Specifications tests for count time series models with covariates

Tobit INARMA models for count time series with negative autocorrelation

Although the INGARCH models for count time series are said to be an integer‐valued counterpart to the generalized autoregressive conditional heteroskedasticity (GARCH) models, they may also be understood as an adaption of the autoregressive moving‐average (ARMA) models to the count‐data case. The stochastic properties of these models as well as some extensions are discussed. In particular, the INGARCH models that are a type of linear conditional regression model, and also nonlinear regression models have been proposed for count time series.

The INARMA models discussed in Chapter 3 used types of thinning operations to transfer the ARMA approach to the count data case. Another popular approach for modeling such stationary processes of counts are the INGARCH models, the definition of which is related to linear regression models. Despite their controversial name, these models are particularly attractive for overdispersed counts with an ARMA-like autocorrelation structure. Results concerning the basic model with a conditional Poisson distribution are presented, but also generalizations with, e. g., a binomial or negative binomial conditional distribution are considered. We conclude with a discussion of multivariate extensions of the INGARCH model.

The article presents a robust quantitative approach for determining significant economic factors for sex trafficking in the United States. The aim is to study monthly counts of sex trafficking-related convictions, and use a wide range of economic variables as covariates to investigate their effect on conviction counts. A count time series model is considered along with a regression setup to include economic time series as covariates (economic factors) to explain the counts on sex trafficking-related convictions. The statistical significance of these economic factors is investigated and the significant factors are ranked based on appropriate model selection methods. The inclusion of time-lagged versions of the economic factor time series in the regression model is also explored. Our findings indicate that economic factors relating to immigration policy, consumer price index and labor market regulations are the most significant in explaining sex trafficking convictions.

The Asian rice Gall midge (Orseolia oryzae (Wood-Mason) is a major insect pest affecting rice cultivation in South and Southeast Asia, leading to significant yield losses. Developing a reliable system for the timely prediction of this insect is crucial for effective pest management. In this study, Gall midge insect populations were recorded using solar light traps from three locations-Nellore, Maruteru, and Ragolu in Andhra Pradesh for the past 10 to 20 years. Simultaneously, automatic weather stations close to these study sites recorded climatological parameters, including sunshine hours, rainfall, morning and evening relative humidity, maximum and minimum temperatures, and sunshine hours. Count time series models (Integer-valued Generalized Autoregressive Conditional Heteroscedastic (INGARCH)) and Machine learning models (Artificial Neural Network (ANN), Support Vector Regression (SVR) and Extreme Learning Machine(ELM)) were used to analyze weekly cumulative Gall midge populations and weekly averages of climatological data. To improve prediction accuracy, hybrid models (INGARCH-ANN, INGARCH-SVR, and INGARCH-ELM) were also created. Mean Squared Error (MSE) and Root Mean Squared Error (RMSE) were used to assess the model's performance. The results indicated that the hybrid models, particularly INGARCH-SVR and INGARCH-ELM, outperformed standalone models in predicting Gall midge populations. The findings highlight the potential of integrating time series modeling with machine learning techniques to improve pest forecasting and aid in proactive, site-specific pest management strategies, thereby minimizing economic losses and ensuring sustainable rice production.

We propose goodness-of-fit tests for models of count responses with covariates. Our main focus is on the null hypothesis that the observed data come from a Poisson, a negative binomial, or a binomial regression model, but the method is fairly general allowing for the responses to follow, conditionally on covariates, any given discrete distribution. The test criteria are formulated by using the probability generating function and they are convenient from a computational point of view. Asymptotic as well as Monte Carlo results are presented. Applications on real data are also reported.

The problem of testing for a centre effect in multi-centre studies following a proportional hazards regression analysis is considered. Two approaches to the problem can be used. One fits a proportional hazards model with a fixed covariate included for each centre (except one). The need for a centre specific adjustment is evaluated using either a score, Wald or likelihood ratio test of the hypothesis that all the centre specific effects are equal to zero. An alternative approach is to introduce a random effect or frailty for each centre into the model. Recently, Commenges and Andersen have proposed a score test for this random effects model. By a Monte Carlo study we compare the performance of these two approaches when either the fixed or random effects model holds true. The study shows that for moderate samples the fixed effects tests have nominal levels much higher than specified, but the random effect test performs as expected under the null hypothesis. Under the alternative hypothesis the random effect test has good power to detect relatively small fixed or random centre effects. Also, if the centre effect is ignored the estimator of the main treatment effect may be quite biased and is inconsistent. The tests are illustrated on a retrospective multi-centre study of recovery from bone marrow transplantation.

Conditional Heteroskedasticity in some Common Count Data Models for Financial Time Series Data

This paper investigates testing for parameter constancy in models for non‐Gaussian time series. Models for discrete valued count time series are investigated as well as more general models with autoregressive conditional expectations. Both sup‐tests and CUSUM procedures are suggested depending on the complexity of the model being used. The asymptotic distribution of the CUSUM test is derived for a general class of conditional autoregressive models.

This article proposes goodness‐of‐fit tests for dynamic regression models, where regressors are allowed to be only weakly exogenous and arbitrarily correlated with past shocks. The null hypothesis is stated in terms of the lack of serial correlation of the errors of the model. The tests are based on a linear transformation of a Bartlett's Tp‐process of the residuals. This transformation approximates the martingale component of the process so that it converges weakly to the standard Brownian motion under the null hypothesis. One feature of our setup is that we do not require to specify the dynamic structure of the regressors. Due to this, the transformation employs a semi‐parametric correction that does not restrict the class of local alternatives that our tests can detect, in contrast with other works using smoothing techniques. A Monte Carlo study illustrates the finite sample performance of the tests.

The new test criterion for testing the homogeneity of parameters of several populations is proposed and the test properties of it is discussed. The asymptotic expansions of the distributions of test criterion are discussed under (i) null hypothesis, (ii) fixed alternative hypothesis and (iii) local alternative hypothesis converging to the null hypothesis with appropriate rate of convergence as the sample size increases. As a particular case the asymptotic theory of a statistic for a homogeneity of variances of normal populations is also discussed and the exact moments of it under a null hypothesis can be used to obtain a percentage point by a Pearsonian curve fitting.

We investigate the instability problem of the covariance structure of time series by combining the non-parametric approach based on the evolutionary spectral density theory of Priestley [Evolutionary spectra and non-stationary processes, J. R. Statist. Soc., 27 (1965), pp. 204–237; Wavelets and time-dependent spectral analysis, J. Time Ser. Anal., 17 (1996), pp. 85–103] and the parametric approach based on linear regression models of Bai and Perron [Estimating and testing linear models with multiple structural changes, Econometrica 66 (1998), pp. 47–78]. A Monte Carlo study is presented to evaluate the performance of some parametric testing and estimation procedures for models characterized by breaks in variance. We attempt to see whether these procedures perform in the same way as models characterized by mean-shifts as investigated by Bai and Perron [Multiple structural change models: a simulation analysis, in: Econometric Theory and Practice: Frontiers of Analysis and Applied Research, D. Corbea, S. Durlauf, and B.E. Hansen, eds., Cambridge University Press, 2006, pp. 212–237]. We also provide an analysis of financial data series, of which the stability of the covariance function is doubtful.

Acknowledgement

In many manufacturing and service industries, the quality department of the organization works continuously to ensure that the mean or location of the process is close to the target value. In order to understand the process, it is necessary to provide numerical statements of the processes that are being investigated. That is why the researcher needs to check the validity of the hypotheses that are concerned with some physical phenomena. It is usually assumed that the collected data behave well. However, sometimes the data may contain outliers. The presence of one or more outliers might seriously distort the statistical inference. Since the sample mean is very sensitive to outliers, this research will use the smooth adaptive (SA) estimator to estimate the population mean. The SA estimator will be used to construct testing procedures, called smooth adaptive test (SA test), for testing various null hypotheses. A Monte Carlo study is used to simulate the values of the probability of a Type I error and the power of the SA test. This is accomplished by constructing confidence intervals of the process mean by using the SA estimator and bootstrap methods. The SA test will be compared with other tests such as the normal test, t test and a nonparametric statistical method, namely, the Wilcoxon signed-rank test. Also, the cases with and without outliers will be considered. For the right-skewed distributions, the SA test is the best choice. When the population is a right-skewed distribution with one outlier, the SA test controls the probability of a Type I error better than other tests and is recommended.

The approximate slopes of several tests of the independence of two covariance stationary time series are derived and compared. It is shown that the approximate slopes of regression tests are at least as great as those based on the residuals of univariate ARIMA models, and that there are cases in which the former are arbitrarily great while the latter are arbitrarily small. These analytical findings are supported by a Monte Carlo study that shows that in samples of size 100 and 250 the asymptotic distribution theory under the null hypothesis is adequate for all tests, but under alternatives to the null hypothesis the rate of Type II error for the test based on ARIMA model residuals is often more than double that of the regression tests.