Box-Jenkins Autoregressive Integrated Moving Average Research Articles

ARIMA Based Wind Speed Modeling for Wind Farm Reliability Analysis and Cost Estimation

Necessity has compelled man to improve upon the art of tapping wind energy for power generation; an apt reliever of strain exerted on the non-renewable fossil fuel. The power generation in a Wind Farm (WF) depends on site and wind velocity which varies with time and season which in turn determine wind power modeling. It implies, the development of an accurate wind speed model to predict wind power fluctuations at a particular site is significant. In this paper, Box-Jenkins ARIMA (Auto Regressive Integrated Moving Average) time series model for wind speed is developed for a 99MW wind farm in the southern region of India. Because of the uncertainty in wind power developed, the economic viability and reliability of power generation is significant. Life Cycle Costing (LCC) method is used to determine the economic viability of WF generated power. Reliability models of WF are developed with the help of load curve of the utility grid and Capacity Outage Probability Table (COPT). ARIMA wind speed model is used for developing COPT. The values of annual reliability indices and variations of risk index of the WF with system peak load are calculated. Such reliability models of large WF can be used in generation system planning.

Time series analysis of aerosol optical depth over New Delhi using Box–Jenkins ARIMA modeling approach

The present study focuses on the application of stochastic modeling technique in analyzing the future trends of aerosol optical properties. For this, the Box–Jenkins ARIMA (Autoregressive Integrated Moving Average) model has been used for simulating the monthly average Aerosol Optical Depth (AOD550 nm) retrieved from Terra MODIS (Moderate Resolution Imaging Spectroradiometer) over New Delhi, the urban capital of India. The satellite dataset has been collected for a period of ten years from 2004 to 2014. The analysis of autocorrelation function indicates existence of seasonality in the AOD time series. Several seasonal ARIMA models have been generated and their validation has been verified by assessing various estimation parameters, using the Statistical Package for the Social Sciences (SPSS, version 20). After rigorous evaluation of the selected models, the ARIMA (1,0,0)x(0,1,2)12 is identified as the best fit model w.r.t. measures of goodness-of-fit like Stationary R-square (0.530), R-square (0.674), Root Mean Squared Error (0.128); Mean Absolute Error (0.095); Mean Absolute Percentage Error (16.942); and normalized Bayesian Information Criteria (−3.941). The selected models have been further used to forecast AOD values for the year 2014 at 95% level of confidence. However, the ARIMA (1,0,0)x(2,1,1)12 model is found to have minimum forecasting error, calculated as Mean Percentage Error (0.220). As the difference in BIC of both the models is minimal (0.046), so both the models have been considered as best fit models and utilized for prediction of AOD. Satisfactory results have been obtained using the selected ARIMA models, suggesting that a simplistic modeling technique for determining the future values of AOD is feasible.

INTEGRATION OF EXPONENTIAL SMOOTHING WITH STATE SPACE FORMULATION FOR BUS TRAVEL TIME AND ARRIVAL TIME PREDICTION

In recent years, the problem of bus travel time prediction is becoming more important for applications such as informing passengers regarding the expected bus arrival time in order to make public transit more attractive to the urban commuters. One of the popular techniques reported for such prediction is the use of time series analysis. Most of the studies on the application of time series techniques for bus arrival time prediction used Box-Jenkins AutoRegressive Integrated Moving Average (ARIMA) models, which are presently not suited for real time implementation. This is mainly due to the necessity and dependence of ARIMA models on a time series modelling software to execute. Moreover, the ARIMA model building process is time consuming, making it difficult to use for real-time implementations. Alternatively, Exponential Smoothing (ES) methods can be used, as they are easy to understand and implement when compared to ARIMA models. The present study is an attempt in this direction, where the basic equation of ES is used, as the state equation with Kalman filtering to recursively update the travel time estimate as the new observation becomes available. The proposed algorithm of state space formulation of ES with Kalman filtering for bus travel time and arrival time prediction was field tested using 105 actual bus trips data along a particular bus route from Chennai, India. The results are promising and a comparison of the proposed algorithm with ES alone without state space formulation and Kalman filtering has also been performed. An information system based on a webpage for real-time display of bus arrival times has been designed and developed using the proposed algorithm.

Short-term traffic flow prediction using seasonal ARIMA model with limited input data

Accurate prediction of traffic flow is an integral component in most of the Intelligent Transportation Systems (ITS) applications. The data driven approach using Box-Jenkins Autoregressive Integrated Moving Average (ARIMA) models reported in most studies demands sound database for model building. Hence, the applicability of these models remains a question in places where the data availability could be an issue. The present study tries to overcome the above issue by proposing a prediction scheme using Seasonal ARIMA (SARIMA) model for short term prediction of traffic flow using only limited input data. A 3-lane arterial roadway in Chennai, India was selected as the study stretch and limited flow data from only three consecutive days was used for the model development using SARIMA. After necessary differencing to make the input time series a stationary one, the autocorrelation function (ACF) and partial autocorrelation function (PACF) were plotted to identify the suitable order of the SARIMA model. The model parameters were found using maximum likelihood method in R. The developed model was validated by performing 24 hrs. ahead forecast and the predicted flows were compared with the actual flow values. A comparison of the proposed model with historic average and naive method was also attempted. The effect of increase in sample size of input data on prediction results was studied. Short term prediction of traffic flow during morning and evening peak periods was also attempted using both historic and real time data. The mean absolute percentage error (MAPE) between actual and predicted flow was found to be in the range of 4–10, which is acceptable in most of the ITS applications. The prediction scheme proposed in this study for traffic flow prediction could be considered in situations where database is a major constraint during model development using ARIMA.

Applications of AutoRegressive Integrated Moving Average (ARIMA) approach in time-series prediction of traffic noise pollution

The paper analyzes the long-term noise monitoring data using the AutoRegressive Integrated Moving Average (ARIMA) modeling technique. Box-Jenkins ARIMA approach has been adapted to simulate the daily mean LDay (06-22 h) and LNight (22-06 h) in A- and C-weightings in conjunction with single-noise metrics, day-night average sound level (DNL) for a period of 6 months. The autocorrelation function (ACF) and partial autocorrelation function (PACF) have been obtained to find suitable orders of autoregressive (p) and moving average (q) parameters for ARIMA (p, d, q) models so developed for all the single-noise metrics. The ARIMA models, namely, ARIMA(0,0,14), ARIMA(0,1,1), ARIMA(7,0,0), ARIMA(1,0,0) and ARIMA(0,1,14), have been developed as the most suitable for simulating and forecasting the daily mean LDay dBA, LNight dBA, LDay dBC, LNight dBC, and day-night average sound level (DNL) respectively. The performance of the model so developed is ascertained using the statistical tests. The work reveals that the ARIMA approach is reliable for time-series modeling of traffic noise levels.

Maize Area and Production Forecasting in Eastern Region of Madhya Pradesh: An Application of Box-Jenkins ARIMA Model

Maize is an important crop in India. In this study an attempt has been made to forecast the area and production of maize crop in Madhya Pradesh, India. The Madhya Pradesh is one of the traditional and potential maize producing state in the country. Its production and productivity in the recent time call for major concern. Auto Regressive Integrated Moving Average (ARIMA) model have been fitted and projection was made on the basis of the best fitted ARIMA model for acreage and production. Time Series data covering the period of 19901991 to 2011-2012 was used for the Study. The maize area and production forecasts for 2012-13 to 202526 for all the selected districts in the region were made in this study. This projection is important as it helps in framing good policies with respect to relative production, price structure as well as consumption of maize in the region and in the state as a whole. The projection results reflected that maize will play vital role to solve food security problem in the region and in the state in general. Thus, policy makers, stake holders and beneficiaries (farmers) should take necessary steps to check the decline trend in area under maize production without further delay.

Comparative performance of ARIMA and GARCH models in modelling and forecasting volatility of Malaysia market properties and shares

Market properties and shares are important in the field of finance in order to measure the economic growth of a country. These market properties are volatile time series as they have huge price swings in a shortage or an oversupply period. In this study, we use two time series models which are Box-Jenkins Autoregressive Integrated Moving Average (ARIMA) and Generalized Autoregressive Conditional Heterocedasticity (GARCH) models in modelling and forecasting Malaysia property market. The capabilities of ARIMA and GARCH models in modelling and forecasting Malaysia property market will be evaluated by using Akaike's Information Criterion (AIC), Mean Absolute Percentage Error (MAPE) and Root Mean Squared Error (RMSE). It can be concluded that Box-Jenkins ARIMA model perform better compared than GARCH model in modelling and forecasting Malaysia market properties and shares.

Forecasting Malaysian gold using GARCH model

The purpose of the current study is to forecast the prices of Kijang Emas, the official Malaysian gold bullion. Two methods are considered, which are Box-Jenkins Autoregressive Integrated Moving Average (ARIMA) and Generalized Autoregressive Conditional Heteroskedasticity (GARCH). Using Akaike's information criterion (AIC) as the goodness of fit measure and mean absolute percentage error (MAPE) as the forecasting performance measure, the study concludes that GARCH is a more appropriate model. Analysis are carried out by using the E-views software.

The Effect of Community‐Level Unemployment on Preventive Oral Health Care Utilization

To test the hypothesis that high community-level unemployment is associated with reduced use of preventive dental care services by a dentally insured population. The study uses monthly data on population dental visits and unemployment in the Seattle and Spokane areas from 1995 to 2004. Utilization data come from Washington Dental Services. Unemployment data were obtained from the Bureau of Labor Statistics and Washington's Employment Security Department. The study uses a Box-Jenkins Autoregressive Integrated Moving Average (ARIMA) method to measure the association between the variables over time. The approach controls for the effects of autocorrelation, seasonality, and confounding variables. In the Seattle area, an unexpected 10,000 unit increase in the number of unemployed individuals is associated with a 1.24 percent decrease in preventive visits during the month ( p=.0043). In the Spokane area, a similar increase in unemployment is associated with a 5.95 percent decrease in preventive visits ( p=.0326). The findings persist when the independent variable is the number of initial unemployment insurance claims. The analysis suggests that utilization of preventive dental care declines during periods of high community-level unemployment. Community-level unemployment may impede or distract populations from utilizing preventive dental services. The study's findings have implications for insurers, dentists, policy makers, and researchers.

A comparative study of neural network and Box-Jenkins ARIMA modeling in time series prediction

This paper aims to investigate suitable time series models for repairable system failure analysis. A comparative study of the Box-Jenkins autoregressive integrated moving average (ARIMA) models and the artificial neural network models in predicting failures are carried out. The neural network architectures evaluated are the multi-layer feed-forward network and the recurrent network. Simulation results on a set of compressor failures showed that in modeling the stochastic nature of reliability data, both the ARIMA and the recurrent neural network (RNN) models outperform the feed-forward model; in terms of lower predictive errors and higher percentage of correct reversal detection. However, both models perform better with short term forecasting. The effect of varying the damped feedback weights in the recurrent net is also investigated and it was found that RNN at the optimal weighting factor gives satisfactory performances compared to the ARIMA model.

Time series forecasts of international travel demand for Australia

This paper analyses stationary and non-stationary international tourism time series data by formally testing for the presence of unit roots and seasonal unit roots prior to estimation, model selection and forecasting. Various Box–Jenkins Autoregressive Integrated Moving Average (ARIMA) models are estimated over the period 1975(1)–1989(4) for tourist arrivals to Australia from Hong Kong, Malaysia and Singapore. The mean absolute percentage error and root mean squared error (RMSE) are used as measures of forecast accuracy. As the best fitting ARIMA model is found to have the lowest RMSE, this model is used to obtain post-sample forecasts. Tourist arrivals data for 1990(1)–1996(4) are compared with the forecast performance of the ARIMA model for each origin market. The fitted ARIMA model forecasts tourist arrivals from Singapore for the period 1990(1)–1996(4) very well. Although the ARIMA model outperforms the seasonal ARIMA models for Hong Kong and Malaysia, the forecasts of tourist arrivals are not as accurate as in the case of Singapore.

Defense Spending and Export in South Korea: A Causal Analysis

Abstract: The economic effects of defense spending on growth in South Korea is not clear cut. Previous studies have reported mixed findings. Since export has been the main engine of South Korean economic development, I have systematically examined the indirect relationship between defense spending and economic growth via export, employing a Box-Jenkins ARIMA (Autoregressive Integrated Moving Average) causal model. The results of the analysis reveal that an increase in defense expenditures has an immediate dampening effect on export. Thus, reductions in defense spending may lead to an increase in export, which in turn stimulates economic growth. In other words, South Korea may expect some “peace dividend.”

Analysis and interpretation of patterns within and between hydroclimatological time series in an alpine glacier basin

AbstractThis paper explores patterns within and between climatological and hydrological time series from an alpine glacier basin. Time series recorded in the basin of the Haut Glacier d'Arolla over the 1989 ablation season are subdivided into five subperiods. Box‐Jenkins ARIMA (AutoRegressive Integrated Moving Average) and TFN (Transfer Function‐Noise) models are estimated for each of the five subperiods and differences between the models are interpreted in the context of changing glacier hydrology, particularly the changing nature and extent of the glacier drainage network.

Forecasting: Does the Box-Jenkins Method Work Better than Regression?

A difficult exercise, forecasting is key to effective management. Models using time series data are frequently used for forecasting likely values of important variables such as supply and demand. The regression method is the most common, although it involves many critical assumptions that are difficult to satisfy in practice. Efforts to reduce the severity of the assumptions and improve our ability to manipulate data have led to generalized regression and the Box-Jenkins Autoregressive Integrated Moving Average (ARIMA) models. Nanda tests the forecasts from two models in each method, using data on monthly milk procurement by Amul Dairy from January 1965 to December 1975. The regression method produced better forecasts than the Box-Jenkins method.

Stochastic modeling of an industrial activated sludge process

The purpose of this paper is to develop a Box-Jenkins time series transfer function model of the effluent COD using the influent COD, from a sewage treatment process. The data is from an industrial waste treatment plant encompassing a 14-month period. The work was done in 3 steps: (1) Box-Jenkins ARIMA (autoregressive integrated moving average) modeling of the influent COD; (2) ARIMA modeling of the effluent COD; and (3) development of a transfer function model for the waste treatment process. It was found that single difference models best described influent and effluent COD. For the transfer function model, the influent COD had an insignificant effect on the effluent COD.