Quasi-maximum Likelihood Method Research Articles

Fractional stochastic volatility model

This article 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, which is the continuous‐time fractional Ornstein–Uhlenbeck process. 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 quasi 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 quasi 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.

Varying coefficient panel data models and methods under correlated error components: Application to disparities in mental health services in England

The contribution of this paper is twofold. Firstly, it introduces novel regression models that combine two important areas of the methodological development in panel data analysis, namely a varying coefficient specification and spatial error dependence. The former allows relatively flexible nonlinear interactions; the latter enables spatial correlations of the disturbance and thus differ significantly from the other random effect models in the literature. To estimate the model, a new estimation procedure is established that can be viewed as a generalization of the quasi-maximum likelihood method for a spatial panel data model to the well-known conditional local likelihood procedure. Novel inference methods, particularly variable selection and hypothesis testing of the parameter constancy, are introduced and are shown to be effective under the complex spatial error dependence. Equally importantly, this paper makes a substantial contribution to the understanding of financing and expenditure for health and social care. In particular, we empirically analyze and explain the effects of political ideologies on the local fiscal policy in England, especially the expenditure on mental health services.

Iterative QML estimation for asymmetric stochastic volatility models

The paper illustrates a new procedure for estimating asymmetric stochastic volatility models. These models shape the asymmetric effect of negative and positive financial returns on the expected volatility, behaviour often observed in the stock prices, and known as “leverage effect”. The procedure is based on the iterative application of the quasi-maximum likelihood (QML) method and is proposed as an alternative to the procedure presented by Harvey and Shephard in 1996 and based on the application of the QML method on a modified auxiliary model. The estimation results generally converge to constant values after a few iterations. The volatility predictor provided by the new method is conceptually similar to the EGARCH predictor and different from the predictor of the other procedure. A simulation study shows that the iterative QML method provides parameter estimators with RMSEs decreasing as series length increases. The distribution of the estimates is approximately normal, and the approximation improves as the series size increases. Empirical applications of the method provide results similar to ones of the method known in literature. However, the two methods provide two different predictors and smoothers of volatility, which should be compared on a case-by-case basis.

Variable selection via penalized quasi-maximum likelihood method for spatial autoregressive model with missing response

Spatial autoregressive model is widely concerned in the economic field, whereas when the data is missing, variable selection and parameter estimation of the model is quite challenging. Based on this, we discuss the variable selection in spatial autoregressive model with missing data. Under the condition that errors are independent and identically distributed, we have developed a penalized quasi-maximum likelihood method to achieve variable selection and parameter estimation simultaneously in the presence of missing responses. The method’s theoretical properties, including consistency and asymptotical normality, are established under certain assumptions. Meanwhile, an improved expectation–maximization algorithm is provided for optimizing the penalized quasi-maximum likelihood function. Simulations are conducted to examine the proposed method and assess the finite-sample performance. Additionally, we present a practical example to illustrate the method’s application.

A Two-Stage Quasi-Maximum Likelihood Method for Poisson Models with Two Endogenous Binary Variables: An Application to Trade and Investment Agreements

A Two-Stage Quasi-Maximum Likelihood Method for Poisson Models with Two Endogenous Binary Variables: An Application to Trade and Investment Agreements

Egarch Model Prediction for Sale Stock Price

Stock is an investment in the capital market that is very promising for investors. Investors can also get high returns from the shares invested. However, this stock price is not always stable, it can go up and down drastically. The purpose of this study is to predict stock prices because they often experience instability. The method used in this research is using the Exponential generalized autoregressive conditional heteroscedasticity (EGARCH) model with the Quasi Maximum Likelihood (QML) method. The result of this research is the implementation of this model. The EGARCH model used is the stock price index model that is formed, namely the autoregressive integrated moving average (ARIMA) (0, 1, 2) EGARCH (1.4). The conclusion from the results of the research that predictions using the ARIMA model (0, 1, 2) EGARCH (1, 4) is the best model in accommodating the asymmetric nature of the volatility of the stock price index. The results of this egarch model show more optimal prediction results seen from an error of 3% compared to other modes such as the arch model and the GARCH model.

Unified discrete-time factor stochastic volatility and continuous-time Itô models for combining inference based on low-frequency and high-frequency

This paper introduces unified models for high-dimensional factor-based Itô process, which can accommodate both continuous-time Itô diffusion and discrete-time stochastic volatility (SV) models by embedding the discrete SV model in the continuous instantaneous factor volatility process. We call it the SV-Itô model. Based on the series of daily integrated factor volatility matrix estimators, we propose quasi-maximum likelihood and least squares estimation methods. Their asymptotic properties are established. We apply the proposed method to predict future vast volatility matrix whose asymptotic behaviors are studied. A simulation study is conducted to check the finite sample performance of the proposed estimation and prediction method. An empirical analysis is carried out to demonstrate the advantage of the SV-Itô model in volatility prediction and portfolio allocation problems.

High-dimensional volatility matrix estimation with high-frequency financial data: The GARCH-Itô grouped factor model

In the research area of the high-frequency financial data analysis, estimation and prediction of the high-dimensional volatility matrix are challenging problems, especially when the assets of interest have a naturally given group structure. In order to address this issue, we propose a novel GARCH-Itôgrouped factor model, in which we present the log price series of grouped assets with common factors, group-specific factors, and an asset-specific error term. We then embed the discrete GARCH structure into the volatility of the eigenvalue processes to capture the volatility dynamics of the observed price data. We propose a quasi maximum likelihood method for parameter estimation, establish its asymptotic properties and illustrate its good finite-sample performance with simulation. In real data analysis, we compare our method with the ungrouped factor model and the nonparametric high-frequency volatility estimator MSRV using the data from the SSE Main Board and the SZSE ChiNext market, where the proposed method outperforms its competitors in terms of prediction of the volatility matrix.

Simultaneous Spatial Panel Data Models with Common Shocks

We consider a simultaneous spatial panel data model, jointly modeling three effects: simultaneous effects, spatial effects and common shock effects. This joint modeling and consideration of cross-sectional heteroscedasticity result in a large number of incidental parameters. We propose two estimation approaches, a quasi-maximum likelihood method and an iterative generalized principal components method. We develop full inferential theories for the estimation approaches and study the tradeoff between the model specifications and their respective asymptotic properties. We further investigate the finite sample performance of both methods using Monte Carlo simulations. We find that both methods perform well and that the simulation results corroborate the inferential theories. Some extensions of the model are considered. Finally, we apply the model to analyze the relationship between trade and gross domestic product using a panel data over time and across countries.

Temporal aggregation and systematic sampling for INGARCH processes

The temporal aggregation (TA) and systematic sampling (SS) in continuous-valued time series were widely studied, while the TA and SS in integer-valued time series obtain very little attention. In this paper, we thoroughly discuss them based on the integer-valued generalized autoregressive conditional heteroskedasticity (INGARCH) process. On one hand, the TA and SS for INGARCH processes are studied, and related predictors are discussed. We also illustrate that the TA or SS provides approaches to estimate INGARCH processes with different frequencies. On the other hand, definitions of the strong and weak INGARCH processes are given. The aggregated INGARCH and sampled INGARCH processes are shown to be weak, that is, they satisfy a weak characterization of INGARCH processes in terms of linear projection. Quasi maximum likelihood and nonlinear least squares estimation methods are considered for the weak INGARCH processes. Related asymptotic properties and simulation results are discussed. Finally, an empirical example illustrates the applicability of our results.

Forecasting Daily Volatility of Stock Price Index Using Daily Returns and Realized Volatility

A comprehensive comparison of the volatility predictive abilities of different classes of time-varying volatility models is considered. The models include the exponential GARCH (EGARCH) and stochastic volatility (SV) models using daily returns, the heterogeneous autoregressive (HAR) model using daily realized volatility (RV) and the realized EGARCH (REGARCH) and realized SV (RSV) models using both. All the models are extended to accommodate the well-known phenomenon in stock markets of a negative correlation between today’s return and tomorrow’s volatility. The HAR model is estimated by the ordinary least squares method, while the EGARCH and REGARCH models are estimated by the quasi-maximum likelihood method. Since it is not straightforward to evaluate the likelihood of the SV and RSV models, a Bayesian estimation via Markov chain Monte Carlo is employed. The models are applied to daily returns and/or RVs of four stock indices: the Dow Jones Industrial Average, the Nikkei 225, the Financial Times Stock Exchange 100, and the Euro Stoxx 50. By conducting predictive ability tests and analyses based on model confidence sets, it is confirmed that the models that use RV (RSV, REGARCH, and RSV) outperform those that do not (EGARCH and SV); this suggests that RV provides useful information in forecasting volatility. Moreover, it is found that the RSV model performs better than the HAR and REGARCH models.

Estimating the Instantaneous Frequency of Linear and Nonlinear Frequency Modulated Radar Signals-A Comparative Study.

Automatic modulation recognition plays a vital role in electronic warfare. Modern electronic intelligence and electronic support measures systems are able to automatically distinguish the modulation type of an intercepted radar signal by means of real-time intra-pulse analysis. This extra information can facilitate deinterleaving process as well as be utilized in early warning systems or give better insight into the performance of hostile radars. Existing modulation recognition algorithms usually extract signal features from one of the rudimentary waveform characteristics, namely instantaneous frequency (IF). Currently, there are a small number of studies concerning IF estimation methods, specifically for radar signals, whereas estimator accuracy may adversely affect the performance of the whole classification process. In this paper, five popular methods of evaluating the IF–law of frequency modulated radar signals are compared. The considered algorithms incorporate the two most prevalent estimation techniques, i.e., phase finite differences and time-frequency representations. The novel approach based on the generalized quasi-maximum likelihood (QML) method is also proposed. The results of simulation experiments show that the proposed QML estimator is significantly more accurate than the other considered techniques. Furthermore, for the first time in the publicly available literature, multipath influence on IF estimates has been investigated.

A periodic and seasonal statistical model for non-negative integer-valued time series with an application to dispensed medications in respiratory diseases

This paper introduces a new class of models for non-negative integer-valued time series with a periodic and seasonal autoregressive structure. Some properties of the model are discussed and the conditional quasi-maximum likelihood method is used to estimate the parameters. The consistency and asymptotic normality of the estimators are established. Their performances are investigated for finite sample sizes and the empirical results indicate that the method gives accurate estimates. The proposed model is applied to analyse the daily number of antibiotic dispensing medication for the treatment of respiratory diseases, registered in a health center of Vitória, Brazil.

Garchx: Flexible and Robust GARCH-X Modeling

The R package garchx provides a user-friendly, fast, flexible and robust framework for the estimation and inference of GARCH(p,q,r)-X models, where p is the ARCH order, q is the GARCH order, r is the asymmetry or leverage order, and 'X' indicates that covariates can be included. Quasi Maximum Likelihood (QML) methods ensure estimates are consistent and standard errors valid, even when the standardised innovations are non-normal or dependent, or both. Zero-coefficient restrictions by omission enable parsimonious specifications, and functions to facilitate the non-standard inference associated with zero-restrictions in the null-hypothesis are provided. Finally, in formal comparisons of precision and speed, the garchx package performs well relative to other prominent GARCH-packages on CRAN.

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.

Penalized profile quasi-maximum likelihood method of partially linear spatial autoregressive model

In this paper, we develop a class of penalized likelihood method to identify important explanatory variables in parametric component of partially linear spatial autoregressive model. Compared to existing estimation methods, the proposed method can simultaneously select the significant explanatory variables and estimate the nonzero parameters in the parametric component of partially linear spatial autoregressive model. Under appropriate conditions, we establish the consistency, sparsity and asymptotic normality properties of the resulting penalized likelihood estimator. Especially, with proper choice of the penalty function and the regularization parameter, the estimator of the nonzero parameter vector is shown to enjoy the oracle property, in the sense that it is asymptotically normal with the same mean vector and covariance matrix as those it would have if the zero parameters were known in advance. Furthermore, we propose a computationally feasible algorithm to obtain the penalized likelihood estimator. The finite sample performance of the proposed variable selection method is evaluated through extensive simulation studies and illustrated with a real data set.

Spatial dynamic models with intertemporal optimization: Specification and estimation

In this paper, we introduce a dynamic spatial interaction econometric model. There are n forward-looking agents of whom each has a parametric linear-quadratic payoff, and they interact with their neighbors through a spatial network. Considering a Markov perfect equilibrium (MPE), we derive a unique Nash equilibrium equation and construct a new spatial dynamic panel data (SDPD) model. For estimation, we suggest mainly the quasi-maximum likelihood (QML) method. Asymptotic properties of the QML estimator are investigated. In a Monte Carlo study, we estimate the model’s parameters and compare the results with those from traditional SDPD models. The model is applied to an empirical study on counties’ public safety spending in North Carolina.

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.

Statistical analysis of sparse approximate factor models

We consider the problem of estimating sparse approximate factor models. In a first step, we jointly estimate the factor loading parameters and the error - or idiosyncratic - covariance matrix based on the Gaussian quasi-maximum likelihood method. Conditionally on these first step estimators, using the SCAD, MCP and Lasso regularisers, we obtain a sparse error covariance matrix based on a Gaussian QML and, as an alternative criterion, a least squares loss function. Under suitable regularity conditions, we derive error bounds for the regularised idiosyncratic factor model matrix for both Gaussian QML and least squares losses. Moreover, we establish the support recovery property, including the case when the regulariser is non-convex. These theoretical results are supported by empirical studies.

Outliers and misleading leverage effect in asymmetric GARCH-type models

Abstract This paper illustrates how outliers can affect both the estimation and testing of leverage effect by focusing on the TGARCH model. Three estimation methods are compared through Monte Carlo experiments: Gaussian Quasi-Maximum Likelihood, Quasi-Maximum Likelihood based on the Student-t likelihood and Least Absolute Deviation method. The empirical behavior of the t-ratio and the Likelihood Ratio tests for the significance of the leverage parameter is also analyzed. Our results put forward the unreliability of Gaussian Quasi-Maximum Likelihood methods in the presence of outliers. In particular, we show that one isolated outlier could hide true leverage effect whereas two consecutive outliers bias the estimated leverage coefficient in a direction that crucially depends on the sign of the first outlier and could lead to wrongly reject the null of no leverage effect or to estimate asymmetries of the wrong sign. By contrast, we highlight the good performance of the robust estimators in the presence of one isolated outlier. However, when there are patches of outliers, our findings suggest that the sizes and powers of the tests as well as the estimated parameters based on robust methods may still be distorted in some cases. We illustrate these results with two series of daily returns.