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Time Series Analysis for Modeling the Transmission of Dengue Disease
Published in Dinesh C. S. Bisht, Mangey Ram, Recent Advances in Time Series Forecasting, 2021
A.M.C.H. Attanayake, S.S.N. Perera
After the time series plot is examined, stationarity of the series can be tested by applying the Augmented Dickey Fuller test (ADF), Kwiatkowski–Phillips–Schmidt–Shin (KPSS) test or Phillips-Perron (PP) test. These tests are capable of detecting whether a series is a stationary series or not. The null hypothesis for the ADF and PP tests is “series is non-stationary” whereas for the KPSS test, it is “stationary”. If the original series is not stationary, then it can be transformed into a stationary one by differencing the data or using some transformation. The autocorrelation function (ACF) and partial autocorrelation function (PACF) of a stationary series should be inspected when determining the order of processes in the AR and/or MA model or mixed ARIMA model. The most appropriate model is then selected based on accuracy measures such as Akaike Information Criteria (AIC), Corrected Akaike Information Criteria (AICc) and Bayesian Information Criteria (BIC) measures. In model diagnostic checking, residuals of the selected model followed a white noise which is drawn from a constant mean and variance. If the assumptions are not held, then another model needs to be investigated; otherwise, the model can be used to make predictions after validation (Box & Jenkins, 1970). The mean absolute percentage error (MAPE) is less than 10%, revealing that the model is appropriate in forecasting (Lewis, 1982). MAPE criteria for model evaluation is summarized in Table 2.1.
Time series features and models
Published in Elizabeth Ann Maharaj, Pierpaolo D'Urso, Jorge Caiado, Time Series Clustering and Classification, 2019
Elizabeth Ann Maharaj, Pierpaolo D'Urso, Jorge Caiado
Partial autocorrelations are used to measure the relationship between xt and xt−k, with the effect of the other time lags, 1, 2, …, k-1 removed. It is also useful to plot the partial autocorrelation function (PACF) Partial autocorrelation function (PACF) because it, together with the plot of the ACF, can help inform one on a possible appropriate model that can be fitted to the time series. Refer to any of the references mentioned in Section 2.1 for more details on the ACF and PACF including their sampling distributions which enable the determination of the significance limits. PACF
Autocorrelation and Time Series Analysis
Published in Nong Ye, Data Mining, 2013
The lag-k partial autocorrelation function (PACF) coefficient measures the autocorrelation of lag-k, which is not accounted for by the autocorrelation of lags 1 to k−1. PACF for lag-1 and lag-2 are given next (Yaffee and McGee, 2000): ()PACF(1)=ρ1 ()PACF(2)=ρ2−ρ121−ρ12.
Comparative analysis of deep learning and classical time series methods to forecast natural gas demand during COVID-19 pandemic
Published in Energy Sources, Part B: Economics, Planning, and Policy, 2023
The Box-Jenkins approach to modeling ARIMA processes includes four main stages: (1) identification of the model, (2) parameter estimation and selection, (3) validating the model, and (4) forecasting. The autocorrelation function (ACF) and partial autocorrelation function (PACF) of the data are used to find the and order of the ARIMA model. Besides, statistical measures such as Akaike Information Criteria (AIC, or corrected AIC(AICc)) and Bayesian information criterion (BIC) are used to determine the optimal parameter of the ARIMA model (Pradeep et al. 2021):
Effect of management on water quality and perception of ecosystem services provided by an urban lake
Published in Lake and Reservoir Management, 2021
Laura Costadone, Mark D. Sytsma, Yangdong Pan, Mark Rosenkranz
Data analysis was performed using R Statistical Software (R Development Core Team 2020). The seasonal Mann–Kendall test was used to detect the presence of positive or negative trends in the monthly average values of the water quality data. Median slope of all ranked seasonal regression slopes was calculated to estimate the magnitude of trend (Helsel and Hirsch 1992). The mean value of each water quality parameter that showed a significant monotonic trend was used as the dependent variable in the generalized least-square (GLS) model to assess the influence of management interventions on water quality. Independent variables included surface aluminum application, hypolimnetic aeration, and drawdown events. The partial autocorrelation function (PACF) was used to identify the order of the autoregressive model. A chi-squared test of independence was used to test whether people’s perception of water quality was linked to the length of residence time.
Integration of time series forecasting in a dynamic decision support system for multiple reservoir management to conserve water sources
Published in Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 2018
Hamed Zamani Sabzi, Shalamu Abudu, Reza Alizadeh, Leili Soltanisehat, Naci Dilekli, James Phillip King
The ARIMA models originally were developed by Box and Jenkins (1976). The ARIMA model is a generalized version of the autoregressive moving average (ARMA) model. The represents the non-seasonal model, in which the parameters are the number of autoregressive lags, the order of differencing, and the number of moving average lags in the ARIMA model. For both developed monthly and daily models in this paper, Box and Jenkins’ three defined stages of identification, estimation, and diagnostic check were followed and examined. Evaluation of the autocorrelation function (ACF) and partial autocorrelation function (PACF) leads to exploring the system behavior through time dependency and selecting the most appropriate parameters (p and q) for the time series model (Abudu et al. 2010; Abudu, King, and Bawazir 2011; Sabzi 2016; Sabzi, King, and Abudu 2017).