Box-Jenkins Research Articles

Forecasting USA GDP Base on ARIMA Model

Since the international tendency is more serious and complex today, GDP as the standard of evaluating economic final output has been paid more attention. GDP is the market value of all final goods and services produced within a country in a given period of time. In this paper, Box-Jenkins method is used to build ARIMA model for forecasting American GDP from 2000 to 2010. The most appropriate model for USA GDP is ARIMA (1, 1, 2). At last, this paper uses the model to forecast American GDP for next a few years. According to the forecasting plot, the trend decreases slowly, which means that GDP will decrease in several future years. In the case, America can take action like increasing job opportunities, encouraging consumption immediately to prevent the decreasing trend. The significant meaning of forecasting GDP is to let countries notice the possible future trend of the whole country’s economy and change policies in time to make the situation better instead of being unprepared to face problems.

Application of Time Series Analysis in Modelling an Integrated Moving Average for Predicting Caesarean Sections Births

Purpose: Periodic variations in caesarean sections incidences at the University of Cape Coast Hospital is currently unclear and the model that can best represent its movement is unknown. This study sought to model and predict the monthly incidence of caesarean sections at the hospital.
 Methods: The study employed a monthly periodicity of 115 time-series data sourced from District health information management systems Two on caesarean section births at the University of Cape Coast Hospital over a 9-year period. The auto regressive integrated moving average models of the classical Box-Jenkins methods of Time Series Analysis were used to analyse the data. Analysis was performed in EViews 12 and R (version 4.0.4)
 Findings: There were six non-seasonal tentative candidate models for the hospital. The best fit model had an autoregressive integrated moving average with a first-order autoregressive and a second-order moving average. The findings revealed an overall rising trend in the incidence of caesarean section rates in the hospital over the study period with an average of 30.54% per month. This is expected to increase to over 40% per month over the next five-year period of August 2021 to July 2026 according to projections.
 Conclusion: The best fit model can be used to forecast the expected number of caesarean section births.
 Recommendations: Clinicians should be trained to improve their skills in the use of instruments in deliveries as well as in the safe conduct of vaginal breech deliveries.

Analysis of Air Pollution (SO2) at Some Point of Congestion in DKI Jakarta

Background: Air pollution is the entry or inclusion of energy substances from other components into the air by humans so that air quality drops to a certain level which causes the air to not meet the requirements. This study aims to determine concentration levels of particulates (PM10, PM25), sulfur dioxide (SO2), carbon monoxide (CO), ozone (O3), and nitrogen dioxide (NO2) at several congestion points in Daerah Khusus Ibukota (DKI) Jakarta. Method: The research location based on the purposive sampling method was carried out at 5 congestion points in DKI Jakarta namely Bundaran Hotel Indonesia (HI), Kelapa Gading, Jagakarsa, Lubang Buaya, and Kebon Jeruk. The data used in the process of forming the model using the Box-Jenkins method and analyzed manually, so this process can be done using ARIMA Forecasting. Results: Based on the time series of hourly data, which was calculated on average into daily data, the concentration of PM10, PM25, SO2, CO, O3, and NO2 from January to October 2021 has decreased from the previous months at several congestion points in DKI. Conclusion: The conclusion of this study is the decreased concentration of PM10, PM25, SO2, CO, O3, and NO2 at several points in DKI Jakarta, so it is recommended to the Government and the Community make efforts/activities to maintain the healthy air quality in DKI Jakarta.

Using Time Series Models and Neural Networks to Predict the Sales of Motor Oils in Iraq

Time series are the basis for statistical forecasting through building models that depend as a basis in economic analysis, and the most important of these models are Box-Jenkins models, which depends on the interpretation of the relationship between autocorrelation and partial autocorrelation, and when compared with the Artificial Neural Network (ANN) methodology which is considered as one of the new important means in building models, analyzing, evaluating data, forecasting and controlling it without referring to a common statistical model or method to pre-diagnose the behavior of the phenomenon, where the data is processed to reach the best model. This leads to the least possible number of errors and is close to reality and can be used in most cases. One of the goals of time series analysis is to obtain an accurate description of the time series, build a model to explain its behavior, and use the results for the purpose of predicting the series’ behavior in the future, and to achieve this, it requires an analytical study of time series models based on statistical and computer methods.

Tracking the trajectory of an object in a noisy environment with unknown statistics: A novel robust Kalman filter residue-based approach

A novel robust Kalman filter (KF)-based controller design approach is proposed to accurately track a specified trajectory under unknown stochastic disturbance, known deterministic disturbance, and measurement noise. The system is nonlinear and is approximated by a piecewise-linear dynamic model. The Box–Jenkins model is an augmented model of the signal and the disturbance, is non-controllable and observable, while the signal model is controllable and observable. An emulator-based two-stage identification is employed to obtain an accurate system model needed to design the robust controller. The system and its KF are identified, and the signal and output errors are estimated. From the identified models, the signal, its KF, the disturbance model, and the whitening filter are all obtained using balanced model reduction techniques. It is shown that the signal model is a transfer matrix description relating the system output and KF residual, and the residual is the whitened output error. The disturbance model is identified by inverse filtering. A new combined feedforward–feedback controller is designed and implemented using an internal model of the reference driven by both the error between the reference and the signal estimate, and by the feedforwarded reference signal. The proposed scheme was successfully evaluated on a simulated autonomously guided drone.

Expectations of non-COVID-19 deaths during the pre-vaccine pandemic: a process-control approach

BackgroundDebate over “social distancing” as a response to the pandemic includes the claim that disrupting clinical and public health programming dependent on human-to-human contact increased non-COVID-19 deaths. This claim warrants testing because novel pathogens will continue to emerge. Tests, however, appear frustrated by lack of a convention for estimating non-COVID-19 deaths that would have occurred had clinical and public health programming during the pre-vaccine pandemic remained as efficacious as in the pre-pandemic era. Intending to hasten the emergence of such a convention, we describe and demonstrate “new-signal, prior-response expectations” suggested by research and methods at the intersection of epidemiology and process control engineering.MethodsUsing German data, we estimate pre-pandemic public health efficacy by applying Box-Jenkins methods to 271 weekly counts of all-cause deaths from December 29 2014 through March 8 2020. We devise new-signal, prior-response expectations by applying the model to weekly non-COVID-19 deaths from March 9 2020 through December 26 2020.ResultsThe COVID-19 pandemic did not coincide with more non-COVID-19 deaths than expected from the efficacy of responses to pre-pandemic all-cause deaths.ConclusionsNew-signal, prior-response estimates can contribute to evaluating the efficacy of public health programming in reducing non-COVID-19 deaths during the pre-vaccine pandemic.

A novel indicator of selection in utero.

Selection in utero predicts that population stressors raise the standard for how quickly fetuses must grow to avoid spontaneous abortion. Tests of this prediction must use indirect indicators of fetal loss in birth cohorts because vital statistics systems typically register fetal deaths at the 20th week of gestation or later, well after most have occurred. We argue that tests of selection in utero would make greater progress if researchers adopted an indicator of selection against slow-growing fetuses that followed from theory, allowed sex-specific tests and used readily available data. We propose such an indicator and assess its validity as a dependent variable by comparing its values among monthly birth cohorts before, and during, the first 10 months of the COVID-19 pandemic in Sweden. We apply Box-Jenkins methods to 50 pre-pandemic birth cohorts (i.e., December 2016 through January 2020) and use the resulting transfer functions to predict counterfactual values in our suggested indicator for selection for ten subsequent birth cohorts beginning in February 2020. We then plot all 60 residual values as well as their 95% detection interval. If birth cohorts in gestation at the onset of the pandemic lost more slow-growing fetuses than expected from history, more than one of the last 10 (i.e. pandemic-exposed) residuals would fall below the detection interval. Four of the last 10 residuals of our indicator for males and for females fell below the 95% detection interval. Consistent with selection in utero, Swedish birth cohorts in gestation at the outset of the COVID-19 pandemic included fewer than expected infants who grew slowly in utero.

Predicting Long Term Prices of Nifty Index using Linear Regression and ARIMA: A comparative study

Stocks are traded continuously in the financial market, creating huge time series data. Stock market time series is very volatile and highly complex to model. There are many methods to forecast a time series. This study predicts and compares the performance of two statical methods, linear regression, and ARIMA also referred to as the Box Jenkins method, which stands for Autoregressive Integrated Moving Average, is a robust time series forecasting technique used frequently by researchers. Simple linear regression is generally assumed unsuitable for non-linear stock time series data. However, a literature gap exists in comparing linear regression and the ARIMA method for forecasting stock prices. Hence, this study compares the ARIMA and linear regression methods to forecast stock prices using daily and weekly NIFTY data. Further, this study also experiments using a different length of time series, namely 1-year and 2-year data. The result shows that ARIMA outperformed regression on daily and weekly data when the test for 1 year of data. When 2-year data is taken, linear regression outperformed ARIMA on both daily and weekly data. Hence, the linear regression model and ARIMA are sensitive to input parameters such as the number of days for training and forecasting. An automated method or algorithm could improve the robustness of the model. Further, as stock price data is non-linear, machine learning algorithms such as neural networks and support vector regression can be more suitable for prediction.

A Comparison of a Radial Basis Function Neural Network with other Methods for Estimating Missing Values in Univariate Time Series

Missing values in the time-series data set have an impact on the correct decision-making in the future. Since complete data helps to obtain high accuracy in the estimation process, the reason for missing values is a malfunction of the measuring device or an error in the data entry process by the person. The research aims to compare the radial basis function methods with other methods to estimate missing values in univariate time series data. the simulation method was used to compare the methods to estimate the missing values, and that was used the Box-Jenkins model AR(1) once with the value of and once with the value of and with different sample sizes (60,100,300), assuming four percentages of missing from data values are missing at random MAR (5%,10%,15%,20%). The accuracy of the estimation of the methods was evaluated by using the standard of accuracy, the mean sum of squares error (MSE). from the results obtained using simulation, it was found that the(RBF) method is the best method for estimating the missing values in both values, in all sizes, and all loss ratios because it produces the lowest value of the average square error compared to other methods.
 
 Paper type: Research paper

Determination of The Best Box-Jenkins’ Seasonal Model to Inflows of Reservoir of Bekhme Dam

Prediction of water inflow to a reservoir is of great interest in the policy of the reservoir operation throughout the year. When significant amounts of inflow series entering to the reservoir are nondeterministic events, the utilization of stochastic models to check the reliability of the recorded data and forecast the future events become preferable. One of the most powerful and widely used methodology for forecasting time series is the class of models called the Box-Jenkins models. In this study, time series analysis was applied to records of 69 monthly mean inflows to Bekhme reservoir, in the northern part of Iraq, for the water year period from 1933 to 2006. Nine multiplicative seasonal models were fitted to this series; these were the seasonal autoregressive integrated (SARI) (1, 1, 0) × (1, 1, 0)12, (2, 1, 0) × (1, 1, 0)12, and (1, 1, 0) × (2, 1, 0)12 models, the seasonal autoregressive integrated moving average (SARIMA) (1, 1, 1) × (1, 1, 1)12, (2, 1, 2) × (1, 1, 1)12, and (1, 1, 1) × (2, 1, 2)12 models, and the seasonal integrated moving average (SIMA) (0, 1, 1) × (0, 1, 1)12, (0, 1, 2) × (0, 1, 1)12, and (0, 1, 1) × (0, 1, 2)12 models. The unconditional sum of squares method was used to estimate the parameters of the models and to compute the sum of squared errors for each one. It was found that the best model which corresponded to the minimum sum of squared errors was the SIMA (0, 1, 1) × (0, 1, 1)12 model. The estimated moving average parameters of this model were 0.378 and 0.953 for both θ and Θ respectively. The adequacy of this model was checked by plotting the normalized cumulative periodogram which does not indicate nonrandomness of the residuals. Forecasts of monthly inflow for the period from October, 2002, to September, 2006 were graphically compared with observed inflow for the same period and since agreement was very precise, adequacy of the selected model was confirmed.

Modeling and Forecasting Somali Economic Growth Using ARIMA Models

The study investigated the empirical role of past values of Somalia’s GDP growth rates in its future realizations. Using the Box–Jenkins modeling method, the study utilized 250 in-sample quarterly time series data to forecast out-of-the-sample Somali GDP growth rates for fourteen quarters. Balancing between parsimony and fitness criteria of model selection, the study found Autoregressive Integrated Moving Average ARIMA (5,1,2) to be the most appropriate model to estimate and forecast the trajectory of Somali economic growth. The study sourced the GDP growth data from World Bank World Development Indicators (WDI) for the period between 1960 to 2022. The study results predict that Somalia’s GDP will, on average, experience 4 percent quarterly growth rates for the coming three and half years. To solidify the validity of the forecasting results, the study conducted several ARIMA and rolling window diagnostic tests. The model errors proved to be white noise, the moving average (MA) and Autoregressive (AR) components are covariances stationary, and the rolling window test shows model stability within a 95% confidence interval. These optimistic economic growth forecasts represent a policy dividend for the government of Somalia after almost a decade-long stick-and-carrot economic policies between strict IMF fiscal disciplinary measures and World Bank development investments on target projects. The study, however, acknowledges that the developments of current severe droughts, locust infestations, COVID-19 pandemic, internal political, and security stability, and that the active involvement of international development partners will play a crucial role in the realization of these promising growth projections.

Development and Investigation of a Synthetic Inertia Algorithm

In this article, we present a synthetic inertia (SI) algorithm that allows for the simulation of the inertia response of a traditional generator to an electrical power system. To obtain the algorithm, detailed dynamic calculations were performed using a large real-system dynamic model in Siemens PSS/E modeling packages (PSS/E). Output error (OE), autoregressive moving average model with exogenous inputs (ARMAX), and Box–Jenkins (BJ) models of parametric identification were used to obtain the SI algorithm. The dynamic calculation results such as active power output, frequency variation in the presence of the active power deficit, surplus, and short circuit in the power system were used to compare the algorithm accuracy with comparable generator results. For this purpose, the power system stabilizer (PSS) and the turbine governor were not evaluated to obtain the most accurate possible active power change due to the characteristics of the generator. The errors were evaluated by using the models to determine the error estimates for the correlation coefficient (Ryŷ), root mean square deviation (RMSE), and coefficient of determination (R2). Based on the obtained results, we established that the OE mathematical model should be used, as it is more efficient compared to the ARMAX and BJ models.

Modeling of Climatic Variables using Stochastic Approaches in Sudan

The climatic variables take a significant role in agricultural process and irrigation management because we need to know all changes related to the climate which absolutely will be affected agricultural yield. For this purpose, the ARIMA models were suggested in this study for modeling daily average temperature, relative humidity, and solar radiation variables related to five main meteorological stations (Wad Madani, Khartoum, Al Gadaref, Al Damazin, and Dongola) in Sudan. The daily variables were obtained from the period 2013-to 2020 years. Time series analysis methods are used for estimating and modeling the climatic variables using ARIMA (Autoregressive Integrated Moving Average Models) which are called Box Jenkins models. For modeling purposes, linear stochastic models were used to estimate future values of daily variables. The Augmented Dickey-Fuller test (ADF) was applied to the time series to check the stationarity at 1%, 5%, and 10% confidence levels. The time series of variables were stationarity and without trend. Diagnostic checks were used for checking models and selecting the best models from the autocorrelation (ACF) and partial autocorrelation (PACF) function graphs. The best models were selected according to the adjusted R2, Standard error (S.E), Akaike information criterion (AIC), and Bayesian information criterion (BIC) values. The best results were observed in ARIMA (1,0,1) and (1,0,2) which can be effective for predicting future values. The ARIMA models obtained satisfactory results for temperature, relative humidity, and solar radiation variables. So, this study might be extremely helpful for agricultural engineers to achieve all the processes related to agricultural practices.

Inflation Forecasting In East Java Using Autoregressive Integrated Moving Average Method

Inflation is an economic event that often occurs even though it is not wanted. Based on data from Badan Pusat Statistik in 2015-2020 inflation in East Java was 3.08%, 2.74%, 4.04%, 2.86%, 2.12%, 1.44%. From these data, it can be seen that inflation data is fluctuating. Therefore it is necessary to control inflation because high and unstable inflation can have a negative impact on the socio-economic conditions of the community. In addition, it also makes it difficult for the government to determine future policies. Seeing the importance of controlling inflation, it is necessary to study to predict the inflation rate in the future. One of the studies/methods to predict that is often used is the Autoregressive Integrated Moving Average (ARIMA) method or also known as the Box-Jenkins method. The ARIMA method is a method that is easy to use because it is flexible in following existing data patterns and has high accuracy and tends to have a small error value because of the detailed process. From the analysis results, the best ARIMA (p,d,q) model is the ARIMA model (2,1,1) with an AIC value of 76.77. The results of forecasting with the ARIMA model (2,1,1) respectively are 0.2593698, 0.1892990, 0.1340639, 0.1368309, 0.1572021, 0.1642381, 0.1598897, 0.1557251, 0.1556074, 0.1570151, 0.1576092, 0.1573511, 0.1570423, and 0.1570111.

Forecasting the exchange rate of Nigerian Naira to United State’ Dollar using ARIMA-GARCH Model

In order to model and forecast exchange rates in both developed and emerging countries, majority of time series analysts have employed various technical and fundamental approaches, the forecast outcome differs depending on the approach chosen or implemented. In this view, this study is about hybridization of Autoregressive Integrated Moving Average (ARIMA) with Generalized Autoregressive Conditional Heteroscedastic (GARCH) model in forecasting exchange rate using monthly data of the Nigerian Naira against the U.S. Dollar for the period of January 2002 to February 2020. The stationarity of the exchange rate series is examined using unit root test of Augmented Dickey Fuller (ADF) test and Kwaitkowski-Philips-Schmidt-Shin (KPSS) which showed that the series is non stationary. To make the exchange rate series stationary, the data was transformed by first differencing and appropriate ARIMA models were obtained using Box-Jenkins method. ARIMA (0,1,1) and ARIMA(0,1,2) models were selected using AIC criteria and the residuals of these models were found to be serially correlated and heteroscedastic; hence the need for the hybridization of ARIMA with GARCH model. Therefore ARIMA models were hybridized with GARCH(1,1) to form ARIMA(0,1,1)-GARCH(1,1) and ARIMA(0,1,2)-GARCH(1,1). The results of forecast performance indicates that the best model is ARIMA(0,1,1)–GARCH(1,1) which has the lowest Root Means Square Error (RMSE) and Mean Absolute Error( MAE).

A Comparative Study of Autoregressive Integrated Moving Average and Artificial Neural Networks Models

In this study, the forecasting capabilities of nonlinear models as Artificial Neural Networks and linear ARIMA models were compared. The comparison was conducted using the daily data of Nigeria’s All Share Index for 11 years. The empirical findings revealed ARIMA (1,1,2) model as the best fit for Nigeria’s All Share Index among other Box Jenkins models. This was supported by the most fit statistic test. Also, ANN model with three units in the hidden layer, two lags and the learning rate equal to 0.1, returned as the best fit for the Nigeria All Share Index forecasting. Furthermore, while comparing the performance of the two models, the RMSE of the ARIMA model equivalent to 0.0136 is higher than the RMSE of the ANN model (0.0048), indicating the efficiency of the ANN model. Thus, we can conclude from the above statistics that the ANN model is more efficient. As a result, the study recommends taking advantage of the high capacity of artificial neural networks as a forecasting technique in other fields, such as medical research, genetics research, industrial research, energy, and military research.

Forecasting time trends of fatal motor vehicle crashes in Iran using an ensemble learning algorithm

Objective This study aimed to introduce the random forest (RF) method as a valuable tool for short-term crash frequency prediction. Besides, the study compares the forecast efficiency of the RF model with the classical seasonal autoregressive integrated moving average (SARIMA) model in the multivariate time-series analysis of crash counts. Methods To this end, fatal accidents reported by the police and intercity traffic flow extracted from the loop detectors were aggregated in intercity highways at the country’s level monthly from Farvardin 1395 to Mordad 1400. The first 55 data points were used as the training sample, and the remaining ten months were considered the test sample. The Box-Jenkins and random forest machine learning methods were employed for short-term crash frequency prediction. The mean absolute percentage error (MAPE) criterion was utilized to compare the forecast accuracy of the developed models. Results The performance of the random forest model (MAPE = 2.6) with the exogenous variables of traffic flow, crash year, and month outperformed the best SARIMA ( 1 , 0 , 0 ) ( 1 , 0 , 0 ) 12 model (MAPE = 5.7) with traffic flow as the regressor. Conclusions This study suggests that the random forest as an ensemble learning algorithm is a better crash prediction tool compared to the classical Box-Jenkins method, accounting for the non-linear dependencies in crash count time-series. Besides, the results illustrate that the multivariate SARIMA (SARIMAX) model significantly outperforms its univariate counterpart, accounting for the simultaneous impacts of exogenous variables.

A Novel Interval Type-2 Fuzzy System Identification Method Based on the Modified Fuzzy C-Regression Model.

In this article, a novel interval type-2 Takagi-Sugeno fuzzy c -regression modeling method with a modified distance definition is proposed. The modified distance definition is developed to describe the distance between each data point and the local type-2 fuzzy model. To improve the robustness of the proposed identification method, a modified objective function is presented. In addition, different from most previous studies that require numerous free parameters to be determined, an interval type-2 fuzzy c -regression model is developed to reduce the number of such free parameters. Furthermore, an improved ratio between the upper and lower weights is proposed based on the upper and lower membership function with each input data, and the ordinary least-squares method is adopted to establish the type-2 fuzzy model. The Box-Jenkins model and two numerical models are given to illustrate the effectiveness and robustness of the proposed results.

A Novel Model Predictive Controller for Distributed Generation in Isolated Microgrids—Part I: Development and Parameterization of the Data-Driven Predictive Model

In a low-voltage islanded microgrid, the distribution line impedance and relatively large power angle may lead to active and reactive power coupling during voltage and frequency control actions, which cause errors for conventional droop control at interfacing inverters of distributed generation (DG) units. To overcome this issue, in this two-part article, a novel model predictive controller for DGs is proposed to regulate voltage and frequency at the point of common coupling in isolated microgrids. In Part 1 of the article, a data-driven predictive model is developed and parameterized by system identification approach using nonlinear least square (NLS) method. Four NLS optimization algorithms (Gauss–Newton (GN), adaptive GN, Levenberg–Marquardt, and trust region reflective)] are evaluated and GN is chosen as the best performing algorithm. To initialize the iteration for NLS, the Backcast technique is chosen after comparing with Zero and Estimate techniques. Two optimization methods, “simulation” and “prediction” focus, are considered; and the prediction focus shows higher prediction accuracy and faster convergence, and the ability to avoid the necessity of data prefiltering by introducing a built-in weighted filter in the objective function. The polynomial input–output Box–Jenkins model is chosen as the model structure. The model incorporates distribution line parameters into the control algorithm and allows a wider variation of power angle without initiating nonlinearity. Therefore, it can substantially reduce the controller size and complexity, and widen the controller's operational range. The model is further implemented in the proposed model predictive controller in Part 2 of the article.

A STUDY ON FORECASTING THE IMPACT OF COVID-19 ON EMERGENCY SERVICE IN A PUBLIC HOSPITAL

The COVID-19 pandemic has seriously threatened human life all over the world since the first quarter of 2020. Hospitals have fought on the frontlines against this threat. The aim of this study is to predict the number of monthly emergency service patients for a public hospital. In particular, the impact of the COVID-19 pandemic on the number of emergency service patients was examined. While the data set for the period January 2012- June 2021 (114 months) is used in the analyses, two different data sets were created for the Box- Jenkins (B-J) and Gray Prediction approaches. Then, the number of monthly emergency service patients was predicted using the SARIMA model, GM (1,1) and TGM. In the analyses, while examining the long-term trend of the number emergency services patients’ using the SARIMA model, GM (1,1) and TGM were used to focus on the COVID-19 period. The findings suggest that the TGM has the most successful results in terms of evaluation criteria.