from 1983 to 2030. The parameters of price of rice, area irrigated by different improved methods, area, and fertilizer were found to have a significant and positive impact on rice production in this study, both in the short run and the long run, according to the ARDL model. According to the lowest Root Mean Squared Error, Mean Absolute Error and Theil Inequality Coefficient criteria, the linear hybrid ARIMA (11, 1, 11)–EGARCH (1, 1)–M model performed better in predicting the rice production in Bangladesh. IUBAT Review—A Multidisciplinary Academic Journal, 5 (1): 1-14

The hybrid model of autoregressive integrated moving average and fuzzy time series Markov chain on long-memory data

IntroductionThe price of crude oil as an essential commodity in the world economy shows a pattern and identifies the component factors that influence it in the short and long term. The long pattern of the price movement of crude oil is identified by a fractionally time series model where the accuracy can still be improved by making a hybrid residual model using a fuzzy time series approach.MethodsTime series data containing long-memory elements can be modified into a stationary model through the autoregressive fractional integrated moving average (ARFIMA). This fractional model can provide better accuracy on long-memory data than the classic autoregressive integrated moving average (ARIMA) model. The long-memory data are indicated by a high level of fluctuation and the autocorrelation value between lags that decreases slowly. However, a more accurate model is proposed as a hybridization time series model with fuzzy time series Markov chain (FTSMC).ResultsThe time series data collected from the monthly period of West Texas Intermediate (WTI) oil price as the standard for world oil prices for the 2003–2021 time period. The data of WTI oil price has a long-memory data pattern to be modeled fractionally, and subsequently their hybrids. The times series model of crude oil price is obtained as the new target model of hybrid ARIMA and ARFIMA with FTSMC, denoted as ARIMA-FTSMC and ARFIMA-FTSMC, respectively.DiscussionThe accuracy model measured by MAE, RMSE, and MAPE shows that the hybrid model of ARIMA-FTSMC has better performance than ARIMA and ARFIMA, but the hybrid model of ARFIMA-FTSMC provides the best accuracy compared to all models. The superiority of the hybrid time series model of ARFIMA-FTSMC on long-memory data provides an opportunity for the hybrid model as the best and more precise forecasting method.

Forecasting of Beijing PM2.5 with a hybrid ARIMA model based on integrated AIC and improved GS fixed-order methods and seasonal decomposition

Accurate particulate matter 2.5 (PM2.5) prediction plays a crucial role in the accurate management of air pollution and prevention of respiratory diseases. However, PM2.5, as a nonlinear time series with great volatility, is difficult to achieve accurate prediction. In this paper, a hybrid autoregressive integrated moving average (ARIMA) model is proposed based on the Augmented Dickey-Fuller test (ADF root test) of annual PM2.5 data, thus demonstrating the necessity of first-order difference. The new method of using integrated akaike information criterion (AIC) and improved grid search (GS) methods is proposed to avoid the bias caused by using AIC alone to determine the order because the data are not exactly normally distributed. The comprehensive evaluation coefficient (CEC) is used to select the optimal parameter structure of the prediction model by considering multiple evaluation perspectives. The entropy value of the decomposed series is obtained by using range entropy A (RangeEn_A), and the series is reconstructed according to the entropy value, and finally the reconstructed series is predicted. We used Beijing PM2.5 data for validation and the results showed that the new hybrid ARIMA model improved values of RMSE 99.23%, MAE 99.20%, R2 118.61%, TIC 99.28%, NMAE 98.71%, NMSE 99.97%, OPC 43.13%, MOPC 98.43% and CEC 99.25% compared with the traditional ARIMA model. The results show that the method does greatly improve the prediction performance and provides a convincing tool for policy formulation and governance.

Influence of Anomalies on the Models for Nitrogen Oxides and Ozone Series

Nowadays, observing, recording, and modeling the dynamics of atmospheric pollutants represent actual study areas given the effects of pollution on the population and ecosystems. The existence of aberrant values may influence reports on air quality when they are based on average values over a period. This may also influence the quality of models, which are further used in forecasting. Therefore, correct data collection and analysis is necessary before modeling. This study aimed to detect aberrant values in a nitrogen oxide concentration series recorded in the interval 1 January–8 June 2016 in Timisoara, Romania, and retrieved from the official reports of the National Network for Monitoring the Air Quality, Romania. Four methods were utilized, including the interquartile range (IQR), isolation forest, local outlier factor (LOF) methods, and the generalized extreme studentized deviate (GESD) test. Autoregressive integrated moving average (ARIMA), Generalized Regression Neural Networks (GRNN), and hybrid ARIMA-GRNN models were built for the series before and after the removal of aberrant values. The results show that the first approach provided a good model (from a statistical viewpoint) for the series after the anomalies removal. The best model was obtained by the hybrid ARIMA-GRNN. For example, for the raw NO2 series, the ARIMA model was not statistically validated, whereas, for the series without outliers, the ARIMA(1,1,1) was validated. The GRNN model for the raw series was able to learn the data well: R2 = 76.135%, the correlation between the actual and predicted values (rap) was 0.8778, the mean standard errors (MSE) = 0.177, the mean absolute error MAE = 0.2839, and the mean absolute percentage error MAPE = 9.9786. Still, on the test set, the results were worse: MSE = 1.5101, MAE = 0.8175, rap = 0.4482. For the series without outliers, the model was able to learn the data in the training set better than for the raw series (R2 = 0.996), whereas, on the test set, the results were not very good (R2 = 0.473). The performances of the hybrid ARIMA–GRNN on the initial series were not satisfactory on the test (the pattern of the computed values was almost linear) but were very good on the series without outliers (the correlation between the predicted values on the test set was very close to 1). The same was true for the models built for O3.

A hybrid ARIMA–WNN approach to model vehicle operating behavior and detect unhealthy states

As modern vehicles system becomes increasingly complex, there is an urgent need to develop a framework to monitor the behavior and detect the unhealthy states to appropriately arrange the maintenance in order to extend the vehicle life cycle. Sensors installed in vehicles are able to record a huge amount of multiple channel time series data. This paper develops a prediction model and an unhealthy state detection strategy for monitoring the behavior of the operating vehicle by analyzing multiple channel time series data channels. Due to the complexity of the underlying process of multiple channel time series data, a hybrid ARIMA–WNN model is proposed by combining the Auto-Regressive Integrated Moving Average (ARIMA) and Wavelet Neural Network (WNN) models. This model exploits the ARIMA capacity for predicting the unseen patterns without labeled historical data and WNN’s flexibility in analyzing different variations of time series data. Furthermore, a threshold-based anomaly detection strategy is developed to timely recognize the unhealthy states of the vehicle. To test the performance of the proposed hybrid ARIMA–WNN, a large scale multiple-channel time series data including three months of second-wise records of 101 channels of an operating vehicle is used. Results reveal the higher accuracy of the proposed ARIMA–WNN compared with the ARIMA and WNN models in modeling the behavior of different data channels. By estimating the proper distribution of the threshold, the proposed anomaly detection method is also efficient for identifying the unhealthy states of the vehicle.

Improved of Forecasting Sea Surface Temperature based on Hybrid ARIMA and Support Vector Machines Models

Forecasting is a very effortful task owing to its features which simultaneously contain linear and nonlinear patterns. The Autoregressive Integrated Moving Average (ARIMA) model has been one the most widely utilized linear model in time series forecasting. Unfortunately, the ARIMA model cannot effortlessly handle nonlinear patterns alone. Thus, Support Vector Machine (SVM) model is introduced to solve nonlinear behavior in the datasets with high variance and uncertainty. The purposes of this study are twofold. First, to propose a hybrid ARIMA models using SVM. Secondly, to test the effectiveness of the proposed hybrid model using sea surface temperature (SST) data. Our investigation is based on two well-known real datasets, i.e., SST (modis) and in-situ SST (hycom). Statistical measurement such as MAE, MAPE, MSE, and RMSE are carried out to investigate the efficacy of the proposed models as compared to the previous ARIMA and SVMs models. The empirical results reveal that the proposed models produce lesser MAE, MAPE, MSE, and RMSE values in comparison to the single ARIMA and SVMs models. In additional, ARIMA-SVM are much better than compared to the existing models since the forecasting values are closer to the actual value. Therefore, we conclude that the presented models can be used to generate superior predicting values in time series forecasting with a way higher forecast precision.

Electric Load Forecasting for Internet of Things Smart Home Using Hybrid PCA and ARIMA Algorithm

Many types of research have been conducted for the development of Internet of Things (IoT) devices and energy consumption forecasting. In this research, the electric load forecasting is designed with the development of microcontrollers, sensors, and actuators, added with cameras, Liquid Crystal Display (LCD) touch screen, and minicomputers, to improve the IoT smart home system. Using the Python program, Principal Component Analysis (PCA) and Autoregressive Integrated Moving Average (ARIMA) algorithms are integrated into the website interface for electric load forecasting. As provisions for forecasting, a monthly dataset is needed which consists of electric current variables, number of individuals living in the house, room light intensity, weather conditions in terms of temperature, humidity, and wind speed. The main hardware parts are ESP32, ACS712, electromechanical relay, Raspberry Pi, RPi Camera, infrared Light Emitting Diode (LED), Light Dependent Resistor (LDR) sensor, and LCD touch screen. While the main software applications are Arduino Interactive Development Environment (IDE), Visual Studio Code, and Raspberry Pi OS, added with many libraries for Python 3 IDE. The experimental results provided the fact that PCA and ARIMA can predict short-term household electric load accurately. Furthermore, by using Amazon Web Services (AWS) cloud computing server, the IoT smart home system has excellent data package performances.

A novel hybrid ARIMA and regression tree model for the interval-valued time series

With the arrival of the big data era, the interval-valued time series (ITS) has become a research hot spot. This study proposes a novel hybrid model combining the auto-regressive integrated moving average (ARIMA) and regression tree (RT) models for the ITS. Following the idea of hybrid ‘linear and nonlinear’ modeling framework, the ARIMA and RT models capture the linear and nonlinear components hidden in the ITS. The proposed ARIMA-RT model is compared with other competitors through a simulated experiment and a real ITS. Based on the experimental analysis, we find that the performance of the proposed ARIMA-RT model is strikingly superior to other competitors, notably in forecasting the nonlinear ITS. It indicates that the ARIMA-RT model has strong ability to capture the nonlinear ITS in stock markets.

A hybrid ARIMA–ANN method to forecast daily global solar radiation in three different cities in Morocco

The aim of this paper is to propose and introduce an innovative hybrid model to forecasted the daily global solar radiation (DGSR) in three different cities in Morocco. The DGSR depends on several meteorological parameters and it is difficult to determine its behaviour. The used data have been collected from three different cities with different meteorological data. In this context, we compared 3-year forecasting performance of two methods widely used in forecasting research with a hybrid method. The first model uses the artificial neural network (ANN) and the second one, known as autoregressive integrated moving average (ARIMA), is based on both statistic regression and time series analysis. The third model is based on the combination between ANN and ARIMA methodologies. The three methods have been trained within the same experimental data, thereby allowing a much needed homogeneous correlation that is completely missing in the existing research. The forecasted DGSR generated by the hybrid ARIMA–ANN approach shows a high correlation with experimental results and a relatively small error rate. The forecast of DGSR obtained by hybrid ARIMA–ANN method is compared with the single ANN and ARIMA methods and experimental data. In order to be more accurate, an empirical error is measured and contrasted to check the significance of the expected outcomes and the accuracy of the model. In order to assure results reliability, statistical errors are computed and compared to verify the validity of the forecasted results and the performance of the model. The compared results through statistical error are very accurate compared with a single model in term of R2, MBE, RMSE, NRMSE, MAPE, TS and Sd. Generally, the obtained value using the hybrid model is the most adequate which can adjust the experimental data with satisfactory precision. In the end, the ARIMA–ANN model can be used in forecasting photovoltaic power or temperature.

Predicting Primary Energy Consumption Using Hybrid ARIMA and GA-SVR Based on EEMD Decomposition

Forecasting energy consumption is not easy because of the nonlinear nature of the time series for energy consumptions, which cannot be accurately predicted by traditional forecasting methods. Therefore, a novel hybrid forecasting framework based on the ensemble empirical mode decomposition (EEMD) approach and a combination of individual forecasting models is proposed. The hybrid models include the autoregressive integrated moving average (ARIMA), the support vector regression (SVR), and the genetic algorithm (GA). The integrated framework, the so-called EEMD-ARIMA-GA-SVR, will be used to predict the primary energy consumption of an economy. An empirical study case based on the Taiwanese consumption of energy will be used to verify the feasibility of the proposed forecast framework. According to the empirical study results, the proposed hybrid framework is feasible. Compared with prediction results derived from other forecasting mechanisms, the proposed framework demonstrates better precisions, but such a hybrid system can also be seen as a basis for energy management and policy definition.

A Kalman filter-based hybridization model of statistical and intelligent approaches for exchange rate forecasting

Purpose The purpose of this paper is to propose a comprehensive version of a hybrid autoregressive integrated moving average (ARIMA), and artificial neural networks (ANNs) in order to yield a more general and more accurate hybrid model for exchange rates forecasting. For this purpose, the Kalman filter technique is used in the proposed model to preprocess and detect the trend of raw data. It is basically done to reduce the existing noise in the underlying data and better modeling, respectively. Design/methodology/approach In this paper, ARIMA models are applied to construct a new hybrid model to overcome the above-mentioned limitations of ANNs and to yield a more general and more accurate model than traditional hybrid ARIMA and ANNs models. In our proposed model, a time series is considered as a function of a linear and nonlinear component, so, in the first phase, an ARIMA model is first used to identify and magnify the existing linear structures in data. In the second phase, a multilayer perceptron is used as a nonlinear neural network to model the preprocessed data, in which the existing linear structures are identified and magnified by ARIMA and to predict the future value of time series. Findings In this paper, a new Kalman filter based hybrid artificial neural network and ARIMA model are proposed as an alternate forecasting technique to the traditional hybrid ARIMA/ANNs models. In the proposed model, similar to the traditional hybrid ARIMA/ANNs models, the unique strengths of ARIMA and ANN in linear and nonlinear modeling are jointly used, aiming to capture different forms of relationship in the data; especially, in complex problems that have both linear and nonlinear correlation structures. However, there are no aforementioned assumptions in the modeling process of the proposed model. Therefore, in the proposed model, in contrast to the traditional hybrid ARIMA/ANNs, it can be generally guaranteed that the performance of the proposed model will not be worse than either of their components used separately. In addition, empirical results in both weekly and daily exchange rate forecasting indicate that the proposed model can be an effective way to improve forecasting accuracy achieved by traditional hybrid ARIMA/ANNs models. Originality/value In the proposed model, in contrast to the traditional hybrid ARIMA/ANNs, it can be guaranteed that the performance of the proposed model will not be worse than either of the components used separately. In addition, empirical results in exchange rate forecasting indicate that the proposed model can be an effective way to improve forecasting accuracy achieved by traditional hybrid ARIMA/ANNs models. Therefore, it can be used as an appropriate alternate model for forecasting in exchange ratemarkets, especially when higher forecasting accuracy is needed.

Application of a Hybrid ARIMA–SVR Model Based on the SPI for the Forecast of Drought—A Case Study in Henan Province, China

AbstractDrought forecasts could effectively reduce the risk of drought. Data-driven models are suitable forecast tools because of their minimal information requirements. The motivation for this study is that because most data-driven models, such as autoregressive integrated moving average (ARIMA) models, can capture linear relationships but cannot capture nonlinear relationships they are insufficient for long-term prediction. The hybrid ARIMA–support vector regression (SVR) model proposed in this paper is based on the advantages of a linear model and a nonlinear model. The multiscale standard precipitation indices (SPI: SPI1, SPI3, SPI6, and SPI12) were forecast and compared using the ARIMA model and the hybrid ARIMA–SVR model. The performance of all models was compared using measures of persistence, such as the coefficient of determination, root-mean-square error, mean absolute error, Nash–Sutcliffe coefficient, and kriging interpolation method in the ArcGIS software. The results show that the prediction accuracies of the multiscale SPI of the combined ARIMA–SVR model and the single ARIMA model were related to the time scale of the index, and they gradually increase with an increase in time scale. The predicted value decreases with increase in lead time. Comparing the measured data with the predicted data from the model shows that the combined ARIMA–SVR model had higher prediction accuracy than the single ARIMA model and that the predicted results 1–2 months ahead show reasonably good agreement with the actual data.

Application of Hybrid ARIMA and Artificial Neural Network Modelling for Electromagnetic Propagation: An Alternative to the Least Squares Method and ITU Recommendation P.1546-5 for Amazon Urbanized Cities

This study sets out an empirical hybrid autoregressive integrated moving average (ARIMA) and artificial neural network (ANN) model designed to estimate electromagnetic wave propagation in densely forested urban areas. Received signal power intensity data was acquired through measurement campaigns carried out in the Metropolitan Area of Belém (MAB), in the Brazilian Amazon. Comparisons were made between estimates from classical least squares (LS) fitting and ITU (International Telecommunication Union) recommendation P. 1546-5. The results indicate the model is, at least, 44% more precise than every ITU estimate and, in some situations, is at least 11% better than an LS estimate, depending on the respective values of the relative error (RE).

Hybrid ARIMA and Neural Network Modelling Applied to Telecommunications in Urban Environments in the Amazon Region

This study explores the use of a hybrid Autoregressive Integrated Moving Average (ARIMA) and Neural Network modelling for estimates of the electric field along vertical paths (buildings) close to Digital Television (DTV) transmitters. The work was carried out in Belém city, one of the most urbanized cities in the Brazilian Amazon and includes a case study of the application of this modelling within the subscenarios found in Belém. Its results were compared with the ITU recommendations P. 1546-5 and proved to be better in every subscenario analysed. In the worst case, the estimate of the model was approximately 65% better than that of the ITU. We also compared this modelling with a classic modelling technique: the Least Squares (LS) method. In most situations, the hybrid model achieved better results than the LS.

Forecasting stock index based on hybrid artificial neural network models

Forecasting stock index is a crucial financial problem which is recently received a lot of interests in the field of artificial intelligence. In this paper we are going to study some hybrid artificial neural network models. As main result, we show that hybrid models offer us effective tools to forecast stock index accurately. Within this study, we have analyzed the performance of classical models such as Autoregressive Integrated Moving Average (ARIMA), Artificial Neural Network (ANN) model and the Hybrid model, in connection with real data coming from Vietnam Index (VNINDEX). Based on some previous foreign data sets, for most of the complex time series, the novel hybrid models have a good performance comparing to individual models like ARIMA and ANN. Regarding Vietnamese stock market, our results also show that the Hybrid model gives much better forecasting accuracy compared with ARIMA and ANN models. Specifically, our results tell that the Hybrid combination model delivers smaller Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) than ARIMA and ANN models. The fitting curves demonstrate that the Hybrid model produces closer trend so better describing the actual data. Via our study with Vietnam Index, it is confirmed that the characteristics of ARIMA model are more suitable for linear time series while ANN model is good to work with nonlinear time series. The Hybrid model takes into account both of these features, so it could be employed in case of more generalized time series. As the financial market is increasingly complex, the time series corresponding to stock indexes naturally consist of linear and non-linear components. Because of these characteristic, the Hybrid ARIMA model with ANN produces better prediction and estimation than other traditional models.&#x0D;

A hybrid ARIMA–SVM model for the study of the remaining useful life of aircraft engines

In this research, an algorithm is presented for predicting the remaining useful life (RUL) of aircraft engines from a set of predictor variables measured by several sensors located in the engine. RUL prediction is essential for the safety of those aboard, but also to reduce engine maintenance and repair costs. The algorithm combines time series analysis methods to forecast the values of the predictor variables with machine learning techniques to predict RUL from those variables. First, an auto-regressive integrated moving average (ARIMA) model is used to estimate the values of the predictor variables in advance. Then, we use the result of the previous step as the input of a support vector regression model (SVM), where RUL is the response variable. The validity of the method was checked on an extensive public database, and the results compared with those obtained using a vector auto-regressive moving average (VARMA) model. Our algorithm showed a high prediction capability, far greater than that provided by the VARMA model. • A method to forecast the remaining useful life of aircraft engines is proposed. • The predictor variables were obtained from sensors located in the engine. • The proposed method combines ARIMA and SVM models. • Results of our method unsurpassed those obtained using a VARMA model.