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Analyzing Big Data
Published in Stephan S. Jones, Ronald J. Kovac, Frank M. Groom, Introduction to COMMUNICATIONS TECHNOLOGIES, 2015
Stephan S. Jones, Ronald J. Kovac, Frank M. Groom
Time series techniques allow forecasting of the data by isolating and projecting the patterns (trend and seasonality) of past data into the future. A commonly employed time series analysis methodology is the Box–Jenkins method developed by George Box at the University of Wisconsin. It is formally known as ARIMA or autoregressive integrated moving average forecasting. The Box–Jenkins method projects long-term patterns based upon analysis of the series itself at particular influential points of the past. These influential points are plotted and smoothed to remove peaks and valleys in the data by applying 1 and 12-month differencing. This technique may be applied to quickly determine forecasts that are uncomplicated in form or that involve a number of economic variables. In either case, use of this technique enables efficient utilization of other predictive information contained in the data. It offers assurance of obtaining the highest forecasting accuracy possible in terms of the variables on which the forecast is based.
Business modeling and forecasting
Published in Adedeji B. Badiru, Ibidapo-Obe Oye, Babatunde J. Ayeni, Manufacturing and Enterprise, 2018
Adedeji B. Badiru, Ibidapo-Obe Oye, Babatunde J. Ayeni
The Box-Jenkins technique consists of a family of time-series models. It comprises of many different models. These models can be grouped into three basic classes – autoregressive (AR) models, MA models, and autoregressive integrated moving average (ARIMA) models. For many problems in business, engineering, and physical and environmental sciences, the Box-Jenkins technique may be applied to related variables of interest. An analysis may be obtained by considering individual series as components of a multivariate or vector time series and analyzing the series jointly. The Box-Jenkins technique is used to study the relationship among variables. This involves the development of statistical models and methods of analysis that describe the inter relationships among the series.
Descriptive and predictive analytics of agricultural data using machine learning algorithms
Published in Govind Singh Patel, Amrita Rai, Nripendra Narayan Das, R. P. Singh, Smart Agriculture, 2021
Time series analysis designed by George Box and Gwilym-Jenkins together is called Box–Jenkins methodology. The major processes of this method are Selecting a modelFinding optimal parametersBuilding ARIMA modelMaking predictions
Modification of ARL for detecting changes on the double EWMA chart in time series data with the autoregressive model
Published in Connection Science, 2023
Kotchaporn Karoon, Yupaporn Areepong, Saowanit Sukparungsee
The time series is a collection of chronologically organised data. The time series is observed and studied in order to identify its patterns of change and development and forecast its future trend. Time-series data can be divided into two categories: stationary data and non-stationary data. The time-series data collection with stationary data does not show a trend or a seasonal influence. The data collection solely contains random error as a cause of variation, whereas non-stationary time-series data is a time-series data set that exhibits a trend or a seasonal effect. There are other sources of variation in the data set besides just random error. The Box–Jenkins method is currently the most complete and accurate algorithm for analysing and predicting time series data. Methods for measuring timed data are referred to as times series. Autoregression (AR), Moving Average (MA), Autoregressive Moving Average (ARMA), Autoregressive Integrated Moving Average (ARIMA), and Seasonal Autoregressive Integrated Moving-Average (SARIMA) are examples of common types.
A multimodal hybrid stochastic-based deterministic ARFIMA model for the sustainable analysis of COVID-19 pandemic
Published in Waves in Random and Complex Media, 2023
Ayaz Hussain Bukhari, Ejaz Ahmed, Muhammad Asif Zahoor Raja, YangQuan Chen, Muhammad Shoaib
The mathematical representation of the Auto-Regressive Integrated Moving Average (ARIMA) Model was first introduced by Box and Jenkin [50] in their book in 1970 to forecast the future trend consisting of three parameters (p, d, q) also known as the Box Jenkins method. ARIMA uses past values of a series x to build a regression equation with parameters represented by the following equations: where in the series expansion form the above equation can be written as follows: and are autoregressive and moving average parameters. is the representing white noise with mean zero and variance . S Lacroix [51] presented a generalized integer-order definition for positive integers of the function . The nth-order derivative is defined as follows: Legendre used Gamma Symbol for fractional-order derivatives. He expressed the fractional derivative as follows:
Optimal site selection for wind energy: a case study
Published in Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 2022
ARIMA is also known as the Box–Jenkins methodology. For a long time, ARIMA models are used in the many estimate problems. In an ARIMA (p, d, q) model, the future values of variable and past observations are assumed to be a linear function of the random error (Khashei and Bijari 2011). The ARIMA (p, d, q) methodology consists of four steps. Initially, the stationarity test is performed and for this test, autocorrelation function (ACF) and partial autocorrelation function (PACF) graphs are looked at (Box and Jenkins 1976). If it is understood that the data is not stable as a result of a visual examination of ACF and PACF graphics; until the non-stationary data disappears, the process of stabilization is applied by differentiating it. Then, the appropriate parameter (p, d, q) values of the model are determined based on the stationary data after differentiation and its correlogram (Erdogdu 2010). In the second step, the model is created and predicted based on the results obtained from the first step, and then the diagnostic check is performed in the third step. To check if the model fits the data reasonably, it is looked at the values of the prediction in the previous step and checked whether any of the ACF and PACF of the residues individually are statistically significant. If they are not statistically significant, this means that the ARIMA (p, d, q) values are completely random and there is no need to look at another ARIMA (p, d, q) model. In the last stage, estimation is made according to the applied, controlled, and statistically significant ARIMA (p, d, q) model (Erdogdu 2010). In this study, the steps mentioned above are applied for the ARIMA model, and the SPSS program is used in the ARIMA model stage.