65 results found
Abadir KM, 2022, Explicit minimal representation of variance matrices, and its implication for dynamic volatility models, The Econometrics Journal, ISSN: 1368-4221
We propose a minimal representation of variance matrices of dimension k, where parameterization and positive-definiteness conditions are both explicit. Then, we apply it to the specification of dynamic multivariate volatility processes. Compared to the most parsimonious unrestricted formulation currently available, the required number of covariance parameters (hence processes) is reduced by about a half, which makes them estimable in full parametric generality if needed. Our conditions are easy to implement: there are only k of them, and they are explicit and univariate. To illustrate, we forecast minimum-variance portfolios and show that risk is always reduced (by a factor of 2 to 3 in spite of us using the simplest dynamics) compared to the standard benchmark used in finance, while also improving returns on the investment. Because of our representation, we do not get the usual dimensionality problems of existing unrestricted models, and the performance relative to the benchmark is actually improved substantially as k increases.
Abadir KM, Luati A, Paruolo P, 2022, GARCH density and functional forecasts, Journal of Econometrics, ISSN: 0304-4076
This paper derives the analytic form of the multi-step ahead prediction density for single-period returns, when the latter follow a Gaussian GARCH(1,1) process with a possibly asymmetric news impact curve. The Gaussian density has been used in applications as an approximation of themulti-step ahead prediction density; the analytic form derived here shows that the prediction density, while symmetric, can be far from Gaussian. The explicit form of the prediction density can be used to compute exact tail probabilities and functionals, such as the Value at Risk and the ExpectedShortfall, to quantify expected future required risk capital for single-period returns. Finally, the paper shows how estimation uncertainty can be mapped onto uncertainty regions for any functional of the stated prediction distribution.
Abadir KM, Atanasova C, 2022, Where (and by how much) does a theory break down? With an application to the expectation hypothesis., Advances in Econometrics, Volume 43B: Essays in Honor of M. Hashem Pesaran: Panel Modeling, Micro Applications, and Econometric Methodology:, Editors: Chudik, Hsiao, Timmermann, Publisher: Emerald, Pages: 255-267, ISBN: 978-1-80262-066-5
The authors provide new evidence in favor of the expectation hypothesis (EH) as a long-run theory of the term structure of interest rates. Using nonparametric techniques first, the authors show that the results of conventional tests that reject EH are strongly affected by the presence of extreme observations – only a handful in the case of longer maturities. The authors then provide a new general methodology that determines the number of outliers causing any theory to fail, and their approach quantifies the extent of this failure.
Abadir KM, Distaso W, Giraitis L, 2021, Partially one-sided semiparametric inference for trending persistent and antipersistent processes, Econometrics and Statistics, ISSN: 2452-3062
Hypothesis testing in models allowing for trending processes that are possibly nonstationary and non-Gaussian is considered. Using semiparametric estimators, joint hypothesis testing for these processes is developed, taking into account the one-sided nature of typical hypotheses on the persistence parameter in order to gain power. The results are applicable for a wide class of processes and are easy to implement. They are illustrated with an application to the dynamics of GDP.
Abadir KM, Talmain G, 2021, On an intriguing parallel between economics and cosmology modelling, Publisher: Science
Abadir KM, Cornea-Madeira A, 2019, Link of moments before and after transformations, with an application to resampling from fat-tailed distributions, Econometric Theory, Vol: 35, Pages: 630-652, ISSN: 0266-4666
Let x be a transformation of y, whose distribution is unknown. We derive an expansion formulating the expectations of x in terms of the expectations of y. Apart from the intrinsic interest in such a fundamental relation, our results can be applied to calculating E(x) by the low-order moments of a transformation which can be chosen to give a good approximation for E(x). To do so, we generalize the approach of bounding the terms in expansions of characteristic functions, and use our result to derive an explicit and accurate bound for the remainder when a finite number of terms is taken. We illustrate one of the implications of our method by providing accurate naive bootstrap confidence intervals for the mean of any fat-tailed distribution with an infinite variance, in which case currently available bootstrap methods are asymptotically invalid or unreliable in finite samples.
Abadir KM, Heijmans RDH, Magnus JR, 2018, Statistics:, Publisher: Cambridge University Press, ISBN: 9780521822886
Building on the success of Abadir and Magnus' Matrix Algebra in the Econometric Exercises Series, Statistics serves as a bridge between elementary and specialized statistics.
Abadir KM, Maasoumi E, 2014, OVERVIEW, ECONOMETRIC REVIEWS, Vol: 33, Pages: 429-430, ISSN: 0747-4938
Abadir KM, Distaso W, Žikeš F, 2014, Design-free estimation of variance matrices, Journal of Econometrics, Vol: 181, Pages: 165-180, ISSN: 1872-6895
This paper introduces a new method for estimating variance matrices. Starting from the orthogonal decomposition of the sample variance matrix, we exploit the fact that orthogonal matrices are never ill-conditioned and therefore focus on improving the estimation of the eigenvalues. We estimate the eigenvectors from just a fraction of the data, then use them to transform the data into approximately orthogonal series that deliver a well-conditioned estimator (by construction), even when there are fewer observations than dimensions. We also show that our estimator has lower error norms than the traditional one. Our estimator is design-free: we make no assumptions on the distribution of the random sample or on any parametric structure the variance matrix may have. Simulations confirm our theoretical results and they also show that our simple estimator does very well in comparison with other existing methods.
Abadir KM, Distaso W, Giraitis L, et al., 2014, ASYMPTOTIC NORMALITY FOR WEIGHTED SUMS OF LINEAR PROCESSES, ECONOMETRIC THEORY, Vol: 30, Pages: 252-284, ISSN: 0266-4666
Abadir KM, 2013, Lies, damned lies, and statistics? Examples from finance and economics., Central European Journal of Economic Modelling and Econometrics, Vol: 5, Pages: 231-248, ISSN: 2080-119X
Reliable data analysis is one of the hardest tasks in sciences and socialsciences. Often misleading and sometimes puzzling results arise when theanalysis is done without regard for the special features of the data. In thisexposition, I will focus on designing new statistical tools to deal with someprominent questions in Finance and Economics. In particular, I will talk aboutthe following. (1) How to characterize the randomness of variables, motivated bya problem in the pricing of financial options. (2) Uncovering the relation betweeninterest rates on different maturities, now and in the future; the "term structureof interest rates". (3) Modelling the unconventional nonlinear long-memorydynamics that arise from a general-equilibrium economic model, and theirimplications for exchange rates, stock market indexes, and all macroeconomicvariables; with recommendations for trading in financial markets, but also forthe design of macroeconomic stabilization policies by governments.
Abadir KM, Caggiano G, Talmain G, 2013, Nelson-Plosser revisited: the ACF approach, Journal of Econometrics, Vol: 175, Pages: 22-34
Abadir KM, 2012, The square root of a matrix, Journal of Time Series Econometrics, Vol: 4
Abadir KM, Larsson R, 2012, Biases of correlograms and of AR representations of stationary series, Journal of Time Series Econometrics, Vol: 4 (lead article)
Abadir KM, 2011, Is the economic crisis over (and out)?, Review of Economic Analysis, Vol: 3, Pages: 102-108, ISSN: 1973-3909
This note analyzes the recent global recession: its causes, the predictability of the timingof its start and of its end, and the implications for macro policy. These follow from thegeneral-equilibrium macro model of Abadir and Talmain (2002) and its implications fora new type of macroeconometrics. The note also proposes some banking regulations, andpresents prospects for the future.
Abadir KM, Distaso W, Giraitis L, 2011, An I(d) model with trend and cycles, Journal of Econometrics, Vol: 163, Pages: 186-199
Abadir KM, Talmain G, 2011, The unconventional dynamics of economic and financial aggregates, Handbook of Empirical Economics and Finance, Editors: Ullah, Giles, Publisher: Chapman & Hall/CRC, ISBN: 9781420070354
Abadir KM, Paruolo P, 2009, On efficient simulations in dynamic models, The Methodology and Practice of Econometrics (Refereed Festschrift in honour of David F. Hendry), Editors: Castle, Shephard, Oxford, Publisher: Oxford University Press
Abadir KM, Distaso W, Giraitis L, 2009, Two estimators of the long-run variance: beyond short memory, Journal of Econometrics, Vol: 150, Pages: 56-70
Abadir K M, W Distaso, 2007, Testing joint hypotheses when one of the alternatives is one-sided, Journal of Econometrics, Vol: 140, Pages: 695-718
K M Abadir, J R Magnus, 2007, A statistical proof of the transformation theorem, The Refinement of Econometric Estimation and Test Procedures: Finite Sample and Asymptotic Analysis, Editors: Phillips, Tzavalis, Cambridge, Publisher: Cambridge University Press, ISBN: 9780521870535
Abadir KM, Distaso W, Giraitis L, 2007, Nonstationarity-extended local Whittle estimation, Journal of Econometrics, Vol: 141, Pages: 1353-1384
Abadir KM, Spierdijk L, 2005, Liquidity Constraints and the Demand for Assets: An Application to the Festivity Effect
Abadir KM, Talmain G, 2005, Autocovariance functions of series and of their transforms, Journal of Econometrics, Vol: 124, Pages: 227-252, ISSN: 0304-4076
Abadir KM, 2005, THE MEAN-MEDIAN-MODE INEQUALITY: COUNTEREXAMPLES, Econometric Theory, Vol: 21, Pages: 477-482
Let x be a random variable whose first three moments exist. If the density of x is unimodal and positively skewed, then counterexamples are provided which show that the inequality mode median mean does not necessarily hold.I thank Andrey Vasnev for help with the graphs and Jan Magnus for various helpful discussions. I also thank Martin Bland, Paolo Paruolo, Peter Phillips, Michael Rockinger, and a referee for their comments. ESRC grant R000239538 is gratefully acknowledged.
Abadir KM, Magnus JR, 2005, Matrix algebra, Cambridge, Publisher: Cambridge University Press, ISBN: 9780521537469
Abadir KM, Magnus JR, 2004, 03.3.1. Normal's deconvolution and the independence of sample mean and variance - Solution, Econometric Theory, Vol: 20, Pages: 805-807, ISSN: 0266-4666
Abadir K, Magnus J, 2004, 03.6.1 The Central Limit Theorem for Student's Distribution—Solution, Econometric Theory, Vol: 20, Pages: 1261-1263, ISSN: 0266-4666
Abadir KM, Lucas A, 2004, A comparison of minimum MSE and maximum power for the nearly integrated non-Gaussian model, Journal of Econometrics, Vol: 119, Pages: 45-71, ISSN: 0304-4076
Abadir KM, 2004, Cointegration theory, equilibrium and disequilibrium economics, The Manchester School, Vol: 72, Pages: 60-71, ISSN: 1463-6786
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