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Groundwater Hydrology
Published in Mohammad Karamouz, Azadeh Ahmadi, Masih Akhbari, Groundwater Hydrology, 2020
Mohammad Karamouz, Azadeh Ahmadi, Masih Akhbari
Considering the fact that a time series does not necessarily meet these conditions, a proper transformation is usually performed to generate the time series with the two above conditions. This has been usually achieved by differencing, which is necessary for ARIMA models, which is very powerful for describing a stationary and nonstationary time series, and the process is called an autoregressive integrated moving average process. The nonseasonal form of ARIMA models of order (p, d, q) is expressed as: () φ(B)(1−B)dzt=θ(B)εt
Comparative Forecasts of Confirmed COVID-19 Cases in Botswana Using Box-Jenkin's ARIMA and Exponential Smoothing State-Space Models
Published in Amit Kumar Tyagi, Ajith Abraham, Recurrent Neural Networks, 2023
Ofaletse Mphale, V. Lakshmi Narasimhan
The accurate forecasting of infectious diseases had become prevalent for ensuring economic and the humanitarian welfare of every country. Recently, Botswana had implemented various mitigation strategies to curtail the spread of COVID-19 infections in order to “flatten the curve” of the pandemic. This study employs ARIMA and exponential smoothing state space models (ETS) to forecast confirmed cases in Botswana for the next 60-day period. This is critical to better understand COVID-19 disease and provide support for strategic decisions in order to better manage the disease in Botswana. This chapter compares performances of the ARIMA model and the ETS model based on their forecasting using accuracy metrics of root mean squared error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE). In addition, the models are compared using metrics of execution time, memory utilization, and the Ljung-Box test for residual analysis. The study shows that the ARIMA model outperforms the ETS model in generating more reliable and volatile forecasts. This is depicted by the lowest measures of MAE, RMSE, and MAPE. Furthermore, the ARIMA model had depicted more stationary residuals the forecast errors when compared to ETS model forecasts. However, interestingly, the ETS model outperforms the ARIMA model by requiring less execution time and less memory utilization in generating forecasts. In drawing summary of the best-performing model, we conclude that the ARIMA model is such a model, which gives a higher precision across different evaluation metrics in contrast to the ETS model. However, despite the good performance of the ARIMA model, results suggest that reliability and volatility of the ARIMA model can still be improved and optimized to reduce the model execution time and its memory utilization.
Launch II
Published in Walter R. Paczkowski, Deep Data Analytics for New Product Development, 2020
ARIMA is an acronym for AutoRegressive Integrated Moving Average. This is a family of models that has as special cases some of the models I discussed above. In fact, an econometric model is also a special case of an even wider ARIMA model called a transfer function model. The basics of an ARIMA are discussed in the Appendix to this chapter.
Traffic violation analysis using time series, clustering and panel zero-truncated one-inflated mixed model
Published in International Journal of Injury Control and Safety Promotion, 2022
Zahra Rezaei Ghahroodi, Samaneh Eftekhari Mahabadi, Sara Bourbour, Helia Safarkhanloo, Shokoufa Zeynali
ARIMA (Autoregressive Integrated Moving Average) family of models are mathematical models of the autocorrelation in a time series which describe the behaviour of a variable in terms of its past values. These models are widely used in almost all fields of transportation with marked success; examples of such applications are Lau et al. (2009), Masten (2007), and Smith et al. (2002). Lau et al. (2009) investigated the effectiveness of hourly carbon monoxide concentrations on the traffic pattern. In this study, hourly, monthly and seasonal mean carbon monoxide concentration data are collected from a roadside air monitoring station in Hong Kong over 7-years. Using a SARIMA (Seasonal Autoregressive Integrated Moving Average) model shows that the daily traffic cycle strongly influences concentrations and the hourly carbon monoxide concentrations resemble the traffic pattern of the area and tend to be lower in the summer. In Masten (2007), time series analyses were used to determine whether six states which upgraded to primary enforcement laws experienced changes in night-time and daytime safety belt use based on proxy estimates from fatal crash-involved vehicle occupants.
Transfer function models for forecasting maritime passenger traffic in Greece under an economic crisis environment
Published in Transportation Letters, 2021
Eirini Aivazidou, Ioannis Politis
In fact, the ARIMA models with explanatory variables are based on the transfer function model proposed by Box and Jenkins (1976), further taking into consideration the seasonal polynomials, as well as both the simple and the seasonal difference factors (Ďurka and Pastoreková 2012). In particular, an ARIMA model is denoted as ARIMA(p,d,q)(P,D,Q)s, where p/P constitute, respectively, the orders of the autoregression/seasonal autoregression, d/D the orders of the difference/seasonal difference, q/Q the orders of the moving average/seasonal moving average, while s refers to the number of seasonal periods. In more detail, the autoregression part of the model suggests that the dependent variable is linearly regressed on its own lagged values, while the moving average part indicates that the dependent variable constitutes a linear regression of the current and all prior error terms. Given that the ARIMA models require stationary data, the differencing part (i.e. integration) of the model allows for the elimination of any non-stationarity.
A Method to Predict Random Time-Delay of Networked Control System
Published in IETE Journal of Research, 2022
The basic idea of ARIMA is to make non-stationary time series become stationary series by multiple difference operations, and the number of difference is d. ARMA model with p and q parameters is used to model stationary series. The original sequence is obtained by inverse transformation. The ARIMA prediction equation is as follows. where is the sample value of the sequence, and are the model parameters, and is independent normally distributed white noise.