INGARCH Models Research Articles

Non-Parametric Estimation for Locally Stationary Integer-Valued Processes

This paper aims to study the non parametric Negative Binomial Quasi-Maximum Likelihood Estimation (NBQMLE) for locally stationary integer valued processes. So, we have considered two locally stationary integer-valued models of negative binomial type, namely: INARCH ( p ) and INGARCH ( p , q ) models. Imposing some contraction arguments, we have extended the stationary negative-binomial QMLE to a localized one in our non-stationary environment. This estimation method is based on a kernel function that achieves the convergence rates of n h n order. Under some regularity assumptions, the consistency, as well as the asymptotic normality of the obtained estimator, are established. The performances of the established estimators are evaluated via a simulation study and an application to real data set.

Local influence analysis in the softplus INGARCH model

Local influence analysis in the softplus INGARCH model

Doubly-Inflated Poisson INGARCH Models for Count Time Series

Doubly-Inflated Poisson INGARCH Models for Count Time Series

Climate risks and predictability of the trading volume of gold: Evidence from an INGARCH model

We investigate whether text-based physical or transition climate risks forecast the daily volume of gold trade contracts. Given the count-valued nature of gold volume data, we employ a log-linear Poisson integer-valued generalized autoregressive conditional heteroskedasticity (IN-GARCH) model with a climate-related covariate. We detect that physical risks have a significant predictive power for gold volume at 5- and 22-day-ahead horizons. Additionally, from a full-sample analysis, it emerges that physical risks positively relate with gold volume. Combining these findings, we conclude that gold hedges physical risks at 1-week and 1-month horizons. Similar results hold for platinum and palladium, but not for silver.

Multivariate time series models for mixed data

We introduce a general approach which unifies some previous attempts for modeling the dynamic of multivariate time series or for regression analysis when the data are of mixed type (binary/count/continuous). Our approach is quite flexible since conditionally on past values, each coordinate at time t can have a distribution compatible with a standard univariate time series model such as GARCH, ARMA, INGARCH or logistic models whereas past values of the other coordinates play the role of exogenous covariates in the dynamic. The simultaneous dependence in the multivariate time series can be modeled with a copula. Additional exogenous covariates are also allowed in the dynamic. We first study some usual stability properties of these models and then show that autoregressive parameters can be consistently estimated equation-by-equation using a pseudo-maximum likelihood method, leading to a fast implementation even when the number of time series is large. Moreover, we prove consistency results when a parametric copula model is fitted to the time series and in the case of Gaussian copulas, we show that the likelihood estimator of the correlation matrix is strongly consistent. We carefully check all our assumptions for two prototypical examples: a GARCH/INGARCH model and logistic/log-linear INGARCH model. Our results are illustrated with numerical experiments as well as two real data sets.

Investigation of femicide in Turkey: modeling time series of counts.

This study aims to reveal the relationship between the number of femicide in Turkey, the female unemployment rate, the male unemployment rate, and inflation. The contribution of the study to the literature is that it estimates the relationship between femicides and macroeconomic variables with a method that incorporates the count data. The dataset was analyzed by using the INGARCH model, one of the most popular approaches for count time series data. This model is particularly attractive for dealing with serial dependence and over-dispersion. The findings revealed that an increase in the female unemployment rate and a decrease in the male unemployment rate increases the number of femicide. In addition, it was observed that the number of femicide in the previous month had a negative effect on the current month's number. Increasing the employment rate of women, and women's economic freedom generally, are essential factors in reducing femicide. To prevent femicides, policymakers should aim to increase women's employment.

Soft-clipping INGARCH models for time series of bounded counts

The soft-clipping binomial INGARCH (scBINGARCH) models are proposed as time series models for bounded counts, which have a nearly linear structure and also allow for negative autocor-relations. Conditions that guarantee the existence and certain mixing properties of the scBINGARCH process are derived, and further stochastic properties are discussed. The consistency and asymptotic nor-mality of maximum likelihood estimators are established, and finite-sample properties are studied with simulations. The practical relevance of the scBINGARCH model’s ability to allow for negative parameter and ACF values is demonstrated by some real-data examples.

INGARCH-based fuzzy clustering of count time series with a football application

Although there are many contributions in the time series clustering literature, few studies still deal with count time series data. This paper aims to develop a fuzzy clustering procedure for count time series data. We propose an Integer GARCH-based Fuzzy C-medoids (INGARCH-FCMd) method for clustering count time series based on a Mahalanobis distance between the parameters estimated by an INGARCH model. We show how the proposed clustering method works by clustering football teams according to the number of scored goals.

Asymptotic negative binomial quasi-likelihood inference for periodic integer-valued time series models

This paper establishes the strong consistency and asymptotic normality of the negative binomial quasi-maximum likelihood estimator (NBQMLE) for a general class of integer-valued time series models whose parameters are periodic time-varying. This class of models is specified via its conditional mean, which is expressed as a periodic parametric function of (infinite) past observations. An illustration on specific models, namely the Poisson periodic INGARCH model, the negative binomial periodic INGARCH model, and the periodic INAR(1) model is given. In addition, the performance of the NBQMLE is assessed through a simulation study, and an application of the proposed methodology to a real dataset is provided.

Climate Risks and Predictability of the Trading Volume of Gold:Evidence from an INGARCH Model

Climate Risks and Predictability of the Trading Volume of Gold:Evidence from an INGARCH Model

Periodic stationarity conditions for mixture periodic INGARCH models

<abstract><p>This paper proposes strict periodic stationarity and periodic ergodicity conditions for a finite mixture integer-valued GARCH model with $ S $-periodic time-varying parameters that depend on the state of an independent and periodically distributed regime sequence. In this model, the past conditional mean values depend on the past of the regime variable in the same order, so the model is characterized by path-regime dependence. We also propose sufficient conditions for periodic stationarity when the conditional means are nonlinear of past observations. The results are applied to various discrete conditional distributions.</p></abstract>

Correction: Periodic stationarity conditions for mixture periodic INGARCH models

Correction: Periodic stationarity conditions for mixture periodic INGARCH models

Forecasting transaction counts with integer-valued GARCH models

Abstract Using numerous transaction data on the number of stock trades, we conduct a forecasting exercise with INGARCH models, governed by various conditional distributions; the Poisson, the linear and quadratic negative binomial, the double Poisson and the generalized Poisson. The model parameters are estimated with efficient Markov Chain Monte Carlo methods, while forecast evaluation is done by calculating point and density forecasts.

A note on the stability of multivariate non-linear time series with an application to time series of counts

We introduce a simple criterion for studying stationarity and moments properties of some multivariate Markovian autoregressive processes, under a contracting mapping assumption. We apply our results to the Poisson INGARCH model and to one of its multivariate extension recently introduced in the literature. In particular, we obtain optimal stationarity conditions and existence of some exponential moments.

USING OBSERVATION DRIVEN MODELS TO FIT COUNT DAILY NEW CONFIRMED CASES OF “COVID 19” IN EGYPT

On 11 of March, the World Health Organization declared corona virus as a pandemic. This virus has spread in at least 218 countries with at least one case reported until the end of 2020. In Egypt, the first case was reported on 14/02/2020. At the end of 2020, it confirms its higher daily rise of new This paper suggests to use the autoregressive conditional Poisson (ACP) models, also known as integer-valued GARCH (briefly: INGARCH) models which belong to the observation driven models (ODMs) category to model the count daily new confirmed cases of COVID 19 in Egypt. We compare between the robust and the non-robust estimators for the Poisson INARCH(1) model as a simple class of the INGARCH (p, q) models by simulations. The application results indicate that the robust version of the Poisson INARCH(1) model is more reasonable to fit the number of new confirmed cases of COVID 19.

Modeling and inference for counts time series based on zero-inflated exponential family INGARCH models

This study considers statistical inferences such as parameter estimation and change tests for counts time series models where the conditional density of present observations over past information follow a zero-inflated one-parameter exponential family. We verify that the zero-inflated exponential family (ZIEF) INGARCH process is stationary and ergoic, and the maximum likelihood estimator is consistent and asymptotically normal. We then construct CUSUM tests based on (standardized) residuals and squares of (standardized) residuals as a parameter change test. Their null distributions is shown to converge to the sup of a Brownian bridge in distribution. The validity of the CUSUM tests is confirmed through a simulation study and real data analysis.

Exponential family QMLE-based CUSUM test for integer-valued time series

This study considers testing for parameter changes in integer-valued time series models based on one parameter exponential family quasi-maximum likelihood estimates. We employ the cumulative sum (CUSUM) test as a change point test, based on score vectors, residuals, standardized residuals, and squares of residuals, focusing on performance comparison of negative binomial (NB) quasi-maximum likelihood estimate (QMLE)-based tests. Monte Carlo simulations are conducted with Poisson, NB, zero-inflated Poisson and NB, generalized Poisson INGARCH(1,1) models and Poisson and NB INAR(1) models. Real data analysis using the Korean stock price index (KOSPI) 200 is also included for illustration. The findings validate QMLE-based CUSUM tests using standardized residuals for INGARCH models and residuals for INAR models. Zero proportional change is well detected by the test using squares of residuals.

Comparison of Predictive Models and Impact Assessment of Lockdown for COVID-19 over the United States

The novel Coronavirus Disease 2019 (COVID-19) remains a worldwide threat to community health, social stability, and economic development. Since the first case was recorded on December 29, 2019, in Wuhan of China, the disease has rapidly extended to other nations of the world to claim many lives, especially in the USA, the United Kingdom, and Western Europe. To stay ahead of the curve consequent of the continued increase in case and mortality, predictive tools are needed to guide adequate response. Therefore, this study aims to determine the best predictive models and investigate the impact of lockdown policy on the USA’ COVID-19 incidence and mortality. This study focuses on the statistical modelling of the USA daily COVID-19 incidence and mortality cases based on some intuitive properties of the data such as overdispersion and autoregressive conditional heteroscedasticity. The impact of the lockdown policy on cases and mortality was assessed by comparing the USA incidence case with that of Sweden where there is no strict lockdown. Stochastic models based on negative binomial autoregressive conditional heteroscedasticity [NB INGARCH (p,q)], the negative binomial regression, the autoregressive integrated moving average model with exogenous variables (ARIMAX) and without exogenous variables (ARIMA) models of several orders are presented, to identify the best fitting model for the USA daily incidence cases. The performance of the optimal NB INGARCH model on daily incidence cases was compared with the optimal ARIMA model in terms of their Akaike Information Criteria (AIC). Also, the NB model, ARIMA model and without exogenous variables are formulated for USA daily COVID-19 death cases. It was observed that the incidence and mortality cases show statistically significant increasing trends over the study period. The USA daily COVID-19 incidence is autocorrelated, linear and contains a structural break but exhibits autoregressive conditional heteroscedasticity. Observed data are compared with the fitted data from the optimal models. The results further indicate that the NB INGARCH fits the observed incidence better than ARIMA while the NB models perform better than the optimal ARIMA and ARIMAX models for death counts in terms of AIC and root mean square error (RMSE). The results show a statistically significant relationship between the lockdown policy in the USA and incidence and death counts. This suggests the efficacy of the lockdown policy in the USA.

Time-varying auto-regressive models for count time-series

Count-valued time series data are routinely collected in many application areas. We are particularly motivated to study the count time series of daily new cases, arising from the COVID-19 spread. First, we propose a Bayesian framework to study the time-varying semiparametric AR(p) model for the count and then extend it to a more sophisticated time-varying INGARCH model. We calculate posterior contraction rates of the proposed Bayesian methods with respect to the average Hellinger metric. Our proposed structures of the models are amenable to Hamiltonian Monte Carlo (HMC) sampling for efficient computation. We substantiate our methods by simulations that show superiority compared to some of the existing methods that closely fit this setting. Finally, we analyze the daily time series data of newly confirmed cases in NYC to study the spread of COVID for three months.

Volatility clustering in data breach counts

Insurers face increasing demands for cyber liability; entailed in part by a variety of new forms of risk of data breaches. As data breach occurrences develop, our understanding of the volatility in data breach counts has also become important as well as its expected occurrences. Volatility clustering, the tendency of large changes in a random variable to cluster together in time, are frequently observed in many financial asset prices, asset returns, and it is questioned whether the volatility of data breach occurrences are also clustered in time. We now present volatility analysis based on INGARCH models, i.e., integer-valued generalized autoregressive conditional heteroskedasticity time series model for frequency counts due to data breaches. Using the INGARCH(1, 1) model with data breach samples, we show evidence of temporal volatility clustering for data breaches. In addition, we present that the firms’ volatilities are correlated between some they belong to and that such a clustering effect remains even after excluding the effect of financial covariates such as the VIX and the stock return of S&P500 that have their own volatility clustering.