Multiplicative Error Model Research Articles

Distributed extended object tracking information filter over sensor networks

AbstractThis work aims to design a distributed extended object tracking system over a realistic network, where both the extent and kinematics are required to retain consensus within the entire network. To this end, we resort to the multiplicative error model (MEM) that allows the extent parameters of perpendicular axis‐symmetric objects to have individual uncertainty. To incorporate the MEM into the information filter (IF) style, we use the moment‐matching technique to derive two pair linear models with only additive noise. The separation is merely in a fashion, and the cross‐correlation between states is preserved as parameters in each other's model. As a result, the closed‐form expressions are transferred into an alternating iteration of two linear IFs. With the two models, a centralized IF is proposed wherein the measurements are converted into a summation of innovation parts. Later, under a sensor network with the communication nodes and sensor nodes, we present two distributed IFs through the consensus on information and consensus on measurement schemes, respectively. Moreover, we prove the estimation errors of the proposed filter are exponentially bounded in the mean square. The benefits are testified by numerical experiments in comparison to state‐of‐the‐art filters in literature.

Model-Informed Rationale for Early Therapeutic Drug Monitoring of Colistin in Critically Ill Patients.

Adequate colistin exposure is important for microbiological clearance. This study was performed in critically ill patients >18 years old to develop a simplified nonparametric pharmacokinetic (PK) model of colistin for routine clinical use and to determine the role of dose optimization. The Non-Parametric Adaptive Grid algorithm within the Pmetrics software package for R was used to develop a PK model from 47 patients, and external validation of the final model was performed in 13 patients. A 1-compartment multiplicative gamma error model with 0-order input and first-order elimination of colistin was developed with creatinine clearance and serum albumin as covariates on elimination rate constant. An R2 for observed vs individual predicted colistin concentrations of 0.92 was obtained in the validation cohort. High interindividual variability in colistin steady-state area under the plasma concentration-time curve (AUC) from from 120 hours to 144 hours (coefficient of variation=80.1%) and a high interoccasion variability (median coefficient of variation of AUC from time 0 to hours predicted every 8hours for initial 96hours after starting colistin=23.8) was predicted in patients who received this antibiotic for a period of over 152hours (n=22). With the model-suggested dose regimen, only 20% of simulated profiles achieved AUC from time 0 to 24 hours in the range of 50 to 60mg• h/L due to high variability in population PK. In this group of patients, steady-state colistin concentrations were predicted to be achieved >96hours after initiation of colistimethate sodium. This study advocates the need for early and repeated therapeutic drug monitoring and dose optimization in critically ill patients to achieve adequate therapeutic concentration of colistin.

A method for mixed additive and multiplicative random error models with inequality constraints in geodesy

In the geodetic data processing field, most methods for dealing with inequality constraints model are based on additive random error (ARE) models, and there have been few studies on mixed additive and multiplicative random error (MAAMRE) models with inequality constraints. To address this problem, a MAAMRE model with inequality constraints is first established based on the definition of inequality constraint equations, and then, a corresponding parameter estimation algorithm is proposed based on the idea of an exhaustive search method. In addition, considering a MAAMRE model for an ill-posed problem, an iterative regularization solution for an ill-posed MAAMRE model is first derived, and then, a specific parameter estimation algorithm for an ill-posed MAAMRE model with inequality constraints is further proposed by applying the exhaustive search approach. Finally, the feasibility and advantages of the proposed algorithms are verified by global positioning system (GPS) elevation fitting model and digital terrain model (DTM) examples.Graphical

Deep learning for volatility forecasting in asset management

Predicting volatility is a critical activity for taking risk- adjusted decisions in asset trading and allocation. In order to provide effective decision-making support, in this paper we investigate the profitability of a deep Long Short-Term Memory (LSTM) Neural Network for forecasting daily stock market volatility using a panel of 28 assets representative of the Dow Jones Industrial Average index combined with the market factor proxied by the SPY and, separately, a panel of 92 assets belonging to the NASDAQ 100 index. The Dow Jones plus SPY data are from January 2002 to August 2008, while the NASDAQ 100 is from December 2012 to November 2017. If, on the one hand, we expect that this evolutionary behavior can be effectively captured adaptively through the use of Artificial Intelligence (AI) flexible methods, on the other, in this setting, standard parametric approaches could fail to provide optimal predictions. We compared the volatility forecasts generated by the LSTM approach to those obtained through use of widely recognized benchmarks models in this field, in particular, univariate parametric models such as the Realized Generalized Autoregressive Conditionally Heteroskedastic (R-GARCH) and the Glosten–Jagannathan–Runkle Multiplicative Error Models (GJR-MEM). The results demonstrate the superiority of the LSTM over the widely popular R-GARCH and GJR-MEM univariate parametric methods, when forecasting in condition of high volatility, while still producing comparable predictions for more tranquil periods.

Landslide Deformation Extraction from Terrestrial Laser Scanning Data with Weighted Least Squares Regularization Iteration Solution

The extraction of landslide deformation using terrestrial laser scanning (TLS) has many important applications. The landslide deformation can be extracted based on a digital terrain model (DTM). However, such methods usually suffer from the ill-posed problem of a multiplicative error model as illustrated in previous studies. Moreover, the edge drift of commonly used spherical targets for point cloud registration (PCR) is ignored in the existing method, which will result in the unstable precision of the PCR. In response to these problems, we propose a method for extracting landslide deformations from TLS data. To archive the PCR of different period point clouds, a new triangular pyramid target is designed to eliminate the edge drift. If a fixed target is inconvenient, we also propose a PCR method based on total station orientation. Then, the use of the Tikhonov regularization method to derive the weighted least squares regularization solution is presented. Finally, the landslide deformation is extracted by DTM deference. The experiments are conducted on two datasets with more than 1.5 billion points. The first dataset takes Lashagou NO. 3 landslide in Gansu Province, China, as the research object; the point cloud data were collected on 26 February 2021 and 3 May 2021. The registration accuracy was 0.003 m based on the permanent triangular pyramid target and 0.005 m based on the total station orientation. The landslide deforms within 3 cm due to the ablation of the frozen soil. The second dataset is TLS data from the Lihua landslide in Chongqing, China, collected on 20 April 2021 and 1 May 2021. The overall deformation of the Lihua landslide is small, with a maximum value of 0.011 m. The result shows that the proposed method achieves a better performance than previous sphere-based registration and that the weighted least square regularization iterative solution can effectively reduce the ill-condition of the model.

The improved artificial bee colony algorithm for mixed additive and multiplicative random error model and the bootstrap method for its precision estimation

To solve the complex weight matrix derivative problem when using the weighted least squares method to estimate the parameters of the mixed additive and multiplicative random error model (MAM error model), we use an improved artificial bee colony algorithm without derivative and the bootstrap method to estimate the parameters and evaluate the accuracy of MAM error model. The improved artificial bee colony algorithm can update individuals in multiple dimensions and improve the cooperation ability between individuals by constructing a new search equation based on the idea of quasi-affine transformation. The experimental results show that based on the weighted least squares criterion, the algorithm can get the results consistent with the weighted least squares method without multiple formula derivation. The parameter estimation and accuracy evaluation method based on the bootstrap method can get better parameter estimation and more reasonable accuracy information than existing methods, which provides a new idea for the theory of parameter estimation and accuracy evaluation of the MAM error model.

Unconventional Policies Effects on Stock Market Volatility: The MAP Approach

Abstract Taking the European Central Bank unconventional policies as a reference, we suggest a class of multiplicative error models (MEMs) tailored to analyse the impact such policies have on stock market volatility. The new set of models, called MEM with asymmetry and policy effects, keeps the base volatility dynamics separate from a component reproducing policy effects, with an increase in volatility on announcement days and a decrease unfolding implementation effects. When applied to four Eurozone markets, a model confidence set approach finds a significant improvement of the forecasting power of the proxy after the expanded asset purchase programme implementation. A multi-step ahead forecasting exercise estimates the duration of the effect; by shocking the policy variable, we are able to quantify the reduction in volatility which is more marked for debt-troubled countries.

Multiplicative Error Models: 20 years on

The issue of combining low– and high–frequency components of volatility is addressed within the class of Multiplicative Error Models both in the univariate and multivariate cases. Inference based on the Generalized Method of Moments is suggested, which has the advantage of not requiring a parametric choice for the error distribution. The application relates to several volatility market indices (US, Europe and East Asia, with interdependencies in the short–run components of absolute returns, realized kernel volatility and option–based implied volatility indices): a set of diagnostic tools is used to evaluate the evidence of a relevant low–frequency component across markets, also from a forecasting comparison perspective. The results show that the slow–moving component in the dynamics achieves a better fit to the data and allows for an interpretation of what moves the local average level of volatility.

Enantiospecific pharmacokinetics of intravenous dexmedetomidine in beagles.

The goal of this study was to investigate the pharmacokinetic (PK) behaviour of dexmedetomidine in dogs administered as a pure enantiomer versus as part of a racemic mixture. Eight unmedicated intact purpose‐bread beagles were included. Two intravenous treatments of either medetomidine or dexmedetomidine were administered at 10‐ to 14‐day intervals. Atipamezole or saline solution was administered intramuscularly 45 min later. Venous blood samples were collected into EDTA collection tubes, and the quantification of dexmedetomidine and levomedetomidine was performed by chiral LC–MS/MS. All dogs appeared sedated after each treatment without complication. Plasma concentrations of levomedetomidine were measured only in the racemic group and were 51.4% (51.4%–56.1%) lower than dexmedetomidine. Non‐compartmental analysis (NCA) was performed for both drugs, while dexmedetomidine data were further described using a population pharmacokinetic approach. A standard two‐compartment mammillary model with linear elimination with combined additive and multiplicative error model for residual unexplained variability was established for dexmedetomidine. An exponential model was finally retained to describe inter‐individual variability on parameters of clearance (Cl1) and central and peripheral volumes of distribution (V1, V2). No effect of occurrence, levomedetomidine or atipamezole could be observed on dexmedetomidine PK parameters. Dexmedetomidine did not undergo significantly different PK when administered alone or as part of the racemic mixture in otherwise unmedicated dogs.

Adaptive order flow forecasting with multiplicative error models

A flexible statistical approach for the analysis of time-varying dynamics of transaction data on financial markets is here applied to intra-day trading strategies. A local adaptive technique is used to successfully predict financial time series, i.e. the buyer- and the seller-initiated trading volumes and the order flow dynamics. Analysing order flow series and its information content of mini Nikkei 225 index futures traded at the Osaka Securities Exchange in 2012 and 2013, a data-driven optimal length of local windows up to approximately 1–2 h is reasonable to capture parameter variations and is suitable for short-term prediction. Our proposed trading strategies achieve statistical arbitrage opportunities and are, therefore, beneficial for quantitative finance practice.

Model Averaging Estimation Method by Kullback–Leibler Divergence for Multiplicative Error Model

In this paper, we propose the model averaging estimation method for multiplicative error model and construct the corresponding weight choosing criterion based on the Kullback–Leibler divergence with a hyperparameter to avoid the problem of overfitting. The resulting model average estimator is proved to be asymptotically optimal. It is shown that the Kullback–Leibler model averaging (KLMA) estimator asymptotically minimizes the in‐sample Kullback–Leibler divergence and improves the forecast accuracy of out‐of‐sample even under different loss functions. In simulations, we show that the KLMA estimator compares favorably with smooth‐AIC estimator (SAIC), smooth‐BIC estimator (SBIC), and Mallows model averaging estimator (MMA), especially when some nonlinear noise is added to the data generation process. The empirical applications in the daily range of S&P500 and price duration of IBM show that the out‐of‐sample forecasting capacity of the KLMA estimator is better than that of other methods.

Triple collocation-based error estimation and data fusion of global gridded precipitation products over the Yangtze River basin

Error estimation and data fusion are critical to improving the accuracy of global model- and satellite-based precipitation products for practical applications. However, they face challenges over vast areas of the world due to limited ground observations. Triple collocation (TC) method can overcome this limitation and provide an efficient way for error estimation without the “ground truth” and thus also for data fusion, by leveraging multi-source observations and model outputs, which have been increasingly available in recent years. In this work, we conducted a comprehensive study on error estimation and data fusion of a number of global gridded precipitation products over the Yangtze River basin from 2015 to 2018 using TC and multiplicative TC (MTC) methods. We use three satellite-based precipitation products such as the IMERG Final (IMERG-F), PERSIANN-CDR (PCDR) and SM2RAIN-ASCAT (SM2R), and one reanalysis dataset ERA5 which contains precipitation estimates. They were grouped into two TC triplets based on different combinations: IMERG-F + SM2R + ERA5 and PCDR + SM2R + ERA5. For performance evaluation, the TC-based error estimation methods were compared to the traditional method using rain gauge data, and the TC-based data fusion methods were compared with two widely-used data fusion methods Bayesian Model Averaging (BMA) and Random Forest based MErging Procedure (RF-MEP). Results showed that ERA5 had the best performance with the largest correlation coefficient (CC, 0.435), while PCDR had the worst accuracy with the smallest CC (0.304) and the largest absolute relative bias (RB, 0.365). TC tended to underestimate the root mean square error (RMSE) with respect to the traditional gauged-based method, but MTC showed a consistent result owing to the employment of a multiplicative error model. The performance of TC-based data fusion methods had no significant difference from BMA and RF-MEP. All data fusion results were better than the original triplets, as the mean CC value increased from 0.38 to 0.47 and the mean RMSE decreased from 15.0 to 13.5 mm/day. In addition, we found that the zero value replacement in MTC had great influence on error estimation, while had limited impacts on data fusion.

Virtual Observation Iteration Solution and A-Optimal Design Method for Ill-Posed Mixed Additive and Multiplicative Random Error Model in Geodetic Measurement

AbstractThe mixed additive and multiplicative random error model is a combination of the additive error random model and multiplicative random error model. Weakness is an attribute of the mixed add...

On a Weibull-Distributed Error Component of a Multiplicative Error Model Under Inverse Square Root Transformation

We first consider the Multiplicative Error Model (MEM) introduced in financial econometrics by Engle (2002) as a general class of time series model for positive-valued random variables, which are decomposed into the product of their conditional mean and a positive-valued error term. Considering the possibility that the error component of a MEM can be a Weibull distribution and the need for data transformation as a popular remedial measure to stabilize the variance of a data set prior to statistical modeling, this paper investigates the impact of the inverse square root transformation (ISRT) on the mean and variance of a Weibull-distributed error component of a MEM. The mean and variance of the Weibull distribution and those of the inverse square root transformed distribution are calculated for σ=6, 7,.., 99, 100 with the corresponding values of n for which the mean of the untransformed distribution is equal to one. The paper concludes that the inverse square root would yield better results when using MEM with a Weibull-distributed error component and where data transformation is deemed necessary to stabilize the variance of the data set.

Ridge estimation iterative solution of ill-posed mixed additive and multiplicative random error model with equality constraints

The reasonable prior information between the parameters in the adjustment processing can significantly improve the precision of the parameter solution. Based on the principle of equality constraints, we establish the mixed additive and multiplicative random error model with equality constraints and derive the weighted least squares iterative solution of the model. In addition, aiming at the ill-posed problem of the coefficient matrix, we also propose the ridge estimation iterative solution of ill-posed mixed additive and multiplicative random error model with equality constraints based on the principle of ridge estimation method and derive the U-curve method to determine the ridge parameter. The experimental results show that the weighted least squares iterative solution can obtain more reasonable parameter estimation and precision information than existing solutions, verifying the feasibility of applying the equality constraints to the mixed additive and multiplicative random error model. Furthermore, the ridge estimation iterative solution can obtain more accurate parameter estimation and precision information than the weighted least squares iterative solution.

Weighted least squares regularization iteration solution and precision estimation for ill-posed multiplicative error model

Weighted least squares regularization iteration solution and precision estimation for ill-posed multiplicative error model

The Incidence of Spillover Effects during the Unconventional Monetary Policies Era

In a context characterized by an increasing integration among financial markets, we aim to analyze whether the ECB unconventional monetary policy shields the Eurozone stock markets against spillovers of volatility from the US stock market. We augment the Markov switching Asymmetric Multiplicative Error Model (MS-AMEM) with exogenous variables to measure transmissions of volatility from the S&P500 index, on the one hand, and the announcement and implementation effects of unconventional policy, on the other hand. By estimating our model, the MS-AMEMX, on a sample of daily observations of the realized volatility of four Eurozone stock indices (CAC40, DAX30, FTSEMIB and IBEX35), we find how the increase in volatility brought about by volatility spillovers was mitigated by the implementation of unconventional policy, with a higher benefit for high-debt countries’ stock indices (FTSEMIB and IBEX35). Finally, the out-of-sample analysis certifies the suitability of our proxies also for forecasting purposes.

An improved error decomposition scheme for satellite-based precipitation products

The conventional error decomposition schemes of satellite-based precipitation products (SPPs) suffer from significant drawbacks such as misrepresentation of hit bias (H) component and magnification of random error, which limits their accuracy in deducing reliable conclusions. We propose a novel error decomposition technique by disintegrating the total bias (TB) in SPPs into four different independent components - over-hit (OH), under-hit (–UH), missed (–M) and false (F) precipitation. Further, the systematic and random parts are identified by adopting a multiplicative error model. The efficacy of the proposed scheme is demonstrated by comparing six different SPPs over India with a high-resolution gridded observed reference rainfall dataset by the India Meteorological Department, at daily-time scale for 16 years (2001–2016). The results of the study highlight that the traditional hit component is mostly underestimated due to the cancelling of opposite natured OH and –UH bias components and hence is unreliable. Often, the magnitudes of OH and –UH are found to be higher than TB and H. The proposed OH and –UH bias accurately estimates the “intensity” error in satellite precipitation retrieval process and can be used by both the data producers and users for deriving reliable conclusions. The findings of the study will aid in a more reliable and accurate characterization of error in SPPs, which is a fundamental step in the development of uncertainty modelling and bias-reduction algorithms.

A novel multi-source data fusion method based on Bayesian inference for accurate estimation of chlorophyll-a concentration over eutrophic lakes

A novel multi-source data fusion method based on Bayesian inference (BIF) was proposed in this study to blend the advantages of in-situ observations and remote sensing estimations for obtaining accurate chlorophyll-a (Chla) concentration in Lake Taihu (China). Two error models (additive and multiplicative) were adopted to construct the likelihood function in BIF; the BIF method was also compared with three commonly used data fusion algorithms, including linear and nonlinear regression data fusion (LRF and NLRF) and cumulative distribution function matching data fusion (CDFF). The results showed the multiplicative error model had small normalized residual errors and was a more suitable choice. The BIF method largely outperformed the data fusion algorithms of CDFF, NLRF and LRF, with the largest correlation coefficients and smallest root mean square error. Moreover, the BIF results can capture the high Chla concentrations in the northwest and the low Chla concentrations in the east of Lake Taihu.

On classifying the effects of policy announcements on volatility

The financial turmoil surrounding the Great Recession called for unprecedented intervention by Central Banks: unconventional policies affected various areas in the economy, including stock market volatility. In order to evaluate such effects, by including Markov Switching dynamics within a recent Multiplicative Error Model, we propose a model–based classification of the dates of a Central Bank's announcements to distinguish the cases where the announcement implies an increase or a decrease in volatility, or no effect. In detail, we propose two smoothed probability–based classification methods, obtained as a by–product of the model estimation, which provide very similar results to those coming from a classical k–means clustering procedure. The application on four Eurozone market volatility series shows a successful classification of 144 European Central Bank announcements.