# Erricos John Kontoghiorghes's research while affiliated with Birkbeck, University of London and other places

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## Publications (103)

A novel numerical method for the estimation of large-scale time-varying parameter seemingly unrelated regressions (TVP-SUR) models is proposed. The updating and smoothing estimates of the TVP-SUR model are derived within the context of generalised linear least squares and through numerically stable orthogonal transformations which allow the sequent...

Some regression models for analyzing relationships between random intervals (i.e., random variables taking intervals as outcomes) are presented. The proposed approaches are extensions of previous existing models and they account for cross relationships between midpoints and spreads (or radii) of the intervals in a unique equation based on the inter...

An R package for computing the all-subsets regression problem is presented. The proposed algorithms are based on computational strategies recently developed. A novel algorithm for the best-subset regression problem selects subset models based on a predetermined criterion. The package user can choose from exact and from approximation algorithms. The...

A new strategy for estimating the Simultaneous Equations Model with non full rank variance-covariance matrix is proposed. The Generalized Singular Value Decomposition is the main tool used in the estimation. The block diagonal and banded structures of the matri-ces involved in the factorization are exploited in order to reduce the computational bur...

A new numerical method is proposed that uses the QR decomposition (and its variants) to derive recursively the three-stage least squares (3SLS) estimator of large-scale simultaneous equations models (SEM). The 3SLS estimator is obtained sequentially, once the underlying model is modified, by adding or deleting rows of data. A new theoretical pseudo...

A novel numerical method for the estimation of large time-varying parameter (TVP) models is proposed. The Kalman filter and Kalman smoother estimates of the TVP model are derived within the context of generalised linear least squares and through the use of numerical linear algebra. The method developed is based on numerically stable and computation...

A new numerical method to solve the downdating problem (and variants thereof), namely removing the effect of some observations from the generalized least squares (GLS) estimator of the general linear model (GLM) after it has been estimated, is extensively investigated. It is verified that the solution of the downdated least squares problem can be o...

A multiple interval-valued linear regression model considering all the cross-relationships between the mids and spreads of the intervals has been introduced recently. A least-squares estimation of the regression parameters has been carried out by transforming a quadratic optimization problem with inequality constraints into a linear complementary p...

An efficient optimization algorithm for identifying the best least squares regression model under the condition of non-negative coefficients is proposed. The algorithm exposits an innovative solution via the unrestricted least squares and is based on the regression tree and branch-and-bound techniques for computing the best subset regression. The a...

A linear regression model for interval data based on the natural interval-arithmetic has recently been proposed. Interval data can be identified with 2-dimensional points in ℝ x ℝ+, since they can be parametrized by its mid-point and its semi-amplitude or spread, which is non-negative. The model accounts separately for the contribution of the mid-p...

A jump robust positive semidefinite rank-based estimator for the daily covariance matrix based on high-frequency intraday returns is proposed. It disentangles covariance estimation into variance and correlation components. This allows us to account for ...

A jump robust positive semidefinite rank-based estimator for the daily covariance matrix based on high-frequency intraday returns is proposed. It disentangles covariance estimation into variance and correlation components. This allows us to account for ...

Extensions of previous linear regression models for interval data are
presented. A more flexible simple linear model is formalized. The new model may
express cross-relationships between mid-points and spreads of the interval data
in a unique equation based on the interval arithmetic. Moreover, extensions to
the multiple case are addressed. The asso...

An algorithm for computing the exact least trimmed squares (LTS) estimator of the standard regression model has recently been proposed. The LTS algorithm is adapted to the general linear and seemingly unrelated regressions models with possible singular dispersion matrices. It searches through a regression tree to find the optimal estimates and has...

When forecasts are assessed by a general loss (cost-of-error) function, the optimal point forecast is, in general, not the conditional mean, and depends on the conditional volatility-which, for stock returns, is time-varying. In order to provide forecasts ...

A new algorithm to solve exact least trimmed squares (LTS) regression is presented. The adding row algorithm (ARA) extends existing methods that compute the LTS estimator for a given coverage. It employs a tree-based strategy to compute a set of LTS regressors for a range of coverage values. Thus, prior knowledge of the optimal coverage is not requ...

A Bayesian method for estimation of a hazard term structure is presented in a functional data analysis framework. The hazard terms structure is designed to include the effects of changes in economic conditions, as well as trends in stock prices and accounting ...

A computationally efficient branch-and-bound strategy for finding the subsets of the most statistically significant variables of a vector autoregressive (VAR) model from a given search subspace is proposed. Specifically, the candidate submodels are obtained by deleting columns from the coefficient matrices of the full-specified VAR process. The str...

Computational models and methods are central to the analysis of economic and financial decisions. Simulation and optimisation are widely used as tools of analysis, modelling and testing. The focus of this book is the development of computational methods and analytical models in financial engineering that rely on computation. The book contains eight...

Computational strategies for estimating the seemingly unrelated regressions model after been updated with new observations are proposed. A sequential block algorithm based on orthogonal transformations and rich in BLAS-3 operations is proposed. It exploits efficiently the sparse structure of the data matrix and the Cholesky factor of the variance–c...

A technique suited for the solution of sequences of linear systems is described. This technique is a combination of a low rank update spectral preconditioner and a Krylov solver that computes on the fly approximations of the eigenvectors associated with ...

Several strategies for computing the best subset regression models are proposed. Some of the algorithms are modified versions of existing regression-tree methods, while others are new. The first algorithm selects the best subset models within a given size range. It uses a reduced search space and is found to outperform computationally the existing...

The journal Computational Statistics and Data Analysis aims to have regular issues on computational econometrics. Of particular interest are papers in important areas of econometric applications where both computational techniques and numerical methods have a major impact. The goal is to provide sources of information about the most recent developm...

A regression graph to enumerate and evaluate all possible subset regression models is introduced. The graph is a generalization of a regression tree. All the spanning trees of the graph are minimum spanning trees and provide an optimal computational procedure for generating all possible submodels. Each minimum spanning tree has a different structur...

Optimisation Models and Methods: A Supply Chain Network Perspective for Electric Power Generation, Supply, Transmission, and Consumption.- Worst-Case Modelling for Management Decisions under Incomplete Information, with Application to Electricity Spot Markets.- An Approximate Winner Determination Algorithm for Hybrid Procurement Mechanisms in Logis...

The Vector Autoregressive (VAR) process with zero coefficient constraints can be formulated as a Seemingly Unrelated Regressions (SUR) model. Within the context of subset VAR model selection a computationally efficient strategy to generate and estimate all G! SUR models when permuting the exogenous data matrices is proposed, where G is the number o...

Parallel Givens sequences for computing the QR decomposition of an m×n (m>n) matrix are considered. The Givens rotations operate on adjacent planes. A pipeline strategy for updating the pair of elements in the affected rows of the matrix is employed. This allows a Givens rotation to use rows that have been partially updated by previous rotations. T...

An efficient branch-and-bound algorithm for computing the best-subset regression models is proposed. The algorithm avoids the computation of the whole regression tree that generates all possible subset models. It is formally shown that if the branch-and-bound test holds, then the current subtree together with its right-hand side subtrees are cut. T...

Computationally efficient serial and parallel algorithms for estimating the general linear model are proposed. The sequential block-recursive algorithm is an adaptation of a known Givens strategy that has as a main component the Generalized QR decomposition. The proposed algorithm is based on orthogonal transformations and exploits the triangular s...

A regression graph which can be employed to enumerate and evaluate all possible subset regression models is introduced. The graph can be seen as a generalization of a previously introduced regression tree. Specifically, the regression tree describes a non-unique shortest path for traversing the graph. Furthermore, all the subtrees of the graph cont...

Computationally efficient parallel algorithms for downdating the least squares estimator of the ordinary linear regression are proposed. The algorithms, which are based on the QR decomposition, are block versions of sequential Givens strategies and efficiently exploit the triangular structure of the data matrices. The first strategy utilizes only p...

Algorithms for computing the subset Vector Autoregressive (VAR) models are proposed. These algorithms can be used to choose a subset of the most statistically-significant variables of a VAR model. In such cases, the selection criteria are based on the residual sum of squares or the estimated residual covariance matrix. The VAR model with zero coeff...

A computationally efficient method to estimate seemingly unrelated regression equations models with orthogonal regressors is presented. The method considers the estimation problem as a generalized linear least squares problem (GLLSP). The basic tool for solving the GLLSP is the generalized QR decomposition of the block-diagonal exogenous matrix and...

The QR decomposition of a set of matrices which have common columns
is investigated. The triangular factors of the QR decompositions
are represented as nodes of a weighted directed graph. An edge
between two nodes exists if and only if the columns of one of the
matrices is a subset of the columns of the other. The weight of an
edge denotes the comp...

Five computationally efficient algorithms for block downdating of the least squares solutions are proposed. The algorithms are block versions of Givens rotations strategies and are rich in BLAS-3 operations. They efficiently exploit the triangular structure of the matrices. The theoretical complexities of the algorithms are derived and analyzed. Th...

The three-dimensional problem of advection-dispersion associated with an elliptical non-aqueous-phase liquid (NAPL) pool is addressed using the boundary element method. The boundary condition on the plane of the pool is such that over the pool the concentration is equal to the saturation concentration while a no flux boundary condition is imposed i...

Computational efficient methods for updating seemingly unrelated regressions models with new observations are proposed. A recursive algorithm to solve a series of updating problems is developed. The algorithm is based on orthogonal transformations and has as main computational tool the updated generalized QR decomposition (UGQRD). Strategies to com...

This paper explores empirically the link between stocks returns Value-at-Risk (VaR) and the state of financial markets cycle. The econometric analysis is based on a simple vector autoregression setup. Using quarterly data from 1970Q4 to 2008Q4 for France, Germany and the United-Kingdom, it turns out that the k-year VaR of equities is actually depen...

The conventional test for leptokurtosis is based on the fourth moment of the standardized sample. This test suffers from various weaknesses: It cannot account for peakedness and fat tails separately and it is extremely sensitive with respect to outliers ...

Efficient parallel algorithms for computing all possible subset regression models are proposed. The algorithms are based on the dropping columns method that generates a regression tree. The properties of the tree are exploited in order to provide an efficient load balancing which results in no inter-processor communication. Theoretical measures of...

Handbook of Computational Econometrics examines the state of the art of computational econometrics and provides exemplary studies dealing with computational issues arising from a wide spectrum of econometric fields including such topics as bootstrapping, the evaluation of econometric software, and algorithms for control, optimization, and estimatio...

The Vector Autoregressive (VAR) model with zero coefficient restrictions canbe formulated as a Seemingly Unrelated Regression Equation (SURE) model. Boththe response vectors and the coefficient matrix of the regression equationscomprise columns from a Toeplitz matrix. Efficient numerical and computationalmethods which exploit the Toeplitz and Krone...

The numerical solution of seemingly unrelated regression (SUR) models with vector autoregressive disturbances is considered. Initially, an orthogonal transformation is applied to reduce the model to one with smaller dimensions. The transformed model is expressed as a reduced-size SUR model with stochastic constraints. The generalized QR decompositi...

The computational solution of the seemingly unrelated regression model with unequal size observations is considered. Two algorithms to solve the model when treated as a generalized linear least-squares problem are proposed. The algorithms have as a basic tool the generalized QR decomposition (GQRD) and efficiently exploit the block-sparse structure...

A Greedy Givens algorithm for computing the rank-1 updating of the QR decomposition is proposed. An exclusive-read exclusive-write parallel random access machine computational model is assumed. The complexity of the algorithms is calculated in two different ways. In the unlimited parallelism case a single time unit is required to apply a compound d...

Redistribution algorithms for dense linear algebra kernels on heterogeneous platforms are considered. In this context, processor speeds may well vary during the execution of a large kernel, which requires efficient strategies for redistributing the data ...

Computationally efficient and numerically stable methods for solving Seemingly Unrelated Regression (SUR) models are proposed. The iterative feasible generalized least squares estimator of SUR módels where the regression equations have common exogenous variables is derived. At each iteration an estimator of the SUR model is obtained from the soluti...

Computing has become essential for the modeling, analysis, and optimization of systems. This book is devoted to algorithms, computational analysis, and decision models. The chapters are organized in two parts: optimization models of decisions and models of pricing and equilibria.

Parallel strategies based on Givens rotations are proposed for updating the QR decomposition of an n × n matrix after a rank-k change (k < n). The complexity analyses of the Givens algorithms are based on the total number of Givens rotations applied to a 2-element vector. The algorithms, which are extensions of the rank-1 updating method, achieve t...

The solution of the SURE model with singular variance-covariance matrix results in redundancies and possibly inconsistencies among the observations of the model. A numerical procedure is proposed and investigated that generates a consistent model from an inconsistent one. The use of SVD has been used to compute the various factorizations arising in...

Computationally efficient and numerically stable methods for solving Seemingly Unrelated Regression Equations (SURE) models
are proposed. The iterative feasible generalized least squares estimator of SURE models where the regression equations have
common exogenous variables is derived. At each iteration an estimator of the SURE model is obtained fr...

Parallel Givens sequences for solving the General Linear Model (GLM) are developed and analyzed. The block updating GLM estimation problem is also considered. The solution of the GLM employs as a main computational device the Generalized QR Decomposition, where one of the two matrices is initially upper triangular. The proposed Givens sequences eff...

The problem of computing estimates of parameters in SURE models withvariance inequalities and positivity of correlations constraintsis considered. Efficient algorithms that exploit the blockbi-diagonal structure of the data matrix are presented. Thecomputational complexity of the main matrix factorizations isanalyzed. A compact method to solve the...

The problem of estimation for a system of regression equations where the random disturbances are correlated with each other is investigated. That is, the regression equations are linked statistically, even though not structurally, through the non-diagonality of the associated variance-covariance matrix. The expression Seemingly Unrelated Regression...

Consider the General Linear Model (GLM)
$$
y = Ax + \varepsilon ,\,\varepsilon \sim {\rm N}\left( {0,\sigma ^2 \Omega } \right)
$$ (4.1)
where y ∈ ℜm is the response vector, A∈ ℜmx(n-1) is the exogenous data matrix with full rank, y ∈ ℜ(n-1) is the vector of parameters to be estimated and ε ∈ ℜm is the noise vector normally distributed with zero me...

The General Linear Model (GLM) is the parent model of econometrics. Simultaneous equations and seemingly unrelated regression equation (SURE) models, to name but a few, can be formulated as a GLM. The estimation of the GLM can be viewed as a Generalized Linear Least-Squares problem (GLLSP). The solution of the GLLSP has been considered extensively....

The estimation of simultaneous equations models (SEMs) is of great importance in econometrics [34, 35, 62, 64, 96, 124, 130, 132, 149]. The most commonly used estimation procedures are the Three Stage Least-Squares (3SLS) procedure and the computationally expensive maximum likelihood procedure [33, 60, 97, 106, 107, 119, 120, 143, 153]. Here the me...

In many applications, it is desirable to re-estimate the coefficient parameters of the OLM after it has been updated or downdated by observations or variables. For example, in real time applications updated solutions of a model should be obtained where observations are repeatedly added or deleted. In computationally intensive applications such as m...

A common problem in statistics is that of estimating parameters of some assumed relationship between one or more variables. One such relationship is where y is the dependent (endogenous, explained) variable and a 1 … a n ) are the independent (exogenous, explanatory) variables. Regression analysis estimates the form of the relationship (1.1) by usi...

Vector Autoregressive processes of order p (VAR(p)) with coefficient restrictions can be formulated as a SURE model. The response vectors and the coefficient matrices of the regression equations comprise columns from a Toeplitz matrix. Numerical and computational methods that solve the SURE models by efficiently exploiting the Toeplitz structure of...

Consider the Ordinary Linear Model (OLM)
$$
y = Ax + \varepsilon ,
$$ (2.1)
where A ∈ ℜmxn (m > n) is the exogenous data matrix, y ∈ ℜm is the response vector and ε ∈ ℜm is the noise vector with zero mean and dispersion matrix σ2Im}. The least squares estimator of the parameter vector x ℜm$$
\arg \min \varepsilon ^T \varepsilon = \mathop {\arg \min...

Within the context of recursive least-squares, the implementation of a Householder algorithm for block updating the QR decomposition, on massively parallel SIMD systems, is considered. Initially, two implementations based on different mapping strategies for distributing the data matrices over the processing elements of the parallel computer are inv...

Efficient algorithms for estimating the coefficient parameters of the ordinary linear model on a massively parallel SIMD computer are presented. The numerical stability of the algorithms is ensured by using orthogonal transformations in the form of Householder reflections and Givens plane rotations to compute the complete orthogonal decomposition o...

Parallel strategies based on compound disjoint Givens rotations are proposed for computing the main two factorizations that
are used in the solution of seemingly unrelated regression and simultaneous equations models. The first factorization requires
the triangularization of a set of upper-trapezoidals after deleting columns. The second factorizati...

Algorithms for computing the three-stage least squares (3SLS) estimator usually require the disturbance convariance matrix to be non-singular. However, the solution of a reformulated simultaneous equation model (SEM) results into the redundancy of this condition. Having as a basic tool the QR decomposition, the 3SLS estimator, its dispersion matrix...

The solution of least squares subject to linear equality constraints (LSE), where the data is sequentially accumulated, has been considered using a SIMD array processor. The study is based on the method of constructing an orthogonal basis for the null space (BNS) of the constraints matrix. The implementation and performance of the BNS method on an...

The various problems associated with block modifying the standard regression model are described. The performance, on a SIMD computer, of a new bitonic algorithm for solving the updating problem is considered and its adaptation for solving the downdating problem is discussed.

Solution of triangular seemingly unrelated regression equations (tSURE) models has been investigated. An efficient parallel iterative algorithm based on orthogonal transformations, is proposed for solving an alternative formulation of tSURE models, where the disturbance covariance matrix may be singular. A method to overcome inconsistencies occurri...

An alternative approach to compute the coefficients of a Seemingly Unrelated Regression Equations (SURE) model is proposed. Orthogonal transformations are employed to avoid the difficulties in directly computing the inverse of the variance-covariance matrix (or its estimate) which often lead to unnecessary loss of accuracy. The solution of the spec...

Parallel strategies are proposed for updating the QR decomposition of an mxn matrix after adding k rows (k n). These strategies are based on Givens rotations and are found to complete the updating in fewer steps by comparison to a recently published algorithm. An efficient adaptation of the first parallel strategy to compute the QR decomposition of...

We describe parallel programming techniques and methods applied to
the implementation of two parallel algorithms on an SIMD array
processor. These programming techniques and methods can be employed to
parallel numerical algorithms for improving their performance and
efficiency. First we implemented the column sweep algorithm to solve a
lower triang...

We propose new stable parallel algorithms based on Householder
transformations and compound Given's rotations to compute the QR
decomposition of a rectangular matrix. The predicted execution time of
all algorithms on the massively parallel SIMD array processor AMT DAP
510, have been obtained and analyzed. Modified versions of these
algorithms are a...

This paper presents a concurrent model for fine to medium grain
object based parallelism which can be taken as a basis for the design of
parallel architectures. Our proposal is motivated by the observation
that conventional architectures are inadequate to efficiently support
object based parallelism, especially fine to medium grain. Our model
combi...

In this paper we employ Householder transformations and compound Givens rotations to compute the Complete Orthogonal Decomposition of a rectangular matrix, using a SIMD array processor. Algorithms are proposed for the reconstruction of the orthogonal matrices involved in the decompositions and the estimated execution time of all parallel algorithms...

In this note we propose a method based on compound disjoint Given's rotations, for reorthogonalizing the QR decomposition after deleting columns.

Several algorithms have appeared for solving the Ordinary Linear Model (OLM), after a number of observations have been added or deleted. In this paper we employ Householder transformations and Givens rotations to solve the updated and downdated OLM, using a massively parallel SIMD computer. Some of our methods are modified versions of serial algori...

Abstract,The value function of an American put option defined in a discrete domain,may be given as a solution of a Linear Complementarity Problem (LCP). However, the state of the art methods that solve LCP converge slowly. Recently, Dempster, Hutton & Richards have proposed,a Linear Program (LP) formulation of the American put and a special simplex...

## Citations

... We used the nls function in R to derive non-linear height-diameter and crown radius-height models. For multiple analyses we used the lmSubsets function [100], and the ggplot2 package to visualise the results [101]. ...

... To date, existing models have been developed either within the framework of random sets or symbolic data analysis (SDA) [8], [9]. In the random set framework, intervals are viewed as compact convex sets in R, and their interaction is modelled according to set arithmetic [10]- [14]. On the other hand, in the SDA setting, the classical regression model is expanded to interval-valued data where intervals are treated as bivariate vectors [15]- [22]. ...

... Although some of these interdisciplinary fields such as signal processing and pattern recognition, contain a strong statistical computing component, overall the use of parallelism in statistics and econometrics can be seen as under developed [1]. This is mainly due to the lack of a strong interface between parallel computing and statistics [62,68,75,76,93,124]. ...

... and is such that the effect of the oldest observation is excluded from the current estimate but the new information from the acquired observation will be incorporated. The imaginary unit in (3.21) gives the weight needed to downdate the model, that is, to eliminate the affect of the first datum (Hadjiantoni and Kontoghiorghes, 2016). The window estimation problem is then given by (3.22) where the hyperbolic norm is used together with the imaginary unit ı to downdate the estimate of the TVP-SUR model Steinhardt, 1986, 1988). ...

... Exogenous matrices in the SUR model can have any dimension and structure, but specific characteristics require special treatments. For example efficient estimation algorithms have been proposed for SUR models having a significant numbers of common variables, recursive exogenous matrices, and constraints [4][5][6][7][8]11,14,15,25]. Here SUR models without constraints in the exogenous variables are considered, and thus, the equations can be arranged a priori. ...

... The extension of the simple linear model to the multiple case is also a target to be addressed. Some initial studies on set-arithmetic multivariate linear models for interval-valued variables have already been developed [20,