scholarly journals A Monte Carlo Simulation Study on the Power of Autocorrelation Tests for ARMA Models

2019 ◽  
Vol 16 (3) ◽  
pp. 59-67
Author(s):  
Zachary Wenning ◽  
Emily Valenci
Keyword(s):  
Time Series ◽  
Monte Carlo ◽  
Goodness Of Fit ◽  
Arma Model ◽  
Small Sample ◽  
Arma Models ◽  
Real World Data ◽  
Data Set ◽  
Monte Carlo Simulation Study ◽  
Portmanteau Tests

It is often the case when assessing the goodness of fit for an ARMA time series model that a portmanteau test of the residuals is conducted to assess residual serial correlation of the fitted ARMA model. Of the many portmanteau tests available for this purpose, one of the most famous and widely used is a variant of the original Box-Pierce test, the Ljung-Box test. Despite the popularity of this test, however, there are several other more modern portmanteau tests available to assess residual serial autocorrelation of the fitted ARMA model. These include two portmanteau tests proposed by Monti and Peña and Rodríguez. This paper focuses on the results of a power analysis comparing these three different portmanteau tests against different fits of ARMA - derived time series, as well as the behavior of the three different test statistics examined when applied to a real-world data set. We confirm that for situations in which the moving average component of a fitted ARMA model is underestimated or when the sample size is small, the portmanteau test proposed by Monti is a viable alternative to the Ljung-Box test. We show new evidence that the Peña and Rodríguez may also be a viable option for testing for residual autocorrelation for data with small sample sizes. KEYWORDS: Time Series; Monte Carlo; ARMA Models; Power; Simulation; Autocorrelation Tests; Portmanteau Tests; Monti; Ljung-Box; Peña and Rodríguez

scholarly journals Mixed Portmanteau Test for Diagnostic Checking of Time Series Models

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Sohail Chand ◽  
Shahid Kamal
Keyword(s):  
Time Series ◽  
Monte Carlo ◽  
Goodness Of Fit ◽  
Model Building ◽  
Main Idea ◽  
Dependence Structure ◽  
Time Series Models ◽  
Goodness Of Fit Tests ◽  
Diagnostic Checking ◽  
Portmanteau Tests

Model criticism is an important stage of model building and thus goodness of fit tests provides a set of tools for diagnostic checking of the fitted model. Several tests are suggested in literature for diagnostic checking. These tests use autocorrelation or partial autocorrelation in the residuals to criticize the adequacy of fitted model. The main idea underlying these portmanteau tests is to identify if there is any dependence structure which is yet unexplained by the fitted model. In this paper, we suggest mixed portmanteau tests based on autocorrelation and partial autocorrelation functions of the residuals. We derived the asymptotic distribution of the mixture test and studied its size and power using Monte Carlo simulations.

scholarly journals Inferences for Weibull parameters under progressively first-failure censored data with binomial random removals

2020 ◽  
Vol 9 (1) ◽  
pp. 47-60
Author(s):  
Samir K. Ashour ◽  
Ahmed A. El-Sheikh ◽  
Ahmed Elshahhat
Keyword(s):  
Monte Carlo ◽  
Censored Data ◽  
Real Data ◽  
Unknown Parameters ◽  
Data Set ◽  
Monte Carlo Simulation Study ◽  
Squared Error Loss Function ◽  
Bayes Estimates ◽  
Monte Carlo Techniques ◽  
Credible Intervals

In this paper, the Bayesian and non-Bayesian estimation of a two-parameter Weibull lifetime model in presence of progressive first-failure censored data with binomial random removals are considered. Based on the s-normal approximation to the asymptotic distribution of maximum likelihood estimators, two-sided approximate confidence intervals for the unknown parameters are constructed. Using gamma conjugate priors, several Bayes estimates and associated credible intervals are obtained relative to the squared error loss function. Proposed estimators cannot be expressed in closed forms and can be evaluated numerically by some suitable iterative procedure. A Bayesian approach is developed using Markov chain Monte Carlo techniques to generate samples from the posterior distributions and in turn computing the Bayes estimates and associated credible intervals. To analyze the performance of the proposed estimators, a Monte Carlo simulation study is conducted. Finally, a real data set is discussed for illustration purposes.

scholarly journals A New Robust Diagnostic Plot for Classifying Good and Bad High Leverage Points in a Multiple Linear Regression Model

2015 ◽  
Vol 2015 ◽  
pp. 1-12
Author(s):  
Mohammed Alguraibawi ◽  
Habshah Midi ◽  
A. H. M. Rahmatullah Imon
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Multiple Linear Regression Model ◽  
Parameter Estimates ◽  
Data Sets ◽  
Data Set ◽  
Monte Carlo Simulation Study ◽  
Leverage Points ◽  
Diagnostic Plot ◽  
Leverage Point

Identification of high leverage point is crucial because it is responsible for inaccurate prediction and invalid inferential statement as it has a larger impact on the computed values of various estimates. It is essential to classify the high leverage points into good and bad leverage points because only the bad leverage points have an undue effect on the parameter estimates. It is now evident that when a group of high leverage points is present in a data set, the existing robust diagnostic plot fails to classify them correctly. This problem is due to the masking and swamping effects. In this paper, we propose a new robust diagnostic plot to correctly classify the good and bad leverage points by reducing both masking and swamping effects. The formulation of the proposed plot is based on the Modified Generalized Studentized Residuals. We investigate the performance of our proposed method by employing a Monte Carlo simulation study and some well-known data sets. The results indicate that the proposed method is able to improve the rate of detection of bad leverage points and also to reduce swamping and masking effects.

ON WEIGHTED PORTMANTEAU TESTS FOR TIME-SERIES GOODNESS-OF-FIT

2014 ◽  
Vol 36 (1) ◽  
pp. 67-83 ◽  
Author(s):  
Colin M. Gallagher ◽  
Thomas J. Fisher
Keyword(s):  
Time Series ◽  
Goodness Of Fit ◽  
Portmanteau Tests

scholarly journals A Fuzzy Set-Valued Autoregressive Moving Average Model and Its Applications

Symmetry ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 324 ◽  
Author(s):  
Dabuxilatu Wang ◽  
Liang Zhang
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Empirical Analysis ◽  
Moving Average ◽  
Arma Model ◽  
Autoregressive Moving Average ◽  
Complex Data ◽  
Arma Models ◽  
Linguistic Data ◽  
Series Analysis

Autoregressive moving average (ARMA) models are important in many fields and applications, although they are most widely applied in time series analysis. Expanding the ARMA models to the case of various complex data is arguably one of the more challenging problems in time series analysis and mathematical statistics. In this study, we extended the ARMA model to the case of linguistic data that can be modeled by some symmetric fuzzy sets, and where the relations between the linguistic data of the time series can be considered as the ordinary stochastic correlation rather than fuzzy logical relations. Therefore, the concepts of set-valued or interval-valued random variables can be employed, and the notions of Aumann expectation, Fréchet variance, and covariance, as well as standardized process, were used to construct the ARMA model. We firstly determined that the estimators from the least square estimation of the ARMA (1,1) model under some L2 distance between two sets are weakly consistent. Moreover, the justified linguistic data-valued ARMA model was applied to forecast the linguistic monthly Hang Seng Index (HSI) as an empirical analysis. The obtained results from the empirical analysis indicate that the accuracy of the prediction produced from the proposed model is better than that produced from the classical one-order, two-order, three-order autoregressive (AR(1), AR(2), AR(3)) models, as well as the (1,1)-order autoregressive moving average (ARMA(1,1)) model.

scholarly journals Evaluating the Predictive Power of Ordination Methods in Ecological Context

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 295 ◽  
Author(s):  
Otto Wildi
Keyword(s):  
Goodness Of Fit ◽  
Optimal Choice ◽  
Alternative Methods ◽  
Site Factors ◽  
Real World Data ◽  
Principal Coordinates Analysis ◽  
Data Set ◽  
Ordination Methods ◽  
Principal Coordinates ◽  
Almost All

When striving for the ordination methods best predicting independently measured site factors, the following questions arise: does the optimal choice depend on the kind of biological community analysed? Are there different ordination methods needed to address different site factors? Simultaneously, I explore alternative similarity approaches of entire ordinations, as well as the role of the transformations applied to the scale used in measuring species performance. The combination of methods and data transformations results in 96 alternative solutions for any one data set. These are compared by a graphical display, that is, an ordination of ordinations. The goodness-of-fit of independently measured site factors is assessed by two alternative methods. The resulting 96 performance values serve as independent variables in trend surfaces overlaid to the ordination of ordinations. The results from two real-world data sets indicate that some ordination methods greatly vary with data transformation. Scores close to a binary scale perform best in almost all ordination methods. Methods that intrinsically constrain the range of species scores, such as principal components analysis based on correlation, correspondence analysis (including its detrended version), nonmetric multidimensional scaling, as well as principal coordinates analysis based on the Bray-Curtis distance, always figure among the most successful methods, irrespective of data used.

scholarly journals Autoregressive Prediction with Rolling Mechanism for Time Series Forecasting with Small Sample Size

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Zhihua Wang ◽  
Yongbo Zhang ◽  
Huimin Fu
Keyword(s):  
Time Series ◽  
Sample Size ◽  
Small Sample Size ◽  
Computational Effort ◽  
Small Sample ◽  
Grey Theory ◽  
Data Set ◽  
Rolling Mechanism ◽  
Short Term Forecasting ◽  
Prediction Approach

Reasonable prediction makes significant practical sense to stochastic and unstable time series analysis with small or limited sample size. Motivated by the rolling idea in grey theory and the practical relevance of very short-term forecasting or 1-step-ahead prediction, a novel autoregressive (AR) prediction approach with rolling mechanism is proposed. In the modeling procedure, a new developed AR equation, which can be used to model nonstationary time series, is constructed in each prediction step. Meanwhile, the data window, for the next step ahead forecasting, rolls on by adding the most recent derived prediction result while deleting the first value of the former used sample data set. This rolling mechanism is an efficient technique for its advantages of improved forecasting accuracy, applicability in the case of limited and unstable data situations, and requirement of little computational effort. The general performance, influence of sample size, nonlinearity dynamic mechanism, and significance of the observed trends, as well as innovation variance, are illustrated and verified with Monte Carlo simulations. The proposed methodology is then applied to several practical data sets, including multiple building settlement sequences and two economic series.

scholarly journals Goodness of fit for stochastic actor-oriented models

2019 ◽  
Vol 12 (3) ◽  
pp. 205979911988428 ◽  
Author(s):  
Josh Lospinoso ◽  
Tom AB Snijders
Keyword(s):  
Monte Carlo ◽  
Mahalanobis Distance ◽  
Goodness Of Fit ◽  
Real Data ◽  
Testing Procedure ◽  
Network Evolution ◽  
Data Set ◽  
Modified Model ◽  
Fit Testing ◽  
Distance Estimator

We propose a Mahalanobis distance–based Monte Carlo goodness of fit testing procedure for the family of stochastic actor-oriented models for social network evolution. A modified model distance estimator is proposed to help the researcher identify model extensions that will remediate poor fit. A limited simulation study is provided to establish baseline legitimacy for the Mahalanobis distance–based Monte Carlo test and modified model distance estimator. A forward model selection workflow is proposed, and this procedure is demonstrated on a real data set.

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