scholarly journals On robust estimation of negative binomial INARCH models

METRON ◽  
2021 ◽  
Author(s):  
Hanan Elsaied ◽  
Roland Fried
Keyword(s):  
Time Series ◽  
Maximum Likelihood ◽  
Robust Estimation ◽  
Negative Binomial ◽  
Scale Parameter ◽  
Real Data ◽  
Count Time Series ◽  
Conditional Mean ◽  
Conditional Maximum ◽  
Methods Of Moments

AbstractWe discuss robust estimation of INARCH models for count time series, where each observation conditionally on its past follows a negative binomial distribution with a constant scale parameter, and the conditional mean depends linearly on previous observations. We develop several robust estimators, some of them being computationally fast modifications of methods of moments, and some rather efficient modifications of conditional maximum likelihood. These estimators are compared to related recent proposals using simulations. The usefulness of the proposed methods is illustrated by a real data example.

scholarly journals INARMA Modeling of Count Time Series

Stats ◽  
2019 ◽  
Vol 2 (2) ◽  
pp. 284-320 ◽  
Author(s):  
Christian H. Weiß ◽  
Martin H.-J. M. Feld ◽  
Naushad Mamode Khan ◽  
Yuvraj Sunecher
Keyword(s):  
Time Series ◽  
Maximum Likelihood ◽  
Model Selection ◽  
Maximum Likelihood Estimation ◽  
Moving Average ◽  
Likelihood Estimation ◽  
Real Data ◽  
Autoregressive Moving Average ◽  
Count Time Series ◽  
The Given

While most of the literature about INARMA models (integer-valued autoregressive moving-average) concentrates on the purely autoregressive INAR models, we consider INARMA models that also include a moving-average part. We study moment properties and show how to efficiently implement maximum likelihood estimation. We analyze the estimation performance and consider the topic of model selection. We also analyze the consequences of choosing an inadequate model for the given count process. Two real-data examples are presented for illustration.

SUPERPOSITIONED STATIONARY COUNT TIME SERIES

2019 ◽  
pp. 1-19
Author(s):  
Yisu Jia ◽  
Robert Lund ◽  
James Livsey
Keyword(s):  
Time Series ◽  
Negative Binomial ◽  
Stationary Sequence ◽  
Time Series Models ◽  
Count Time Series ◽  
Marginal Distributions ◽  
Autocovariance Function ◽  
Basic Properties ◽  
Model Class ◽  
Discrete Uniform

Abstract This paper probabilistically explores a class of stationary count time series models built by superpositioning (or otherwise combining) independent copies of a binary stationary sequence of zeroes and ones. Superpositioning methods have proven useful in devising stationary count time series having prespecified marginal distributions. Here, basic properties of this model class are established and the idea is further developed. Specifically, stationary series with binomial, Poisson, negative binomial, discrete uniform, and multinomial marginal distributions are constructed; other marginal distributions are possible. Our primary goal is to derive the autocovariance function of the resulting series.

scholarly journals On Outliers and Interventions in Count Time Series following GLMs

2014 ◽  
Vol 43 (3) ◽  
pp. 181-193 ◽  
Author(s):  
Roland Fried ◽  
Tobias Liboschik ◽  
Hanan Elsaied ◽  
Stella Kitromilidou ◽  
Konstantinos Fokianos
Keyword(s):  
Time Series ◽  
Parameter Estimation ◽  
Robust Estimation ◽  
Linear Models ◽  
Sequential Testing ◽  
Generalised Linear Models ◽  
Count Time Series ◽  
Different Types ◽  
Robust Parameter ◽  
Robust Parameter Estimation

We discuss the analysis of count time series following generalised linear models in the presence of outliers and intervention effects. Different modifications of such models are formulated which allow to incorporate, detect and to a certain degree distinguish extraordinary events (interventions) of different types in count time series retrospectively. An outlook on extensions to the problem of robust parameter estimation, identification of the model orders by robust estimation of autocorrelations and partial autocorrelations, and online surveillance by sequential testing for outlyingness is provided. 

scholarly journals Model GARCH dengan Pendekatan Conditional Maximum Likelihood untuk Prediksi Harga Saham

2018 ◽  
Vol 3 (2) ◽  
pp. 21
Author(s):  
Cipta Rahmadayanti ◽  
Hasbi Rabbani ◽  
Aniq Atiqi Rohmawati
Keyword(s):  
Time Series ◽  
Maximum Likelihood ◽  
Conditional Maximum Likelihood ◽  
Conditional Maximum

<p>Jual beli saham merupakan salah satu bentuk investasi yang menjanjikan para investor, investasi berkaitan dengan return atau keuntungan yang didapatkan oleh suatu investor atas suatu investasi yang dilakukan terhadap saham tertentu. Untuk mendapatkan nilai return pada beberapa periode kedepan dapat dilakukan prediksi, pada dasarnya prediksi dapat dilakukan dengan menggunakan beberapa metode, namun dengan menggunakan model <em>time series </em>diharapkan menghasilkan prediksi yang baik karna karakteristik dari<em> </em>data saham merupakan data <em>time series</em> yang bergerak kontinu terhadap waktu.<em> </em>Pada penelitian ini digunakan model <em>time series Autoregressive (AR) </em>dengan pendekatan <em>Conditional Maximum Likelihood</em> untuk memprediksi nilai return serta dapat melihat pergerakan harga saham. Nilai parameter yang penting pada model <em>Autoregressive</em> orde 1 adalah . Hasil penaksiran parameter dengan <em>Conditional Maximum Likelihood</em> digunakan untuk memperoleh nilai hasil prediksi. Berdasarkan hasil analisis,  model <em>Autoregressive</em> dengan pendekatan <em>Conditional Maximum Likelihood</em> adalah model yang baik untuk memprediksi return dan harga saham NASDAQ dengan RMSE sebesar 0,0002578. Berdasarkan hasil prediksi model AR(1), maka para investor dapat membuat strategi untuk berinvestasi pada indek saham NASDAQ agar dapat menghasilkan keuntungan.</p>

scholarly journals Change Point Test for the Conditional Mean of Time Series of Counts Based on Support Vector Regression

Entropy ◽  
2021 ◽  
Vol 23 (4) ◽  
pp. 433
Author(s):  
Sangyeol Lee ◽  
Sangjo Lee
Keyword(s):  
Time Series ◽  
Support Vector Regression ◽  
Stock Prices ◽  
Change Point ◽  
Real Data ◽  
Support Vector ◽  
Time Series Of Counts ◽  
Conditional Mean ◽  
Change Point Test ◽  
Scope Of Application

This study considers support vector regression (SVR) and twin SVR (TSVR) for the time series of counts, wherein the hyper parameters are tuned using the particle swarm optimization (PSO) method. For prediction, we employ the framework of integer-valued generalized autoregressive conditional heteroskedasticity (INGARCH) models. As an application, we consider change point problems, using the cumulative sum (CUSUM) test based on the residuals obtained from the PSO-SVR and PSO-TSVR methods. We conduct Monte Carlo simulation experiments to illustrate the methods’ validity with various linear and nonlinear INGARCH models. Subsequently, a real data analysis, with the return times of extreme events constructed based on the daily log-returns of Goldman Sachs stock prices, is conducted to exhibit its scope of application.

scholarly journals Robust Estimation for Bivariate Poisson INGARCH Models

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 367
Author(s):  
Byungsoo Kim ◽  
Sangyeol Lee ◽  
Dongwon Kim
Keyword(s):  
Robust Estimation ◽  
New South ◽  
Estimation Method ◽  
Real Data ◽  
Regularity Conditions ◽  
Density Power Divergence ◽  
Asymptotically Normal ◽  
South Wales ◽  
Power Divergence ◽  
Conditional Maximum

In the integer-valued generalized autoregressive conditional heteroscedastic (INGARCH) models, parameter estimation is conventionally based on the conditional maximum likelihood estimator (CMLE). However, because the CMLE is sensitive to outliers, we consider a robust estimation method for bivariate Poisson INGARCH models while using the minimum density power divergence estimator. We demonstrate the proposed estimator is consistent and asymptotically normal under certain regularity conditions. Monte Carlo simulations are conducted to evaluate the performance of the estimator in the presence of outliers. Finally, a real data analysis using monthly count series of crimes in New South Wales and an artificial data example are provided as an illustration.

scholarly journals Statistical modeling of COVID-19 deaths with excess zero counts

2021 ◽  
Vol 10 (s1) ◽  
Author(s):  
Sami Khedhiri
Keyword(s):  
Time Series ◽  
Negative Binomial ◽  
Forecast Accuracy ◽  
Series Data ◽  
Zero Inflation ◽  
Count Time Series ◽  
Forecast Performance ◽  
Intervention Policy ◽  
Auto Regression ◽  
Zero Counts

Abstract Objectives Modeling and forecasting possible trajectories of COVID-19 infections and deaths using statistical methods is one of the most important topics in present time. However, statistical models use different assumptions and methods and thus yield different results. One issue in monitoring disease progression over time is how to handle excess zeros counts. In this research, we assess the statistical empirical performance of these models in terms of their fit and forecast accuracy of COVID-19 deaths. Methods Two types of models are suggested in the literature to study count time series data. The first type of models is based on Poisson and negative binomial conditional probability distributions to account for data over dispersion and using auto regression to account for dependence of the responses. The second type of models is based on zero-inflated mixed auto regression and also uses exponential family conditional distributions. We study the goodness of fit and forecast accuracy of these count time series models based on autoregressive conditional count distributions with and without zero inflation. Results We illustrate these methods using a recently published online COVID-19 data for Tunisia, which reports daily death counts from March 2020 to February 2021. We perform an empirical analysis and we compare the fit and the forecast performance of these models for death counts in presence of an intervention policy. Our statistical findings show that models that account for zero inflation produce better fit and have more accurate forecast of the pandemic deaths. Conclusions This paper shows that infectious disease data with excess zero counts are better modelled with zero-inflated models. These models yield more accurate predictions of deaths related to the pandemic than the generalized count data models. In addition, our statistical results find that the lift of travel restrictions has a significant impact on the surge of COVID-19 deaths. One plausible explanation of the outperformance of zero-inflated models is that the zero values are related to an intervention policy and therefore they are structural.

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