SIMULATION OF MULTINOMIAL PROBIT PROBABILITIES AND IMPUTATION OF MISSING DATA

For multivariate datasets with missing values, we present a procedure of statistical inference and state its “optimal” properties. Two main assumptions are needed: 1 data are missing at random (MAR); 2 the data generating process is a multivariate normal linear regression. Disentangling the problem of convergence of the iterative estimation/imputation procedure, we show that the estimator is a “method of simulated scores” (a particular case of McFadden’s “method of simulated moments”); thus the estimator is equivalent to maximum likelihood if the number of replications is conveniently large, and the whole procedure can be considered an optimal parametric technique for imputation of missing data.

Estimating Nonlinear DSGE Models by the Simulated Method of Moments

Missing data problem is ubiquitous in many real life situations. Information Technology researchers have explored and tried to address this problem in different settings. In this thesis, we undertake research to address missing data problem associated with order book information in stock markets. This is an in-depth and large-scale study with systematic and comprehensive framework to address missing data problem in the finance literature. Orders placed by traders and the corresponding order imbalance (OIB) is informative to predict future stock returns, however, stock exchange rules do not reveal price sensitive complete order book data for traders. Hence, return prediction using the revealed, incomplete trade book data (that contains only matched buy and sell orders and deletes the unmatched orders), does not let traders to completely exploit possible short term trading opportunities. Hence, this can be considered as a classical missing data problem for predicting future returns, by using the information content of order book. This thesis addresses the missing data problem by developing an integrated theoretical framework applied in stock market trading environment. We use relational Markov networks theory and build an empirically testable Algorithm for Imputed Complete Order Book (AICOB). The thesis contributes by developing a new theoretical advancement of information technology research relating to missing data problem and applying it to financial markets. First, the thesis presents the missing data problem as a Missing at Random (MAR) data and builds a systematic framework to estimate single as well as joint log likelihood functions. The thesis demonstrates that estimating by using incomplete records, improves the accuracy of the parameter estimates. Second, the thesis proposes a Relational Markov Network Model for estimation of the joint distribution function of orders, order characteristics and their interactions. Later, the Expectation Maximization Algorithm is proposed to address the missing data problem during the joint estimation procedure. All pooled regression results follow Fama and MacBeth (1973) and Generalized Methods of Moments (GMM) methods. These methods control the cross sectional and time series correlations between the observations and across the pooled stocks. The proposed novel methodology overcomes the estimation problem in the context of missing order book data. Third, the thesis develops an objective evaluation strategy for AICOB, based on efficiency, accuracy and adaptability dimensions. The thesis uses Australian stock market data, which provides not only trade book data but also historical order book data for cross validating the results. This unique setting allows validating the accuracy of AICOB methodology by comparing with complete order book data. The main contribution of the thesis is to show that AICOB based predictions match with the complete order book data. Whereas, trade book based predictions are quite inconsistent to the complete order book data. The AICOB based results are also consistent with the theoretical predictions proposed in finance literature that OIB predicts better as the firm size increases. The results show that large firms, with higher trading activity and more competition for order flows, report more significant OIB prediction of future returns. Trade Book based OIB estimates, which suffer from missing data problem, fail to predict future returns for stock portfolios. Hence, addressing the missing data problem is important before implementing OIB based trading strategies. Overall, the thesis finds that machine learning applications, similar to AICOB, can be helpful in implementing the trading strategies in financial markets. The imputation of missing data, through systematic procedures, based on theoretical distributional properties of the financial variables, can be informative for more accurate prediction of future returns. The thesis contributes towards establishing a common ground for cross-disciplinary research in Finance and Information Technology (IT) by applying the advances in IT research to solve research and corresponding implementation problems in finance. Further, the thesis contributes towards advancing the order imbalance literature by showing that missing data can play a critical role in the predictive ability of order imbalance.

The impact of the missing data mechanism on estimates of model parameters for continuous data has been extensively investigated in the literature. In comparison, minimal research has been carried out for the impact of missing count data. The focus of this article is to investigate the impact of missing data on a transition model, termed the generalized autoregressive model of order 1 for longitudinal count data. The model has several features, including modeling dependence and accounting for overdispersion in the data, that make it appealing for the clinical trial setting. Furthermore, the model can be viewed as a natural extension of the commonly used log-linear model. Following introduction of the model and discussion of its estimation we investigate the impact of different missing data mechanisms on estimates of the model parameters through a simulation experiment. The findings of the simulation experiment show that, as in the case of normally distributed data, estimates under the missing completely at random (MCAR) and missing at random (MAR) mechanisms are close to their analogue for the full dataset and that the missing not at random (MNAR) mechanism has the greatest bias. Furthermore, estimates based on imputing the last observed value carried forward (LOCF) for missing data under the MAR assumption are similar to those of the MAR. This latter finding might be attributed to the Markov property underlying the model and to the high level of dependence among successive observations used in the simulation experiment. Finally, we consider an application of the generalized autoregressive model to a longitudinal epilepsy dataset analyzed in the literature.

This work proposes and evaluates two methods (CM1 and CM2) for detecting non-compliance using concentration-time data and for obtaining estimates of population pharmacokinetic model parameters in a population with prevalent non-compliance. CM1 estimates individual residual variability (RV) and identifies subjects with higher than average RV as non-compliant. Exclusion of subjects with high RV from the analysis dataset reduces the bias in the estimates of the model parameters. Various methods of identification and exclusion of non-compliant subjects were tested, compared, and shown to reduce or eliminate bias in parameter estimates associated with non-compliance. The tested methods were (i) a pre-defined cutoff value of the random effect on RV, (ii) sequential exclusion of subjects with the highest RV percentiles, and (iii) use of a mixture model for RV. CM2 is applicable for the data with a specific sampling pattern that includes a potentially non-compliant outpatient part with several trough samples followed by a dense profile after the inpatient (compliant) dose. It relies only on the doses known to be administered (e.g., inpatient doses). In this method, all concentration measurements during the outpatient part of the study (except the trough value immediately preceding the inpatient dose) are removed from the dataset and an additional parameter (individual relative bioavailability of the outpatient doses) is introduced. For a number of simulated datasets with various sampling schemes and non-compliance patterns the proposed methods allowed to identify subjects with compliance problems and to reduce or eliminate bias in the estimates of the model parameters.

Detecting genetic variants for extreme aging using multiple data sources

This article considers the estimation of the parameters of a copula via a simulated method of moments (MM) type approach. This approach is attractive when the likelihood of the copula model is not known in closed form, or when the researcher has a set of dependence measures or other functionals of the copula that are of particular interest. The proposed approach naturally also nests MM and generalized method of moments estimators. Drawing on results for simulation-based estimation and on recent work in empirical copula process theory, we show the consistency and asymptotic normality of the proposed estimator, and obtain a simple test of overidentifying restrictions as a specification test. The results apply to both iid and time series data. We analyze the finite-sample behavior of these estimators in an extensive simulation study. We apply the model to a group of seven financial stock returns and find evidence of statistically significant tail dependence, and mild evidence that the dependence between these assets is stronger in crashes than booms. Supplementary materials for this article are available online.

The Taming of the Two - Simulation-Based Asset Pricing with Multi-Period Disasters and Two Consumption Goods

This paper considers mixed, or random coefficients, multinomial logit (MMNL) models for discrete response, and establishes the following results. Under mild regularity conditions, any discrete choice model derived from random utility maximization has choice probabilities that can be approximated as closely as one pleases by a MMNL model. Practical estimation of a parametric mixing family can be carried out by Maximum Simulated Likelihood Estimation or Method of Simulated Moments, and easily computed instruments are provided that make the latter procedure fairly efficient. The adequacy of a mixing specification can be tested simply as an omitted variable test with appropriately defined artificial variables. An application to a problem of demand for alternative vehicles shows that MMNL provides a flexible and computationally practical approach to discrete response analysis. Copyright © 2000 John Wiley & Sons, Ltd.

Existing empirical research investigating the size of the equity premium has largely consisted of a series of innovations around a common theme: producing a better estimate of the equity premium by using better data or a better estimation technique. The equity premium estimate that emerges from most of this work matches one moment of the data alone: the mean difference between an estimate of the return to holding equity and a risk-free rate. We instead match multiple moments of U.S. market data, exploiting the joint distribution of the dividend yield, return volatility, and realized excess returns, and find that the equity premium lies within 50 basis points of 3.5%, a range much narrower than was achieved in previous studies. Additionally, statistical tests based on the joint distribution of these moments reveal that only those models of the conditional equity premium that embed time variation, breaks, and/or trends are supported by the data. In order to develop the joint distribution of the dividend yield, return volatility, and excess returns, we need a model of price and return fundamentals. We document that even recently developed analytically tractable models that permit autocorrelated dividend growth rates and discount rates impose restrictions that are rejected by the data. We therefore turn to a wider range of models, requiring numerical solution methods and parameter estimation by the simulated method of moments.

We propose an importance-sampling procedure to improve the computational performance of the simulated method of moments (SMM) for the estimation of structural models with fixed parameter heterogeneity. The main advantage of the procedure is that it does not require to simulate observations every time that the structural parameters change during the minimization of the SMM criterion function. We illustrate the use of our method by estimating a neoclassical model of investment for a sample of US manufacturing companies, allowing the technological parameters to vary across firms.

Utility-Based Pricing of the Weather Derivatives

The combination of the automatic control theory courses, simulation verification and practical implementation of the designed controller algorithms in real-time conditions is very important for training of the control engineers.This contribution present structure and usage of Self-tuning Controllers Simulink Library (STCSL) for real time control.The STCSL was created for design, simulation verification and especially realtime implementation of single input -single output (SISO) digital self-tuning controllers.The proposed adaptive controllers, which are included in the library, can be divided into three groups (PID controllers, controllers based on the polynomial approach and the controllers derived on the other approaches (minimum variance etc.).This Library is very successfully used in Adaptive Control Course in education practice for design and verification of self-tuning control systems in simulation and real-time conditions.It is suitable also for design and verification of industrial digital controllers.The highly nonlinear laboratory model, the DR300 Speed Control with Variable Load, has been chosen as example for real-time control.

In this chapter, we briefly review two other methods for exploiting moment conditions in estimation. Section 10.1 describes simulation based estimators known as Simulated Method of Moments, Indirect Inference and Efficient Method of Moments. Section 10.2 describes the method of Empirical Likelihood. The purpose of this discussion is to provide the intuition behind the methods in question and to explain their connections to GMM. References are provided for those readers interested in a rigourous analysis of the statistical properties of these estimators.

Methods to estimate dynamic stochastic general equilibrium models