3 research outputs found
Parameter Estimation of Heavy-Tailed AR Model with Missing Data via Stochastic EM
The autoregressive (AR) model is a widely used model to understand time
series data. Traditionally, the innovation noise of the AR is modeled as
Gaussian. However, many time series applications, for example, financial time
series data, are non-Gaussian, therefore, the AR model with more general
heavy-tailed innovations is preferred. Another issue that frequently occurs in
time series is missing values, due to system data record failure or unexpected
data loss. Although there are numerous works about Gaussian AR time series with
missing values, as far as we know, there does not exist any work addressing the
issue of missing data for the heavy-tailed AR model. In this paper, we consider
this issue for the first time, and propose an efficient framework for parameter
estimation from incomplete heavy-tailed time series based on a stochastic
approximation expectation maximization (SAEM) coupled with a Markov Chain Monte
Carlo (MCMC) procedure. The proposed algorithm is computationally cheap and
easy to implement. The convergence of the proposed algorithm to a stationary
point of the observed data likelihood is rigorously proved. Extensive
simulations and real datasets analyses demonstrate the efficacy of the proposed
framework.Comment: This is a companion document to a paper that is accepted to IEEE
Transaction on Signal Processing 2019, complemented with the supplementary
materia
A Rolling Optimized Nonlinear Grey Bernoulli Model RONGBM(1,1) and application in predicting total COVID-19 infected cases
The Nonlinear Grey Bernoulli Model NGBM(1, 1) is a recently developed grey
model which has various applications in different fields, mainly due to its
accuracy in handling small time-series datasets with nonlinear variations. In
this paper, to fully improve the accuracy of this model, a novel model is
proposed, namely Rolling Optimized Nonlinear Grey Bernoulli Model RONGBM(1, 1).
This model combines the rolling mechanism with the simultaneous optimization of
all model parameters (exponential, background value and initial condition). The
accuracy of this new model has significantly been proven through forecasting
Vietnam's GDP from 2013 to 2018, before it is applied to predict the total
COVID-19 infected cases globally by day.Comment: Accepted paper at the 2020 International Congress of Grey Systems and
Uncertainty Analysis (GSUA
Autoregressive-Model-Based Methods for Online Time Series Prediction with Missing Values: an Experimental Evaluation
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 basic and widely used one, which assumes that each observation
in the time series is a noisy linear combination of some previous observations
along with a constant shift. To tackle the problem of prediction with missing
values, a number of methods were proposed based on various data models. For
real application scenarios, how do these methods perform over different types
of time series with different levels of data missing remains to be
investigated. In this paper, we focus on online methods for AR-model-based time
series prediction with missing values. We adapted five mainstream methods to
fit in such a scenario. We make detailed discussion on each of them by
introducing their core ideas about how to estimate the AR coefficients and
their different strategies to deal with missing values. We also present
algorithmic implementations for better understanding. In order to
comprehensively evaluate these methods and do the comparison, we conduct
experiments with various configurations of relative parameters over both
synthetic and real data. From the experimental results, we derived several
noteworthy conclusions and shows that imputation is a simple but reliable
strategy to handle missing values in online prediction tasks