Quasi-likelihood Research Articles

A block bootstrap for quasi-likelihood in sparse functional data

This article utilizes bootstrap quasi-likelihood (QL) to model sparse functional data. The proposed method combines parallel block bootstrap and QL to fit the functional data. The parameter space is considered as a finite-dimensional space through a certain optimization rule. Statistical errors of the proposed method are discussed. Some asymptotic properties of the method are established under several mild conditions as well. Several simulations are conducted to examine the finite-sample performance of the method. The performance is also demonstrated by analysing real data.

Revisiting the location of FDI in China: A panel data approach with heterogeneous shocks

Foreign Direct Investment (FDI) is viewed as a primary driving force in shaping the global economy and receives particular attention in empirical studies. In this paper, we argue that many of the existing studies ignore endogeneities that arise from shocks in source and destination countries. To address this endogeneity issue, we take the “controlling through estimating” idea from the econometric literature and propose using panel data models with heterogeneous shocks to deal with it. We consider the quasi maximum likelihood (QML) method to estimate our proposed model. We investigate the asymptotic properties of the QML estimator, including the consistency, the asymptotic representation, and the limiting distribution. We also propose new statistics to test the validity of the use of traditional dynamic and static panel data estimation methods. Applying it to the location determinants of inward FDI in China, we find that the endogeneity issue does exist, and that controlling for heterogeneous shocks helps to improve the estimation results.

Association of genetic polymorphisms related to Johne\u2019s disease with estimated breeding values of Holstein sires for milk ELISA test scores

BackgroundJohne’s disease (JD) is a chronic intestinal inflammatory disease caused by Mycobacterium avium subsp. paratuberculosis (MAP) infection in ruminants. Since there are currently no effective vaccine or treatment options available to control JD, genetic selection may be an alternative strategy to enhance JD resistance. Numerous Single Nucleotide Polymorphisms (SNPs) have been reported to be associated with MAP infection status based on published genome-wide association and candidate gene studies. The main objective of this study was to validate these SNPs that were previously identified to be associated with JD by testing their effect on Holstein bulls’ estimated breeding values (EBVs) for milk ELISA test scores, an indirect indicator of MAP infection status in cattle.ResultsThree SNPs, rs41810662, rs41617133 and rs110225854, located on Bos taurus autosomes (BTA) 16, 23 and 26, respectively, were confirmed as significantly associated with Holstein bulls’ EBVs for milk ELISA test score (FDR < 0.01) based on General Quasi Likelihood Scoring analysis (GQLS) analysis. Single-SNP regression analysis identified four SNPs that were associated with sire EBVs (FDR < 0.05). This includes two SNPs that were common with GQLS (rs41810662 and rs41617133), with the other two SNPs being rs110494981 and rs136182707, located on BTA9 and BTA16, respectively.ConclusionsThe findings of this study validate the association of SNPs with JD MAP infection status and highlight the need to further investigate the genomic regions harboring these SNPs.

Multi‐core hardware realisation of the quasi maximum likelihood PPS estimator

Multi-core hardware realisation of the quasi maximum likelihood algorithm as the state-of-the-art estimator of polynomial phase signals (PPSs) is proposed in this study. Developed multiple-clock-cycle realisation is suitable for real-time implementation. To prove this, the proposed design is implemented on a field programmable gate array circuit. The hardware realisation is tested and verified on PPSs corrupted with various amounts of the Gaussian noise. Obtained results are compared with software simulations showing excellent match between the proposed system-based and the software-based outputs.

Robust estimation and inference of spatial panel data models with fixed effects

It is well established that the quasi maximum likelihood (QML) estimation of the spatial regression models is generally inconsistent under unknown cross-sectional heteroskedasticity (CH) and the CH-robust methods have been developed. The same issue remains for the spatial panel data (SPD) models but the similar studies based on QML approach do not seem to have been carried out. This paper focuses on the SPD model with fixed effects (FE). We argue that under unknown CH the QML estimator for the SPD-FE model is inconsistent in general, but there are ‘special cases’ where it may remain consistent although the exact conditions may not be possible to check, as in practice the type of CH is generally unknown. Thus, we introduce a new set of estimation and inference methods based on the adjusted quasi scores (AQS), which are fully robust against unknown CH. Consistency and asymptotic normality of the proposed AQS estimators are established. Robust standard error estimates are provided and their consistency is proved. To improve the finite sample performance, a set of AQS methods based on concentrated quasi scores is also introduced and its asymptotic properties examined. Extensive Monte Carlo results show that the new estimator outperforms the QML estimator even when the latter seems robust.

On periodic EGARCH models

This article deals with some probabilistic and statistical properties of a periodic exponential model, which is very adequate and appropriate to capture and describe, at the same time, three stylized facts very often encountered in the field of financial time series namely, the volatility clustering, the asymmetry and the periodicity exhibited by the autocovariance structure. Indeed, necessary and sufficient conditions for the periodical stationarity, both in second order and strict, are established. The closed form of the second-order moment is, under these conditions, established. Moreover, the higher order moments structure is studied. The conditional least square (CLS) and the quasi maximum likelihood estimations of the model are obtained. Moreover, the CLS estimations of the non-centered model and the are established. The performances of these estimators were assisted by an intensive simulation study, moreover an application on real data set is provided.

Modelling Global Burden of Disease Measures in Selected European Countries Using Robust Dynamic Spatial Panel Data Models

The aim of the paper is to study relationships between selected socio‑economic factors and health of European citizens. The health level is measured by selected global burden of disease measures – DALYs (Disability Adjusted Life Years) and its two components: YLL (Years of Life Lost) and YLD (Years Lived with Disability). We identify which factors significantly affect these indicators of health. The empirical study uses a panel data comprising 16 countries mostly from the old‑EU in the period 2003–2013. Fixed‑effects dynamic spatial panel data (DSPD) models are used to account for autocorrelations of the dependent variables across time and space. The models are estimated with a novel, modified quasi maximum likelihood Yang method based on M‑estimators. The approach is robust on the distribution of the initial observations. The empirical analysis covers specification, estimation, and verification of the models. The results show that changes in YLD are significantly related to alcohol consumption, healthcare spending, social spending, GDP growth rate and years of education. Exactly the same set of factors is associated with variation in DALYs. Sensitivity of the YLL component to the socio‑economic factors is considerably weaker.

Multiplicative Conditional Correlation Models for Realized Covariance Matrices

We introduce a class of multiplicative dynamic models for realized covariance matrices assumed to be conditionally Wishart distributed. The multiplicative structure enables consistent three-step estimation of the parameters, starting by covariance targeting of a scale matrix. The dynamics of conditional variances and correlations are inspired by specifications akin to the consistent dynamic conditional correlation model of the multivariate GARCH literature, and estimation is performed by quasi maximum likelihood. Simulations show that in finite samples the three-step estimator has smaller bias and root mean squared error than the full estimator when the cross-sectional dimension increases. An empirical application illustrates the flexibility of these models in a low-dimensional setting, and another one illustrates their effectiveness and practical usefulness in high dimensional portfolio allocation strategies.

Bias decomposition in the value-at-risk calculation by a GARCH(1,1)

The recent researches show that value-at-risk (VaR) estimations are biased and is calculated conservatively. Bao and Ullah (2004) proved the bias of an ARCH(1) model for VaR can be decomposed in to two parts: bias due to the returns' misspecification distributional assumption for GARCH(1,1), i.e., (Bias1) and bias due to estimation error, i.e., (Bias2). Using quasi maximum likelihood estimation method this paper intends to find an analytical framework for the two sources of bias. We generate returns from Normal and t-student distributions, then estimate the GARCH(1,1) under Normal and t-student assumptions. Our findings reveal that Bias1 equals to zero for the Normal likelihood function, but Bias2 ≠ 0. Also, Bias1 and Bias2 are not zero for the t-student likelihood function as analytically were expected, however, all the biases become modest, when the number of observations and degree of freedom gets large.

Dynamic Multiple Quantile Models

This paper addresses the problem of estimating multiple quantiles from a time series. A flexible class of dynamic multiple quantile (DMQ) models is specified, ensuring that estimated quantiles do not cross and that extreme quantiles are estimated by exploiting information coming from all the regions of the underlying distribution. DMQ models encompass the baseline model by Catania and Luati (2019), based on two main ideas, i.e. quantile spacings and score-type updates, and provide extension along several directions. First, a specification which includes a heterogeneous reaction of the left and right tails to past observations is included. Secondly, the case where all quantiles react differently to past information is considered. Finally, cross-tail effects are modeled, so that information from the right tail influences the left tail, and vice versa. The last specification allows the model to effectively capture the leverage effect in financial returns. Estimation is carried out by means of two stage quasi maximum likelihood estimators (2SQMLE). In the first stage the quantile intercepts are estimated by employing a targeting scheme. The use of empirical targeting versus parametric targeting is discussed. Consistency and asymptotic normality of 2SQMLE are derived. As closed-form expressions for h-step-ahead predictive quantiles are available, empirical results are assessed also based on comparisons in terms of the news impact curve, the quantile response function and the quantile decay, defined in this paper as the decay over time of quantile levels after an extreme shock.

Persistent and Rough Volatility

This paper introduces a discrete-time fractional stochastic volatility model (FSV) based on fractional Gaussian noise. The new model includes the standard stochastic volatility model as a special case and has the same limit as the fractional integrated stochastic volatility (FISV) model. A simulated maximum likelihood method, which maximizes the time-domain log-likelihood function calculated by the importance sampling technique, and a frequency-domain quasi maximum likelihood method (or Whittle) are employed to estimate the model parameters. Simulation studies suggest that, while both estimation methods can accurately estimate the model, the simulated maximum likelihood method outperforms the Whittle method. As an illustration, we fit the FSV and FISV models with the proposed estimation techniques to the S\&P 500 composite index over a sample period spanning 45 years. Our results reveal that the volatilities of the data series are persistent and rough.

Firth bias correction for estimating variance components of logistics linear mixed model using penalized quasi likelihood method

Firth bias correction originally was applied to correct bias of the variance components estimator that obtained by the maximum likelihood method. Extensive research has shown that Firth bias correction is powerful to reduce bias for normal distributed response model. Questions have been raised about the use of Firth bias correction in binomial distributed response model which has under dispersion problem. The motivation of this study is giving contribution to exploring the Firth bias correction for binomial distributed response model. The binomial distributed response model which is estimated by the maximum likelihood method obtain an under-dispersion estimator. Therefore, the Penalized Quasi-Likelihood (PQL) is used as alternative numerical method to estimate the model. This paper aims to investigate whether the Firth method can reduce bias of the variance components using the PQL technique in longitudinal data.

Location Multiplicative Error Models with Quasi Maximum Likelihood Estimation

Motivated by improving the fitting of non‐negative financial time series, we extend the multiplicative error model and study the semi‐parametric estimation. We first introduce a location parameter and use the sample minimum to a truncate data set. In the case that there is a non‐trivial proportion of zeros in the truncated data, we adopt a zero‐augmented mixture distribution for the innovation terms. For both cases, we propose quasi maximum likelihood estimation for the multiplicative coefficients and establish asymptotic results. We conduct large simulation studies to demonstrate substantial estimation errors with misspecified models, and confirm the asymptotic properties. Moreover, we present an empirical study to illustrate the fitting improvement.

Multivariate spatial autoregressive model for large scale social networks

The rapid growth of social network platforms generates a large amount of social network data, where multivariate responses are frequently collected from users. To statistically model such type of data, the multivariate spatial autoregressive (MSAR) model is studied. To estimate the model, the quasi maximum likelihood estimator (QMLE) is obtained under certain technical conditions. However, it is found that the computational cost of QMLE is expensive. To fix this problem, a least squares estimator (LSE) is developed. The corresponding identification conditions and asymptotic properties are investigated. To gauge the finite sample performance of various estimators, a number of simulation studies are conducted. Lastly, a Sina Weibo dataset is analyzed for illustration purpose.

Semiparametric quasi maximum likelihood estimation of the fractional response model

This paper proposes a new semiparametric estimator of models where the response random variable is a fraction. The estimator is constructed by optimizing a semiparametric quasi-maximum likelihood that utilizes kernel smoothing. Under suitable conditions, the consistency and asymptotic normality of the proposed estimator is established allowing for data-driven bandwidth choices as well as random trimming, and its flexibility and robustness are showcased in a Monte Carlo experiment and an empirical application.

Hybrid estimation for ergodic diffusion processes based on noisy discrete observations

We consider parametric estimation for ergodic diffusion processes with noisy sampled data based on the hybrid method, that is, the multi-step estimation with the initial Bayes type estimators in order to select proper initial values for optimisation of the quasi likelihood function. The asymptotic properties of the initial Bayes type estimators and the hybrid multi-step estimators are shown, and a concrete example and the simulation results are given.

Three regime bivariate normal distribution: a new estimation method for co-value-at-risk, CoVaR

We propose a new distribution for estimation of co-value-at-risk, CoVaR, a financial system risk measure conditional on an institution in a financial distress: a three regime bivariate normal (3RN) distribution which is composed of three bivariate normal distributions with asymmetric variance matrices for the right-tail, left-tail and mid-part corresponding to the return of an institution. The distribution captures explicitly the asymmetric correlation of system return and institution return: usually stronger for bad times than for good times. The 3RN distribution allows simple evaluations of the CoVaR taking full advantage of asymmetric correlation. An implementation for the quasi maximum likelihood estimator (QMLE) is provided. The proposed estimation method is applied to stock price data sets consisting of one financial system and four financial institutions: the US S&P 500 index, Bank of America Corporation, JP Morgan Chase & Co., Goldman Sachs Group, Inc. and Citigroup Inc. The data analysis shows that the proposed method has better in-sample and out-of-sample violation performance than existing methods and some other possible candidates.

Dynamic Spatial Panel Data Models in Identifying Socio-Economic Factors Affecting the Level of Health in Selected European Countries

The aim of the paper is to investigate the relationship between socio-economic factors and the level of health of citizens of selected European countries. Disability-adjusted life years (DALYs) were used as the measure of health. The author applied dynamic spatial panel data models with fixed effects and spatial autocorrelation of the error term. The models were estimated using a novel, modified quasi maximum likelihood method based on M-estimators. The approach is resistant to deviations from the assumptions on the distribution of initial observations. The estimation of initial observations is a severe weakness of standard methods based on the maximization of the quasi-likelihood function in the case of short panels. M-estimators are consistent and asymptotically normally distributed. The empirical analysis covers the specification, estimation, and verification of the models.

Forecasting the realized volatility of CSI 300

According to the characteristics of realized volatility existing in Shanghai and Shenzhen 300 index (China Securities Index 300, CSI 300), the GARCH family model is introduced to describe the ARCH effect of error sequences in HAR, ARFIMA, and ARFIMAX models. Then, the HAR-GARCH family, the ARFIMA-GARCH family, and the ARFIMAX-GARCH family models set is proposed, which contains 33 kinds of models. Using the quasi maximum likelihood method, the parameters of the all models are estimated with normal (N) and skewed student t (SKST) distributions. By rolling window technology, one-step-ahead rolling prediction of realized volatility for CSI 300 is conducted. The results from prediction accuracy by model confidence set (MCS) test show that the realized volatility prediction models with skewed student t distribution possess higher precision than those of normal distribution in general. The ARFIMAX and other six models in ARFIMAX-GARCH family form the optimal prediction models set, which can forecast the realized volatility of CSI 300 with better accuracy.

Generalized quasi maximum likelihood estimation for generalized autoregressive score models: simulations and real applications

In this article, we develop a two-step method for conditional Value at Risk (VaR) estimation in the context of the Generalized Autoregressive Score (GAS) models. The first step consists of estimating the volatility parameter by the generalized Quasi Maximum Likelihood Estimator (gQMLE) and in the second step we estimate the theoretical quantile of the innovations by the empirical quantile of the residuals. When the instrumental density q of the gQMLE is not the Gaussian density used in the standard QMLE, or is not the true distribution of the innovations, both the estimations of the volatility and of the quantile are asymptotically biased. In spite of that the two errors counterbalance each other, and we finally get a consistent estimator of the conditional VaR. We establish the asymptotic properties of the gQMLE for GAS models as well as the conditional VaR two-step estimator. Moreover, we discuss how to apply the gQMLE by giving examples of densities distribution and we get worthwhile results.