Related papers: Why Are the ARIMA and SARIMA not Sufficient

Understanding the time-varying structure of complex temporal systems is one of the main challenges of modern time series analysis. In this paper, we show that every uniformly-positive-definite-in-covariance and sufficiently short-range…

In the study of complex physical and biological systems represented by multivariate stochastic processes, an issue of great relevance is the description of the system dynamics spanning multiple temporal scales. While methods to assess the…

The aim this study is discussed on the detection and correction of data containing the additive outlier (AO) on the model ARIMA (p, d, q). The process of detection and correction of data using an iterative procedure popularized by Box,…

Variance estimation is important for statistical inference. It becomes non-trivial when observations are masked by serial dependence structures and time-varying mean structures. Existing methods either ignore or sub-optimally handle these…

Continuous-time autoregressive moving average (CARMA) processes have recently been used widely in the modeling of non-uniformly spaced data and as a tool for dealing with high-frequency data of the form $Y_{n\Delta}, n=0,1,2,...$, where…

Time series prediction covers a vast field of every-day statistical applications in medical, environmental and economic domains. In this paper we develop nonparametric prediction strategies based on the combination of a set of 'experts' and…

Real time model based control of high dimensional nonlinear systems presents severe computational challenges. Conventional reduced order model control relies heavily on expert tuning or parameter adaptation and seldom offers mechanisms for…

We propose a seasonal AR model with time-varying parameter processes in both the regular and seasonal parameters. The model is parameterized to guarantee stability at every time point and can accommodate multiple seasonal periods. The time…

Symbolic regression via genetic programming is a flexible approach to machine learning that does not require up-front specification of model structure. However, traditional approaches to symbolic regression require the use of protected…

Time series of matrix-valued data are increasingly available in various areas including economics, finance, social science, among others. These data may shed light on the inter-dynamical relationships between two sets of attributes, for…

Anomaly Detection in multivariate time series is a major problem in many fields. Due to their nature, anomalies sparsely occur in real data, thus making the task of anomaly detection a challenging problem for classification algorithms to…

In this work, we offer a theoretical analysis of two modern optimization techniques for training large and complex models: (i) adaptive optimization algorithms, such as Adam, and (ii) the model exponential moving average (EMA).…

Stochastic optimization naturally arises in machine learning. Efficient algorithms with provable guarantees, however, are still largely missing, when the objective function is nonconvex and the data points are dependent. This paper studies…

An accurate forecast of electric demand is essential for the optimal design of a generation system. For district installations, the projected lifespan may extend one or two decades. The reliance on a single-year forecast, combined with a…

With advances in optical sensor technology, heterogeneous camera systems are increasingly used for high-resolution (HR) video acquisition and analysis. However, motion transfer across multiple cameras poses challenges. To address this, we…

This work is devoted to functional ARMA$(p, q)$ processes and approximating vector models based on functional PCA in the context of prediction. After deriving sufficient conditions for the existence of a stationary solution to both the…

The renewable energies prediction and particularly global radiation forecasting is a challenge studied by a growing number of research teams. This paper proposes an original technique to model the insolation time series based on combining…

Many phenomena, both natural and human-influenced, give rise to signals whose statistical properties change under time translation, i.e., are nonstationary. For some practical purposes, a nonstationary time series can be seen as a…

In this paper, we address the problem of adaptive learning for autoregressive moving average (ARMA) model in the quaternion domain. By transforming the original learning problem into a full information optimization task without explicit…

In this paper we propose a recursive online algorithm for estimating the parameters of a time-varying ARCH process. The estimation is done by updating the estimator at time point $t-1$ with observations about the time point $t$ to yield an…