Box-Jenkins Research Articles

On the Fourier Residual Modification of Arima Models in Modeling Malaria Incidence Rates among Pregnant Women

This work provides a general overview and consideration of Box-Jenkins models for temporal data and its extension known as Fourier residual autoregressive moving average models. We examined the modeling and forecasting of malaria incidence rate during pregnancy at Bishop Shannahan Hospital, Nsukka using Autoregressive Integrated Moving Average (ARIMA) Models propounded by Box and Jenkins. We adoptted the Box-Jenkins methodology to build ARIMA model for malaria incidences during pregnancy for a period of 10 years spanning from January 2006 to December 2016. Among the candidate models considered, ARIMA (3,1,1) was identified to be the most robust based on some model performance measures. The model was further improved upon by incorporating Fourier residual modification on the fitted ARIMA model. The Fourier Residual Autoregressive Moving Average (FARIMA) model obtained yielded improved result. Besides, model evaluation criterion such as Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Mean Bias Error (MBE), Mean Bias Error (MBE), Mean Absolute Scaled Error (MASE), were used to access the models. FARIMA Model out performed ARIMA Model. Several time series plots and tests like augmented dickey fuller test, correlogram, Ljung-Box test for serial correlation of the residuals, etc were carried out in this study to test for stationarity, identify the order of ARIMA model and serial correlation residual respectively.

Using the Box-Jenkins Method to Forecast Sesame Exports in Sudan during the Period 1990-2028

This study uses the Box–Jenkins method to predict sesame exports in Sudan. After analysis discriminating via various statistical tests, it is found that AR MA (5,3,5) model is the best model to measure this phenomenon. This model was used to predict till 2028. The results indicate that the predicted values are less than the real values till 2001. Then the predicted value is bigger.
 The study recommended that the foreign economic relations and to search in how to apply it to help in the marketing of products.

Orta Karadeniz Bölgesi Toprak Sıcaklığının Zaman Serisi Analizi Yöntemi İle Modellenmesi

The aim of this study is to estimate the monthly average soil temperature measured in different layers (5, 10, 20, 50, 100 cm) of the Central Black Sea Region by Box Jenkins (BJ) technique. The monthly average soil temperature values of the years 1969-2013 were analyzed and seasonally adjusted and then the models suitable for these datasets were determined. The projections for 2013-2020 were obtained. The appropriate model for each layer of Samsun, Amasya and Ordu is determined as seasonal autoregression. The determination coefficient (R2) values of these stations are between 0.59-0.96, the standard deviation (RMSE) of the estimation error is between 1.55-4.93 and the mean absolute error (MAE) values are 1.24-4.28 values have changed. The appropriate model for each layer of Tokat and Corum was determined as Seasonal Moving Average. The coefficient of determination (R2) of these stations is between 0.83-0.95 and the standard deviation (RMSE) of the estimation error is between 1.79-4.68 and the mean absolute error (MAE) is 0.03-3.91 values have changed. As a result of the study, it was seen that time series models yielded successful results in the monthly average soil temperature calculations in the Central Black Sea Region provinces.

Forecasting Electricity Consumption Using SARIMA Method in IBM SPSS Software

Forecasting is a prediction of future values based on historical data. It can be conducted using various methods such as statistical methods or machine learning techniques. Electricity is a necessity of modern life. Hence, accurate forecasting of electricity demand is important. Overestimation will cause a waste of energy but underestimation leads to higher operation costs. Univesity Tun Hussein Onn Malaysia (UTHM) is a developing Malaysian technical university, therefore there is a need to forecast UTHM electricity consumption for future decisions on generating electric power, load switching, and infrastructure development. The monthly UTHM electricity consumption data exhibits seasonality-periodic fluctuations. Thus, the seasonal Autoregressive Integrated Moving Average (SARIMA) method was applied in IBM SPSS software to predict UTHM electricity consumption for 2019 via Box-Jenkins method and Expert Modeler. There were a total of 120 observations taken from January year 2009 to December year 2018 to build the models. The best model from both methods is SARIMA(0, 1, 1)(0, 1, 1)12. It was found that the result through the Box-Jenkins method is approximately the same with the result generated through Expert Modeler in SPSS with MAPE of 8.4%.

Assessment of prediction performances of stochastic and conceptual hydrological models: monthly stream flow prediction in northwestern Algeria

Determining the link between rainfall and flow for a watershed is one of the most imperative problems and challenging tasks faced by hydrologists and engineers. Conceptual and Box-Jenkins hydrological models represent suitable tools for this purpose in circumstance of data Scarce and climate complexity. This research consists in a comparative study between conceptual models and Box-Jenkins model, namely, GR2M, ABCD, and the autoregressive moving average (ARIMA) which has a numerical design. The three models were applied to three catchments located in the north-west of Algeria. Basins have been selected according to the availability of long-time series of hydrological and climatic data (more than 30 years) to calibrate parsimonious models, taking into account the climatic variables and the stochastic behavior of the natural stream flow. Overall, the conceptual models perform similarly; whereas the results show that the GR2M model performed better than the ABCD in the validation stage, the stochastic model shows better results as opposed to conceptual models in the case of the Mellah Wadi which presents high permeability in its behavior. This is due to the simplicity of the model needed for data (only runoff data) and the ability of the stochastic model to produce stream flow in complex catchments. Such circumstance could be caused by different motivations. On the one hand, the diverse number of model parameters that make the ABCD the less parsimonious approach, with four parameters to be calibrated. On the other hand, the inability of the ABCD and the ARIMA model to capture and describe the groundwater processes, important for the cases study. Moreover, the validation period includes a large drought period, started in the late 1980s, which makes difficult model adaptation to different hydrological regimes.

Analysing and Forecasting Share Price Index in Malaysia

Wilkie investment model is a stochastic investment model that was built by Wilkie in 1984 and was updated in 1995. The model building objective is forecasting. Box-Jenkins method was the basic structure of Wilkie model. It involves various type of forecasting model. Some model handle stationary time series such as autoregressive moving average (ARMA) model while some of them handle non-stationary time series such as autoregressive integrated moving average (ARIMA) model. There are four sub-models in the Wilkie model which is retail price index model, share dividend yield model, share dividend index model and Consols yield model. In this paper, the Wilkie share price model [4] was apply to Malaysia data in analysing and forecasting FTSE Bursa Malaysia KLCI share price index for 36 month ahead from November 2015 to October 2018. Monthly historical data from January 1996 to October 2015 are use as the base. We use ARIMA model to forecast the share price index in Malaysia. ARIMA(0,1,2) model was chosen as the best fit forecasting model. Through forecasting, we are able to evaluate the performance of the share price index in Malaysia.

Selection of Prediction Method of Basic Statistical Work Parameters of N.V. Sklifosovsky Research Institute for Emergency Medicine of the Moscow Healthcare Department

Background The most important part of the state social and economic policy is optimization of the healthcare system, where the loss of public health leads to economic damage. Against this background, forecasting the work of medical institutions is the basis for the successful development of healthcare, despite the fact that the healthcare system, indicators and standards of medical and social welfare are still not stable, and a clear development strategy for the shortand long-term period has not been worked out. Aim of study Determining the most optimal method for predicting the work of a medical institution, based on identification of the main trends in the time series when constructing a model of the dependence of parameters or determining the behavior of data as a stochastic series (i.e. modeling random processes and random events with some random error).Material and methods To predict the main statistical indicators of N.V. Sklifosovsky Research Institute for Emergency Medicine based on a retrospective analysis, data were used that were submitted to the City Bureau of Medical Statistics and entered into official reporting forms (form № 30, approved by Goskomstat of the Russian Federation dated September 10, 2002, № 175): the number of hospitalized patients and mortality rates in inpatient and intensive care units. To select the optimal methodology for the experimental forecast model, data were used for the period from 1991 to 2016. Indicators for 2017 were taken as control values.Results As a result of the comparison of several methods (moving averages, least squares approach, Brown model, Holt–Winters method, autocorrelation model, Box–Jenkins method) as applied to the work of N.V. Sklifosovsky Research Institute for Emergency Medicine, the Holt–Winters model was chosen as the most appropriate one for the data characteristics.Findings 1. When using methods of moving averages, least squares, Box-Jenkins, as well as Brown model and autocorrelation, the forecast result is not always influenced by strictly straight-line indicators of the time series, due to the heterogeneity of the time series and the presence of outliers (often found in a medical institution providing emergency care), which lead to a significant decrease in the reliability of forecasting. 2. The application of the Holt–Winters model, which takes into account the exponential trend (the trend of time series indicators) and additive season (periodic fluctuations observed in the time series), is most suitable for processing statistical data and forecasting for long-term, medium-term and short-term periods taking the specifics of a hospital providing emergency care into account. 3. The choice of the optimal method for predicting the work of a medical institution, based on the identification of the main trends in the time series, taking most of the features in the modeling of random processes and events into account, allowed to reduce the relative forecast error.

EUR/RON EXCHANGE RATE PREDICTION BASED ON BOX-JENKINS TECHNIQUE

The aim of this study consists in analyzing the importance of the exchange rate forecast using the Box-Jenkins models, also known as Auto Regressive Integrated Moving Average (ARIMA) models. The first part of the paper presents the main research in this field, which can be classified in two categories (studies applying classical methods, such as Box-Jenkins models and studies which rely on sophisticated prediction tools), and summarizes the main findings of some of the studies applying Box-Jenkins models. In the second part of the paper we performed a EUR/RON exchange rate analysis and forecasting, based on testing several AR, MA and ARMA candidate processes, in order to find out the best fitting model specification. We adopted the following strategy: i) an initial time series had been used for testing various model specifications, identify the best performing one and making a forecast of the EUR/RON exchange rate; ii) after comparing the accuracy of this forecast with the real level recorded by the exchange rate at end of May 2018, we conducted a second forecast, for the period May 2019 – November 2019. The initial time series employed has daily frequency and covers the timeframe July 4, 2005 – December 5, 2017, while the second time series used covers the period July 4, 2005 – May 6, 2019. The empirical findings have passed the goodness-of-fit tests and show a good predictive power. The first forecast performed for a six month period (December 2017 – May 2018) has indicated a slow pace, persistent increase of the EUR/RON exchange rate, which was confirmed by the expectations of market participants (financial analysts, banks’ research departments). The second forecast, which covers the period May 2019 – November 2019, indicates a similar rising trend and the ongoing depreciation of the national currency.

PERAMALAN JUMLAH PENUMPANG PESAWAT TERBANG DI PINTU KEDATANGAN BANDAR UDARA INTERNASIONAL PATTIMURA AMBON DENGAN MENGGUNAKAN METODE ARIMA BOX-JENKINS

The Autoregressive Integrated Moving Average (ARIMA) model is often used to forecast time series data. In the era of globalization, rapidly progressing times, one of them in the field of transportation. The aircraft is one of the transportation that the residents can use to support their activities, both in business and tourism. The objective of the research is to know the forecasting of the number of passengers of airplanes at the arrival gate of Pattimura Ambon International Airport using ARIMA Box-Jenkins method. The best model selection is ARIMA (0, 1, 3) because it has significant parameter value and MSE value is smaller.

Measures of lower body function as predictors of mortality among Mexican Americans aged 75 and older

We use data from California, where 13% of US births occur, to address two questions arising from efforts in the first decade of this century to avoid stillbirths before 25 6/7 weeks of gestation (i.e., in the periviable period). First, did stillbirths decline in the first decade of this century? Second, if stillbirths did decline, did periviable live births increase simultaneously? Answering these questions is important given that periviable infants represent less than 1% of live births but account for roughly 40% of infant mortality and 20% of hospital-based obstetric costs in the United States.We constructed 240 monthly conception cohorts, starting with that conceived in January 1991, from 9,880,536 singleton pregnancies that reached the 20 0/7 week of gestation. We used time-series design and Box-Jenkins methods that address confounding by autocorrelation, including secular trends and seasonality to answer our questions.We detected a downward shift in stillbirths in April 2007 that coincided with an upward shift in periviable live births.Our findings imply that, since 2007, fewer Californians than expected from history and from the size of conception cohorts reaching 20 0/7 weeks of gestation have had to contend with the sequelae of stillbirths, but more than expected likely have had to contend with those of periviable births.

Exploring multidimensional attributes of high-quality dietary patterns and their association with mortality to inform the Dietary Guidelines for Americans

We use data from California, where 13% of US births occur, to address two questions arising from efforts in the first decade of this century to avoid stillbirths before 25 6/7 weeks of gestation (i.e., in the periviable period). First, did stillbirths decline in the first decade of this century? Second, if stillbirths did decline, did periviable live births increase simultaneously? Answering these questions is important given that periviable infants represent less than 1% of live births but account for roughly 40% of infant mortality and 20% of hospital-based obstetric costs in the United States.We constructed 240 monthly conception cohorts, starting with that conceived in January 1991, from 9,880,536 singleton pregnancies that reached the 20 0/7 week of gestation. We used time-series design and Box-Jenkins methods that address confounding by autocorrelation, including secular trends and seasonality to answer our questions.We detected a downward shift in stillbirths in April 2007 that coincided with an upward shift in periviable live births.Our findings imply that, since 2007, fewer Californians than expected from history and from the size of conception cohorts reaching 20 0/7 weeks of gestation have had to contend with the sequelae of stillbirths, but more than expected likely have had to contend with those of periviable births.

Seasonal forecasting yield of wheat in India by feed-forward neural networks

Wheat is the best principal food-grain of India and is the major food source of millions of Indians, awfully in the western, northern, north-eastern and north-western parts of the country. It has more in proteins, minerals, vitamins, fiber and carbohydrates and affords stable diet for human being. This paper demonstrations that a relative training is supported to explore the forecasting of yield per hectare of Wheat (in Kg) in India by means of Feed-Forward neural networks model and Box-Jenkins methods, which are surrounded by those forecasting models best magnificently practical ,functional and execute into practice. The yield of wheat data is collected from 1966 to 2012 for analysis of this model. The yield of wheat in India depends on two seasons like Kharif and Rabi. This training of yield of wheat examines the presentation of neural networks models and the results of which will be associated with those acquired by Box-Jenkins method. The Final conclusion of this paper is Feed-Forward neural networks models are better and superior than Box-Jenkins models.

Forecasting of red meat and milk prices of Turkey with using the Box-Jenkins models

Zaman serisi analizi, ekonometride geleceğe yönelik tahminleme yapmada sıkça kullanılan bir istatistik analiz yöntemdir. Bu çalışmada, Türkiye’de 2010-2018 yıllarına ait kırmızı et ve süt üretici fiyatları zaman serisi analizi ile çözümlenerek, aynı ürünlerin fiyatlarının 2019-2023 yılları için tahmin edilmesi amaçlanmıştır. Çalışma materyalini; Dünya Gıda ve Tarım Örgütü (FAO), Ulusal Kırmızı Et Konseyi (UKON) ve Ulusal Süt Konseyi (USK)’nden elde edilen 2010-2018 yıllarına ait resmi kırmızı et ve süt üretici fiyatları oluşturmuştur. Bu veriler yardımıyla 2019-2023 yılları için kırmızı et fiyatları ARIMA (1.1.0) modeli ve süt fiyatları ARIMA (2.1.2) modeli kullanılarak tahmin edilmiştir. Çalışma sonucunda, 2023 yılı sonunda kırmızı et fiyatlarının (karkas) dogrusal artış ile ortalama 33,93 TL/kg, süt fiyatlarının ise 2,14 TL/lt olacağı tahmin edilmiştir. Sonuç olarak, zaman serisi analizinin geleceğe yönelik olarak hayvansal ürün fiyatlarının tahmininde kullanılabileceği ancak devamlı olarak güncellenmesi gerektiği ve hem üretici hem de tüketicilerin geleceğe yönelik yapacağı planlamalarda yol gösterici olabileceği kanısına varılmıştır.

Forecasting Monthly Maximum Temperatures in Kerbala Using Seasonal ARIMA Models.

Weather forecasting is an important issue in meteorology and scientific research.In this research, the Seasonal Auto Regressive.Integrated Moving Average.(ARIMA) model which is based on Box-Jenkins method was adopted to build the forecasting model. The max. Monthly temperature data for Kerbala city for the period (Jan.1980 to Dec.2016) was employed. The autocorrelation and partial autocorrelation functions for time series data from years 1980 to 2015 were used to identify the most appropriate orders of the ARIMA models. The validation test of these models were performed using the monthly max. Temperature of the year 2016. To calculate the model's accuracy and compare among them, statistical criteria such as MAE, RMSE, MAPE, and R2 were used. The model (2, 1, 2) × (1, 1, 1)12 gave the most accurate results and used to forecast the monthly max. Temperature for the period (2017 to 2021) for study region.

Forecasting the wind power generation using Box–Jenkins and hybrid artificial intelligence

PurposeThe purpose of this paper is to forecast wind power generation in an area through different methods, and then, recommend the most suitable one using some performance criteria.Design/methodology/approachThe Box–Jenkins modeling and the Neural network modeling approaches are applied to perform forecasting for the last 12 months.FindingsThe results indicated that among the tested artificial neural network (ANN) model and its improved model, artificial neural network-genetic algorithm (ANN-GA) with RMSE of 0.4213 and R2 of 0.9212 gains the best performance in prediction of wind power generation values. Finally, a comparison between ANN-GA and ARIMA method confirmed a far superior power generation prediction performance for ARIMA with RMSE of 0.3443 and R2 of 0.9480.Originality/valuePerformance of the ARIMA method is evaluated in comparison to several types of ANN models including ANN, and its improved model using GA as ANN-GA and particle swarm optimization (PSO) as ANN-PSO.

ARIMA Model Selection for Composite Stock Price Index in Indonesia Stock Exchange

Composite Stock Price Index (CSPI) can be used as a reflection of the national economic condition of a country because it is an indicator to know the development the capital market in a country. Therefore, the movement in the future needs to be forecast. This study aims to build a model for the time series forecasting of Indonesia Composite Index (ICI) using the ARIMA model. The data used is the monthly data of ICI in Indonesia Stock Exchange (IDX) from January 2000 until December 2017 as many as 216 data. The method used in this research is the Box-Jenkins method. The autocorrelation (ACF) and partial autocorrelation function (PACF) are used for stationary test and model identification. The maximum estimated likelihood is used to estimate the parameter model. In addition, to select a model then used Akaike’s Information Criterion (AIC). Ljung-Box Q statistics are used for diagnostic tests. In addition, to show the accuracy of the model, we use Root Mean Squared Error (RMSE), Mean Absolute Error (MAE) and Mean Absolute Percentage Error (MAPE) and the most appropriate model is ARIMA (0, 1, 1).

Forecasting with Feed Forward Neural Network model and adaptive simulated annealing algorithm (Case: world crude oil prices that was published by OPEC)

Today, crude oil trading industry became an important industry in the world, it was caused by highly fuel oil consumption. The price of crude oil has a changing price trend, it makes the prediction of crude oil in the coming periods to be challenging. Various methods can use to forecast price of crude oil, it is using ARIMA Box-Jenkins model with OLS method to estimate the parameter, but this method has several assumptions that must be complete. Overtime, many methods were develop, one of them is artificial neural network can be combine with various parameter optimization methods such as Adaptive Simulated Annealing algorithm. Adaptive Simulated Annealing algorithm is an optimization method it was inspired by the process of crystallization, the advantages of this algorithm has a running time faster than similar algorithms. The combination of artificial neural networks and Adaptive Simulated Annealing algorithms can be used to model the historical data without requiring assumptions in the analysis. Based on the analysis on this research, the best model is obtained FFNN 2-5-1 with MAPE value of 1.0042%.

The forecasting of the exports and imports of paper and paper products of Turkey using Box-Jenkins method

In this study, it is aimed to determine the most suitable time series models with Box-Jenkins method, which is the most widely used in prediction studies. Export and import values have been predicted by 2020 with the most suitable models. The data used in this study were obtained from the Turkey Statistical Institute. Data are monthly data covering from January 2003 to December 2014. Sum of Squared Errors (SSE) and Mean Squared Error (MSE) criteria were taken into consideration when selecting the best Box-Jenkins models. Also, in order to test the success of forecasting of the models, Root mean Error Square (RMSE), Mean Absolute Error (MAE) and Mean Absolute Percentage Error (MAPE) were used. As a result of the analyzes, it was determined that the most suitable models for export and import data were ARIMA (2,1,0) (0,0,1)12 and ARIMA(3,1,2)(1,0,1)12. It was predicted that the rate of exports meeting imports in paper and paper products of Turkey will be approximately 0.86 in 2020.

Is China's air pollution control policy effective? Evidence from Yangtze River Delta cities

Abstract: China is currently facing the threat of serious air pollution and has adopted a series of governance policies. However, the fact that PM2.5 indicator in some regions often reached far higher than the official threshold since 2015 has reflected that China's current Air Quality Index system for measuring and evaluating air quality is still not perfect. Therefore, this paper extended the current air quality indicator system officially used by China. Using improved Entropy-weighted Factor Method and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) Method, we calculated the air quality scores of 26 cities in China's most economically developed region - the Yangtze River Delta region based on their daily average concentration numbers of main air pollutants from February 2015 to January 2018. Based on the air quality calculation result, we further studied the effectiveness of air pollution control policies of this region by using the Box-Jenkins Model with fuzzy strategy parameter adjustment. Our findings are: the pollution control policy is more effective to Shanghai, Jiangsu and Zhejiang. The air quality score of Shanghai has improved by 51.07% compared with its level before the policy. Meanwhile, the air quality improvement in Zhejiang province has shown the characteristics of “Campaign-style Governance” right before the G20 Summit, especially that in Hangzhou, the host city of the Summit. On the other hand, maybe due to late start of air pollution control programs, the cities of Anhui province haven't shown obvious improvements in air quality, and some cities have even seen deterioration in air quality scores during our study period.

APLIKASI METODE ARIMA BOX-JENKINS UNTUK MERAMALKAN KASUS DBD DI PROVINSI JAWA TIMUR

The Box-Jenkins forecasting method is one of the time series forecasting methods. This method uses past values as dependent variables and independent variables are ignored. Box-Jenkins (ARIMA) method has advantages that can be used on non-stationary data, can be used on all data patterns including seasonal data patterns so this method can be used to predict cases of DHF in East Java Province. This research was conducted to determine the best model with seasonal ARIMA forecasting model and also to analyze the result of DHF case forecasting in East Java Province. The analysis result shows that the best model for DHF case in East Java Province is ARIMA (1,1,2)(2,1,1)12. The best model has fulfilled the test requirement that is parameter significance test and diagnostics check. Forecasting results show the number of DHF cases in 2017-2018 will experience an upward trend. The total number of DHF cases in 2017 was 14,277 cases and increased to 22,284.54 DHF cases in 2018. The forecasting results showed that the highest peak of DHF cases occurred in January 2017 with 1,914.22 cases and then decrease in the next month until the lowest case occurred in October with 768.46. The forecast for 2018 also shows that the highest DHF cases occurred in January with 3455.55 and declined to the lowest in October with 1126.49 cases. MAPE value in the forecast is 43.51%. The MAPE value indicates that the forecasting is good enough, adequate and feasible to use.