Multiplicative Error Model Research Articles

Testing weak exogeneity in multiplicative error models

Empirical market microstructure literature widely employs the non-linear and non-Gaussian multiplicative error class of models (MEMs) in modelling the dynamics of trading duration and financial marks. It routinely maintains the weak exogeneity of duration vis-à-vis marks in estimations. However, microstructure theory states that trade duration, volume and transaction prices are simultaneously determined. We propose Lagrange-multiplier (LM) tests for weak exogeneity for the MEMs. Our LM tests are extensions of the weak exogeneity tests applicable to VAR or VECM models with Gaussian distributions. Empirical assessments show that (i) weak exogeneity is widely rejected by the data in the MEMs and (ii) the failure of weak exogeneity seriously biases parameter estimates. We hope our tests will be of interest in future empirical applications.

Chasing volatility: A persistent multiplicative error model with jumps

Persistence and unpredictable large increments characterize the volatility of financial returns. We propose the Multiplicative Error Model with volatility jumps (MEM-J) to describe and predict the probability and the size of these extreme events. Under the MEM-J, the conditional density of the realized measure is a countably infinite mixture of Gamma and Kappa distributions, with closed form conditional moments. We derive stationarity conditions and the asymptotic theory for the maximum likelihood estimation. Estimates of the volatility jump component confirm that the probability of jumps dramatically increases during the financial crises. The MEM-J improves over other models with fat tails.

Reliability based calibration of safety factors for unstiffened cylindrical composite shells

The feasibility of probabilistic design methods to overcome conservatism associated with deterministic design methods for unstiffened cylindrical composite shells has been shown, but studies are frequently based on assumptions regarding relevant uncertainties due to the lack of available data. The reliability based calibration method suggested here relies on extensive measurements regarding the statistical characteristics of thickness, fibre volume fraction, fibre orientation, material stiffness and geometric imperfections of 11 previously tested cylinders. Furthermore, the stiffness of the potting of tested cylinders is estimated using Finite Element Analysis and the introduction of a pre-stress state through the potting process investigated. Following a sensitivity study, Bayesian inference is used to update the information of relevant uncertain variables. Monte Carlo simulation is employed to compute the distribution functions of the buckling load, and these are used to calibrate structural safety factors at a chosen reliability level. A multiplicative error model is established to compute safety factors covering the model uncertainty inherent to the approach. In combining these two safety factors in a Bayesian sense, a transparent, updatable safety-factor concept is developed, leading to less conservative design loads than currently considered.

CYP2B6 Genotype Guided Dosing of Propofol Anesthesia in the Elderly Based on Nonparametric Population Pharmacokinetic Modeling and Simulations

The primary aim of this article is to test the hypothesis that nonparametric pharmacometric modeling will accurately identify CYP2B6 genotype subgroups based on data from a study that reported results based on parametric pharmacokinetics (PK). Propofol concentration-time data were originally reported in the Kansaku et al. 2011 publication. Nonparametric Nonlinear Mixed Effects Modeling (NLME) was conducted using the PMETRICS R package while population pharmacokinetic model parameters were estimated using a FORTRAN compiler. Finally, model-based dosing simulations were conducted in the MATLAB Simbiology. A total of 51 patients were included in the final PK analysis. A two-compartment gamma multiplicative error model adequately described the propofol concentration-time data. The precision of the goodness-of-fit plots resulted in an R2 of 0.927 and an R2 of 0.992 for the population prediction and individual predictions, respectively. Neither the UGT1A9 nor the CYP2B6 G516T gene variants resulted in statistically significant PK parameter differences while the CYP2B6 A785G gene variants resulted in statistically significant differences for the elimination rate. Model-based dosing-simulations comparing patients with the CYP2B6 AA & AG genotypes to both GG genotypes and patients from a multicenter trial suggest a 50% decrease in propofol infusion dose, to 25mg/kg/min, be made to result in approximately equivalent drug exposures. Based on the pharmacometric modeling and simulation, if no dosage adjustments are made for the elderly CYP2B6 AA and AG genotypes, a 250% higher propofol blood exposure will be evident within 1-hour from the start of the infusion. Thus, based on the pharmacokinetic model, genotyping elderly patients for the CYP2B6 AA and AG gene variants will decrease the total propofol blood exposure during anesthesia and sedation when an infusion dose adjustment is made to 25mg/kg/min.

Analysis of the Visibility Data for the Combinations of Foreground and Background Colors by Maximum Likelihood Asymmetric MDS Using the Multiplicative Error Model

Analysis of the Visibility Data for the Combinations of Foreground and Background Colors by Maximum Likelihood Asymmetric MDS Using the Multiplicative Error Model

Fitting a two phase threshold multiplicative error model

The recent literature on financial time series analysis has devoted considerable attention to nonnegative time series, such as financial durations, realized volatility, and squared returns. The class of models, referred to as the multiplicative error models [MEM], is particularly suited to model such nonnegative time series. We develop a lack-of-fit test for fitting a two-phase threshold model for the conditional mean function in an MEM. The proposed testing procedure can also be applied to a class of autoregressive conditional heteroscedastic threshold models. We evaluate the test in a simulation study. The testing procedure is illustrated by using two data examples.

The logarithmic vector multiplicative error model: an application to high frequency NYSE stock data

We develop a general form logarithmic vector multiplicative error model (log-vMEM). The log-vMEM improves on existing models in two ways. First, it is a more general form model as it allows the error terms to be cross-dependent and relaxes weak exogeneity restrictions. Second, the log-vMEM specification guarantees that the conditional means are non-negative without any restrictions imposed on the parameters. We further propose a multivariate lognormal distribution and a joint maximum likelihood estimation strategy. The model is applied to high frequency data associated with a number of NYSE-listed stocks. The results reveal empirical support for full interdependence of trading duration, volume and volatility, with the log-vMEM providing a better fit to the data than a competing model. Moreover, we find that unexpected duration and volume dominate observed duration and volume in terms of information content, and that volatility and volatility shocks affect duration in different directions. These results are interpreted with reference to extant microstructure theory.

A Nonparametric Pharmacokinetic Approach to Determine the Optimal Dosing Regimen for 30-Minute and 3-Hour Meropenem Infusions in Critically Ill Patients.

Pharmacokinetics of meropenem differ widely in the critically ill population. It is imperative to maintain meropenem concentrations above the inhibitory concentrations for most of the interdose interval. A population pharmacokinetic/pharmacodynamic model was developed to determine the probability of target attainment for 3-hour and 30-minute infusion regimens in this population. This study was performed in an intensive care setting among adult patients who were initiated on meropenem at a dose of 1000 mg. Multiple blood specimens were collected at predetermined time points during the interdose period, and meropenem concentrations were measured using high performance liquid chromatography. Using Pmetrics, a pharmacokinetic/pharmacodynamic model was developed and validated. Monte Carlo simulation was performed, and probability of target attainment (100% T > minimum inhibitory concentration (MIC), with a probability >0.9) for doubling MICs was determined for different regimens of meropenem. A 2-compartment multiplicative gamma error model best described the population parameters from 34 patients. The pharmacokinetic parameters used in the final model were Ke (elimination rate constant from the central compartment), Vc (volume of distribution of central compartment), KCP and KPC (intercompartmental rate constants), and IC2 (the fitted amount of meropenem in the peripheral compartment). Inclusion of creatinine clearance (CLcreat) and body weight as covariates improved the model prediction (Ke = Ke0 × (Equation is included in full-text article.), Vc = Vc0 × Weight). The Ke and Vc [geometric mean (range)] of the individuals were 0.54 (0.01-2.61)/h and 9.36 (4.35-21.62) L, respectively. The probability of attaining the target, T > MIC of 100%, was higher for 3-hour infusion regimens compared with 30-minute infusion regimens for all ranges of CLcreat. This study emphasizes that extended regimens of meropenem are preferable for treating infections caused by bacteria with higher MICs. The nonparametric analysis using body weight and CLcreat as covariate adequately predicted the pharmacokinetics of meropenem in critically ill patients with a wide range of renal function.

Causes and consequences of energy price shocks on petroleum-based stock market using the spillover asymmetric multiplicative error model

We employ the spillover Asymmetric Multiplicative Error Model (SAMEM) to investigate the impacts of the global financial crises and the geopolitical instability in the oil rich countries. Consequently, such these events have a significant impact on the petroleum-based stock markets in the Gulf Cooperation Council (GCC) countries. The geopolitical instability includes several sources such as the Iran nuclear negotiations, the ISIS and other jihadist organizations, the continuous interruption in Iraq, the civil war in Syria, Libya, Yemen, as well as the rivalry between Shiite Iran and Sunni Saudi Arabia is the engine of conflict in the Middle East have a great impact on the oil price fluctuation. We find that the recent global financial crises and the geopolitical instability have a significant impact on both oil and natural gas prices. These shocks also have a significant impact on the selected petroleum-based stock markets during the period (July 18th, 2006–July 30th, 2015). The policy implications of the results are important for portfolio managers in the financial markets and the policy makers in the petroleum-based economies (as represented by the GCC stock markets).

The dependence structure in volatility between Shanghai and Shenzhen stock market in China

Purpose – The purpose of this paper is to analyse the dependence structure in volatility between Shanghai and Shenzhen stock market in China based on high-frequency data. Design/methodology/approach – Using a multiplicative error model (hereinafter MEM) to describe the margins in volatility of China’s Shanghai and Shenzhen stock market, this study adopts static and time-varying copulas, respectively, estimated by maximum likelihood estimation method to describe the dependence structure in volatility between Shanghai and Shenzhen stock market in China. Findings – This paper has identified the asymmetrical dependence structure in financial market volatility more precisely. Gumbel copula could best fit the empirical distribution as it can capture the relatively high dependence degree in the upper tail part corresponding to the period of volatile price fluctuation in both static and dynamic view. Originality/value – Previous scholars mostly use GARCH model to describe the margins for price volatility. As MEM can efficiently characterize the volatility estimators, this paper uses MEM to model the margins for the market volatility directly based on high-frequency data, and proposes a proper distribution for the innovation in the marginal models. Then we could use copula-MEM other than copula-GARCH model to study on the dependence structure in volatility between Shanghai and Shenzhen stock market in China from a microstructural perspective.

Local Adaptive Multiplicative Error Models for High- Frequency Forecasts

We propose a local adaptive multiplicative error model (MEM) accommodating time-varying parameters. MEM parameters are adaptively estimated based on a sequential testing procedure. A data-driven optimal length of local windows is selected, yielding adaptive forecasts at each point in time. Analyzing one-minute cumulative trading volumes of five large NASDAQ stocks in 2008, we show that local windows of approximately 3 to 4 hours are reasonable to capture parameter variations while balancing modelling bias and estimation (in)efficiency. In forecasting, the proposed adaptive approach significantly outperforms a MEM where local estimation windows are fixed on an ad hoc basis.

Generalized Degrees of Freedom

Two popular regression methods for the multiplicative-error model are the Minimum-Unbiased-Percent Error and Minimum-Percentage Error under the Zero-Percentage Bias methods. The Minimum-Unbiased-Percent Error method, an Iteratively Reweighted Least Squares regression, does not use any constraints, while the Minimum-Percentage Error under the Zero-Percentage Bias method requires a constraint as part of the curve-fitting process. However, Minimum-Percentage Error under the Zero-Percentage Bias users do not adjust the degrees of freedom to account for constraints included in the regression process. As a result, fit statistics for the Minimum-Percentage Error under the Zero-Percentage bias equations, e.g., the standard percent error and generalized R2, can be incorrect and misleading. This results in incompatible fit statistics between Minimum-Percentage Error under the Zero-Percentage Bias and Minimum-Unbiased-Percent Error equations. This article details why degrees of freedom should be adjusted and recomme...

Copula-Based Specification of Vector MEMs

The Multiplicative Error Model (Engle (2002)) for nonnegative valued processes is specified as the product of a (conditionally autoregressive) scale factor and an innovation process with nonnegative support. A multivariate extension allows for the innovations to be contemporaneously correlated. We overcome the lack of sufficiently flexible probability density functions for such processes by suggesting a copula function approach to estimate the parameters of the scale factors and of the correlations of the innovation processes. We illustrate this vector MEM with an application to the interactions between realized volatility, volume and the number of trades. We show that significantly superior realized volatility forecasts are delivered in the presence of other trading activity indicators and contemporaneous correlations.

On estimating the nonparametric multiplicative error models

In a nonparametric multiplicative error model, this paper considers estimation of the regression mean function when the error is conditional homoscedastic. To exploit the conditional homoscedasticity information, we propose to estimate the conditional mean function using nonparametric generalized method of moments. The resulted estimator is shown to be asymptotically normal and enjoy superior finite sample properties in Monte Carlo simulations.

Generalized multiple indicators, multiple causes measurement error models

Generalized Multiple Indicators, Multiple Causes Measurement Error Models (G-MIMIC ME) can be used to study the effects of an unobservable latent variable on a set of outcomes when the causes of the latent variables are unobserved. The errors associated with the unobserved causal variables can be due to either bias recall or day-to-day variability. Another potential source of error, the Berkson error, is due to individual variations that arise from the assignment of group data to individual subjects. In this article, we accomplish the following: (a) extend the classical linear MIMIC models to allow both Berkson and classical measurement errors where the distributions of the outcome variables belong in the exponential family, (b) develop likelihood based estimation methods using the MC-EM algorithm and (c) estimate the variance of the classical measurement error associated with the approximation of the amount of radiation dose received by atomic bomb survivors at the time of their exposure. The G-MIMIC ME model is applied to study the effect of genetic damage, a latent construct based on exposure to radiation, and the effect of radiation dose on physical indicators of genetic damage.

SPECIFICATION TESTS FOR MULTIPLICATIVE ERROR MODELS

The family of multiplicative error models is important for studying non-negative variables such as realized volatility, trading volume, and duration between consecutive financial transactions. Methods are developed for testing the parametric specification of a multiplicative error model, which consists of separate parametric models for the conditional mean and the error distribution. The same method can also be used for testing the specification of the error distribution provided the conditional mean is correctly specified. A bootstrap method is proposed for computing the p-values of the tests and is shown to be consistent. The proposed tests have nontrivial asymptotic power against a class of O(n−1/2)-local alternatives. The tests performed well in a simulation study, and they are illustrated using a data example on realized volatility.

Forecasting Intraday Trading Volume: A Kalman Filter Approach

An accurate forecast of intraday volume is a key aspect of algorithmic trading. This manuscript proposes a state-space model to forecast intraday trading volume via the Kalman filter and derives closed-form expectation-maximization (EM) solutions for model calibration. The model is extended to handle outliers in real-time market data by applying a sparse regularization technique. Empirical studies using thirty securities on eight exchanges show that the proposed model substantially outperforms the rolling means (RM) and the state-of-the-art Component Multiplicative Error Model (CMEM) by 64% and 29%, respectively, in volume prediction and by 15% and 9%, respectively, in Volume Weighted Average Price (VWAP) trading.

Dynamic conditional correlation multiplicative error processes

We introduce a dynamic model for multivariate processes of (non-negative) high-frequency trading variables revealing time-varying conditional variances and correlations. Modeling the variables' conditional mean processes using a multiplicative error model, we map the resulting residuals into a Gaussian domain using a copula-type transformation. Based on high-frequency volatility, cumulative trading volumes, trade counts and market depth of various stocks traded at the NYSE, we show that the proposed transformation is supported by the data and allows capturing (multivariate) dynamics in higher order moments. The latter are modeled using a DCC-GARCH specification. We suggest estimating the model by composite maximum likelihood which is sufficiently flexible to be applicable in high dimensions. Strong empirical evidence for time-varying conditional (co-)variances in trading processes supports the usefulness of the approach. Taking these higher-order dynamics explicitly into account significantly improves the goodness-of-fit and out-of-sample forecasts of the multiplicative error model.

Evaluation of Precipitation Retrievals From Orbital Data Products of TRMM Over a Subtropical Basin in India

The spatial error structure of daily precipitation derived from the latest version 7 (v7) tropical rainfall measuring mission (TRMM) level 2 data products are studied through comparison with the Asian precipitation highly resolved observational data integration toward evaluation of the water resources (APHRODITE) data over a subtropical region of the Indian subcontinent for the seasonal rainfall over 6 years from June 2002 to September 2007. The data products examined include v7 data from the TRMM radiometer Microwave Imager (TMI) and radar precipitation radar (PR), namely, 2A12, 2A25, and 2B31 (combined data from PR and TMI). The spatial distribution of uncertainty from these data products were quantified based on performance metrics derived from the contingency table. For the seasonal daily precipitation over a subtropical basin in India, the data product of 2A12 showed greater skill in detecting and quantifying the volume of rainfall when compared with the 2A25 and 2B31 data products. Error characterization using various error models revealed that random errors from multiplicative error models were homoscedastic and that they better represented rainfall estimates from 2A12 algorithm. Error decomposition techniques performed to disentangle systematic and random errors verify that the multiplicative error model representing rainfall from 2A12 algorithm successfully estimated a greater percentage of systematic error than 2A25 or 2B31 algorithms. Results verify that although the radiometer derived 2A12 rainfall data is known to suffer from many sources of uncertainties, spatial analysis over the case study region of India testifies that the 2A12 rainfall estimates are in a very good agreement with the reference estimates for the data period considered.

Testando o poder preditivo do VIX: uma aplicação do modelo de erro multiplicativo

O VIX -- Volatility Index -- surgiu como uma alternativa no cálculo da volatilidade implícita, visando mitigar alguns problemas encontrados em modelos da família Black-Scholes. Este tipo de volatilidade é tida como a melhor previsora da volatilidade futura, dado que as expectativas dos operadores de opções se encontram embutidas em seus valores. O objetivo deste trabalho é testar se o VIX apresenta maior poder preditivo da volatilidade futura e contém informações relevantes não presentes em modelos de séries temporais para variáveis não-negativas, tratadas através do modelo de erro multiplicativo. Os resultados indicam que o VIX apresenta maior poder preditivo em períodos de estabilidade econômica, mas não contém informação relevante frente à volatilidade realizada considerada aqui como a "verdadeira volatilidade". Em períodos de crise econômica o resultado se altera, com o VIX apresentando o mesmo poder explicativo, mas contendo informações relevantes no curto prazo.