Related papers: Parameter Estimation of Heavy-Tailed AR Model with…
Time series prediction with missing values is an important problem of time series analysis since complete data is usually hard to obtain in many real-world applications. To model the generation of time series, autoregressive (AR) model is a…
The autoregressive (AR) models are used to represent the time-varying random process in which output depends linearly on previous terms and a stochastic term (the innovation). In the classical version, the AR models are based on normal…
Efficient estimation methods for simultaneous autoregressive (SAR) models with missing data in the response variable have been well-explored in the literature. A common practice is to introduce measurement error into SAR models to separate…
Standard simultaneous autoregressive (SAR) models typically assume normally distributed errors, an assumption often violated in real-world datasets that frequently exhibit non-normal, skewed, or heavy-tailed characteristics. New SAR models…
Data derived from remote sensing or numerical simulations often have a regular gridded structure and are large in volume, making it challenging to find accurate spatial models that can fill in missing grid cells or simulate the process…
A new multivariate integer-valued Generalized AutoRegressive Conditional Heteroscedastic process based on a multivariate Poisson generalized inverse Gaussian distribution is proposed. The estimation of parameters of the proposed…
High-dimensional time series data appear in many scientific areas in the current data-rich environment. Analysis of such data poses new challenges to data analysts because of not only the complicated dynamic dependence between the series,…
Inferring dynamics from time series is an important objective in data analysis. In particular, it is challenging to infer stochastic dynamics given incomplete data. We propose an expectation maximization (EM) algorithm that iterates between…
This work addresses the problem of missing data in time-series analysis focusing on (a) estimation of model parameters in the presence of missing data and (b) reconstruction of missing data. Standard approaches used to solve these problems…
We study the problem of modelling high-dimensional, heavy-tailed time series data via a factor-adjusted vector autoregressive (VAR) model, which simultaneously accounts for pervasive co-movements of the variables by a handful of factors, as…
High-dimensional time series data exist in numerous areas such as finance, genomics, healthcare, and neuroscience. An unavoidable aspect of all such datasets is missing data, and dealing with this issue has been an important focus in…
The Stochastic Approximation EM (SAEM) algorithm, a variant stochastic approximation of EM, is a versatile tool for inference in incomplete data models. In this paper, we review the fundamental EM algorithm and then focus especially on the…
High dimensional Vector Autoregressions (VAR) have received a lot of interest recently due to novel applications in health, engineering, finance and the social sciences. Three issues arise when analyzing VAR's: (a) The high dimensional…
This report presents an Expectation-Maximization (EM) algorithm for estimation of the maximum-likelihood parameter values of constrained multivariate autoregressive Gaussian state-space (MARSS) models. The MARSS model can be written:…
Estimating hidden processes from non-linear noisy observations is particularly difficult when the parameters of these processes are not known. This paper adopts a machine learning approach to devise variational Bayesian inference for such…
We study the problem of robust time series analysis under the standard auto-regressive (AR) time series model in the presence of arbitrary outliers. We devise an efficient hard thresholding based algorithm which can obtain a consistent…
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…
We propose a sparse coefficient estimation and automated model selection procedure for autoregressive (AR) processes with heavy-tailed innovations based on penalized conditional maximum likelihood. Under mild moment conditions on the…
This paper develops a novel two-step estimating procedure for heavy-tailed AR models with non-zero median GARCH-type noises, allowing for time-varying volatility. We first establish the self-weighted quantile regression estimator (SQE)…
Although the standard formulations of prediction problems involve fully-observed and noiseless data drawn in an i.i.d. manner, many applications involve noisy and/or missing data, possibly involving dependence, as well. We study these…