A characterization of ARMA and Fractional ARIMA models with infinitely divisible innovations

ARMA Model Development and Analysis for Global Temperature Uncertainty

Temperature uncertainty models for land and sea surfaces can be developed based on statistical methods. In this paper, we developed a novel time series temperature uncertainty model which is the Auto-regressive Moving Average (ARMA)(1, 1) model. The model was developed for observed annual mean temperature anomaly X(t) which is a combination of true (latent) global anomaly Y (t) for a year (t) and normal variable w(t). The uncertainty is taken as the variance of w(t) which was decomposed to Land Surface Temperature (LST) uncertainty, Sea Surface Temperature (SST) uncertainty, and the correspond…

Why Are the ARIMA and SARIMA not Sufficient

The autoregressive moving average (ARMA) model takes the significant position in time series analysis for a wide-sense stationary time series. The difference operator and seasonal difference operator, which are bases of ARIMA and SARIMA (Seasonal ARIMA), respectively, were introduced to remove the trend and seasonal component so that the original non-stationary time series could be transformed into a wide-sense stationary one, which could then be handled by Box-Jenkins methodology. However, such difference operators are more practical experiences than exact theories by now. In this paper, we i…

创新ARIMA模型在水供应网络中用于预测压力变化的应用。诺贾（坎特布雷亚，西班牙）案例研究

Innovation ARIMA models application to predict pressure variations in water supply networks with open-loop control. Case study in Noja (Cantabria, Spain)

本研究创新性地将ARIMA模型应用于水供应网络压力管理，通过分析水头损失预测P3压力，提升网络压力调控效率与系统可靠性。

K-ARMA Models for Clustering Time Series Data

We present an approach to clustering time series data using a model-based generalization of the K-Means algorithm which we call K-Models. We prove the convergence of this general algorithm and relate it to the hard-EM algorithm for mixture modeling. We then apply our method first with an AR($p$) clustering example and show how the clustering algorithm can be made robust to outliers using a least-absolute deviations criteria. We then build our clustering algorithm up for ARMA($p,q$) models and extend this to ARIMA($p,d,q$) models. We develop a goodness of fit statistic for the models fitted to …