The aim of this thesis is the development and the application of econometric models with time-varying parameters in a policy environment. The popularity of these methods has run in parallel with advances in computing power, which has made feasible estimation methods that until the late '90s would have been unfeasible. Bayesian methods, in particular, benefitted from these technological advances, as sampling from complicated posterior distributions of the model parameters became less and less time-consuming. Building on the seminal work by Carter and Kohn (1994) and Jacquier, Polson, and Rossi (1994), bayesian algorithms for estimating Vector Autoregressions (VARs) with drifting coefficients and volatility were independently derived by Cogley and Sargent (2005) and Primiceri (2005). Despite their increased popularity, bayesian methods still suffer from some limitations, from both a theoretical and a practical viewpoint. First, they typically assume that parameters evolve as independent driftless random walks. It is therefore unclear whether the output that one obtains from these estimators is accurate when the model parameters are generated by a different stochastic process. Second, some computational limitations remain as only a limited number of time series can be jointly modeled in this environment. These shortcomings have prompted a new line of research that uses non-parametric methods to estimate random time-varying coefficients models. Giraitis, Kapetanios, and Yates (2014) develop kernel estimators for autoregressive models with random time-varying coefficients and derive the conditions under which such estimators consistently recover the true path of the model coefficients. The method has been suitably adapted by Giraitis, Kapetanios, and Yates (2012) to a multivariate context. In this thesis I make use of both bayesian and non-parametric methods, adapting them (and in some cases extending them) to answer some of the research questions that, as a Central Bank economist, I have been tackling in the past five years. The variety of empirical exercises proposed throughout the work testifies the wide range of applicability of these models, be it in the area of macroeconomic forecasting (both at short and long horizons) or in the investigation of structural change in the relationship among macroeconomic variables. The first chapter develops a mixed frequency dynamic factor model in which the disturbances of both the latent common factor and of the idiosyncratic components have time varying stochastic volatility. The model is used to investigate business cycle dynamics in the euro area, and to perform point and density forecast. The main result is that introducing stochastic volatility in the model contributes to an improvement in both point and density forecast accuracy. Chapter 2 introduces a nonparametric estimation method for a large Vector Autoregression (VAR) with time-varying parameters. The estimators and their asymptotic distributions are available in closed form. This makes the method computationally efficient and capable of handling information sets as large as those typically handled by factor models and Factor Augmented VARs (FAVAR). When applied to the problem of forecasting key macroeconomic variables, the method outperforms constant parameter benchmarks and large Bayesian VARs with time-varying parameters. The tool is also used for structural analysis to study the time-varying effects of oil price innovations on sectorial U.S. industrial output. Chapter 3 uses a bayesian VAR to provide novel evidence on changes in the relationship between the real price of oil and real exports in the euro area. By combining robust predictions on the sign of the impulse responses obtained from a theoretical model with restrictions on the slope of the oil demand and oil supply curves, oil supply and foreign productivity shocks are identified. The main finding is that from the 1980s onwards the relationship between oil prices and euro area exports has become less negative conditional on oil supply shortfalls and more positive conditional on foreign productivity shocks. A general equilibrium model is used to shed some light on the plausible reasons for these changes. Chapter 4 investigates the failure of conventional constant parameter models in anticipating the sharp fall in inflation in the euro area in 2013- 2014. This forecasting failure can be partly attributed to a break in the elasticity of inflation to the output gap. Using structural break tests and non-parametric time varying parameter models this study shows that this elasticity has indeed increased substantially after 2013. Two structural interpretations of this finding are offered. The first is that the increase in the cyclicality of inflation has stemmed from lower nominal rigidities or weaker strategic complementarity in price setting. A second possibility is that real time output gap estimates are understating the amount of spare capacity in the economy. I estimate that, in order to reconcile the observed fall in inflation with the historical correlation between consumer prices and the business cycle, the output gap should be wider by around one third.

This thesis considers two important problems in finance, namely, correlation stress testing and multivariate volatility modeling. Correlation stress testing refers to the correlation matrix adjustment to evaluate potential impact of the changes in correlations under financial crises. Very often, some correlations are explicitly adjusted (core correlations), with the remainder left unspecified (peripheral correlations), although it would be more natural for both core correlations and peripheral correlations to vary. However, most existing methods ignored the potential change in peripheral correlations. Inspiring from this idea, two methods are proposed in which the stress impact on the core correlations is transmitted to the peripheral correlations through the dependence structure of the empirical correlations. The first method is based on a Bayesian framework in which a prior for a population correlation matrix is proposed that gives flexibility in specifying the dependence structure of correlations. In order to increase the rate of convergence, the algorithm of posterior simulation is extended so that two correlations can be updated in one Gibbs sampler step. To achieve this, an algorithm is developed to find the region of two correlations keeping the correlation matrix positive definite given that all other correlations are held fixed. The second method is a Black-Litterman approach applied to correlation matrices. A new correlation matrix is constructed by maximizing the posterior density. The proposed method can be viewed as a two-step procedure: first constructing a target matrix in a data-driven manner, and then regularizing the target matrix by minimizing a matrix norm that reasonably reflects the dependence structure of the empirical correlations. Multivariate volatility modeling is important in finance since variances and covariances of asset returns move together over time. Recently, much interest has been aroused by an approach involving the use of the realized covariance (RCOV) matrix constructed from high frequency returns as the ex-post realization of the covariance matrix of low frequency returns. For the analysis of dynamics of RCOV matrices, the generalized conditional autoregressive Wishart model is proposed. Both the noncentrality matrix and scale matrix of the Wishart distribution are driven by the lagged values of RCOV matrices, and represent two different sources of dynamics, respectively. The proposed model is a generalization of the existing models, and accounts for symmetry and positive definiteness of RCOV matrices without imposing any parametric restriction. Some important properties such as conditional moments, unconditional moments and stationarity are discussed. The forecasting performance of the proposed model is compared with the existing models. Outliers exist in the series of realized volatility which is often decomposed into continuous and jump components. The vector multiplicative error model is a natural choice to jointly model these two non-negative components of the realized volatility, which is also a popular multivariate time series model for other non-negative volatility measures. Diagnostic checking of such models is considered by deriving the asymptotic distribution of residual autocorrelations. A multivariate portmanteau test is then devised. Simulation experiments are carried out to investigate the performance of the asymptotic result in finite samples. / published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

University of Macau / Faculty of Science and Technology / Department of Computer and Information Science

published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

Kwong, Wai Ming. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 34-35). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also in Chinese.

Recursive estimation is an essential procedure in econometrics which appears in many applications when the underlying dataset or model is modi ed. Data arrive consecutively and thus already estimated models will have to be updated with new available information. Moreover, in many cases, data will have to be deleted from a model in order to remove their effect, either because they are old (obsolete) or because they have been detected to be outliers or extreme values and further investigation is required. The aim of this thesis is to develop numerically stable and computationally efficient methods for the recursive estimation of large-scale linear econometric models. Estimation of multivariate linear models is a computationally costly procedure even for moderate-sized models. In particular, when the model needs to be estimated recursively, its estimation will be even more computationally demanding. Moreover, conventional methods yield often, misleading results. The aim is to derive new methods which effectively utilise previous computations, in order to reduce the high computational cost, and which provide accurate results as well. Novel numerical methods for the recursive estimation of the general linear, the seemingly unrelated regressions, the simultaneous equations, the univariate and multivariate timevarying parameters models are developed. The proposed methods are based on numerically stable strategies which provide accurate and precise results. Moreover, the new methods estimate the unknown parameters of the modi ed model even when the variance covariance matrix is singular.

The relevance of domestic and foreign capacity utilization rates in forecasting future inflation rate has been investigated empirically, using five industrialized countries for which the comparable data are available. It has been found that capacity utilization rates, both domestic and foreign, have a long run stable relationship with domestic inflation rate and a positive shock in the capacity utilization rate results in a significant, although a little bit delayed, acceleration in the domestic inflation rate. Various econometric techniques have been used and led to consistent empirical findings. The results in the present study, therefore, dispute the claim that an increase in capacity utilization rate may not necessarily lead to an accelerated inflation down the road. / Graduation date: 1995

Thesis (Ph. D.)--University of Hawaii at Manoa, 2004. / Includes bibliographical references (leaves 191-201). / Also available by subscription via World Wide Web / vii, 201 leaves, bound ill. 29 cm

Thesis (M.Com. (Business Finance))--University of the Witwatersrand, Faculty of Commerce, Law and Management, School of Economic and Business Sciences, 2017 / The writer studies the short-run determinants of bond yield volatility in South Africa (SA) by analyzing the impact that global factors –representing global funding conditions – have on the changes to the rand denominated generic 10-year government bond yield (SAGB). This is followed by a one-period forward forecast of this volatility. The explanatory variables tested in this study are as follows: net bond purchases by foreign investors, Chicago Board Options Volatility Index (VIX), JP Morgan Emerging Market Bond Index (JP EMBI) spread, the US dollar to SA rand (USDZAR) exchange rate, the SA 5 year credit default swap (CDS) rate, the 12 month interest rate expectation/9x12 forward rate agreement (FRA), dollar spot price of gold and dollar spot price of oil. The study period ranges from January 2000 to December 2015. The GARCH modelling technique is used due to its ability to capture the volatility clustering effects observed in time series return data. The writer used the Gaussian distribution as the default model, however in order to control for the skewness and fat-tails in financial market return data, the Student-T and Generalised Error distributions are also tested to see if the non-normally distributed bond returns could be better captured by alternative parametric assumptions. The results show that all the explanatory variables, with the exception of the FRA, are statistically significant in explaining volatility in the local generic 10-year government bond. / GR2018

本文由三篇文章構成。首篇是關於多維變或然分佈預測的檢驗。第三篇是關於非貝斯結構性轉變的VAR 模型。或然分佈預測的檢驗是基於檢驗PIT(probability integral transformation) 序的均勻份佈性質與獨性質。第一篇文章基於Clements and Smith (2002) 的方法提出新的位置正變換。這新的變換改善原有的對稱問題，以及提高檢驗的power。第二篇文章建對於多變或然分佈預測的data-driven smooth 檢驗。通過蒙特卡模擬，本文驗證這種方法在小樣本下的有效性。在此之前，由於高維模型的複雜性，大部分的研究止於二維模型。我們在文中提出有效的方法把多維變換至單變。蒙特卡模擬實驗，以及在組融據的應用中，都證實這種方法的優勢。最後一篇文章提出非貝斯結構性轉變的VAR 模型。在此之前，Chib(1998) 建的貝斯結構性轉變模型須要預先假定構性轉變的目。因此他的方法須要比較同構性轉變目模型的優。而本文提出的stick-breaking 先驗概，可以使構性轉變目在估計中一同估計出。因此我們的方法具有robust 之性質。通過蒙特卡模擬，我們考察存在著四個構性轉變的autoregressive VAR(2) 模型。結果顯示我們的方法能準確地估計出構性轉變的發生位置。而模型中的65 個估計都十分接近真實值。我們把這方法應用在多個對沖基回報序。驗測出的構性轉變位置與市場大跌的時段十分吻合。 / This thesis consists of three essays on financial econometrics. The first two essays are about multivariate density forecast evaluations. The third essay is on nonparametric Bayesian change-point VAR model. We develop a method for multivariate density forecast evaluations. The density forecast evaluation is based on checking uniformity and independence conditions of the probability integral transformation of the observed series in question. In the first essay, we propose a new method which is a location-adjusted version of Clements and Smith (2002) that corrects asymmetry problem and increases testing power. In the second essay, we develop a data-driven smooth test for multivariate density forecast evaluation and show some evidences on its finite sample performance using Monte Carlo simulations. Previous to our study, most of the works are up to bivariate model as it is difficult to evaluate with the existing methods. We propose an efficient dimensional reduction approach to reduce the dimension of multivariate density evaluation to a univariate one. We perform various Monte Carlo simulations and two applications on financial asset returns which show that our test performs well. The last essay proposes a nonparametric extension to existing Bayesian change-point model in a multivariate setting. Previous change-point model of Chib (1998) requires specification of the number of change points a priori. Hence a posterior model comparison is needed for di erent change-point models. We introduce the stick-breaking prior to the change-point process that allows us to endogenize the number of change points into the estimation procedure. Hence, the number of change points is simultaneously determined with other unknown parameters. Therefore our model is robust to model specification. We preform a Monte Carlo simulation of bivariate vector autoregressive VAR(2) process which is subject to four structural breaks. Our model estimate the break locations with high accuracy and the posterior estimates of the 65 parameters are closed to the true values. We apply our model to various hedge fund return processes and the detected change points coincide with market crashes. / Detailed summary in vernacular field only. / Ko, Iat Meng. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 176-194). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also in Chinese. / Abstract --- p.i / Acknowledgement --- p.v / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Multivariate Density Forecast Evaluation: A Modified Approach --- p.7 / Chapter 2.1 --- Introduction --- p.7 / Chapter 2.2 --- Evaluating Density Forecasts --- p.13 / Chapter 2.3 --- Monte Carlo Simulations --- p.18 / Chapter 2.3.1 --- Bivariate normal distribution --- p.19 / Chapter 2.3.2 --- The Ramberg distribution --- p.21 / Chapter 2.3.3 --- Student’s t and uniform distributions --- p.24 / Chapter 2.4 --- Empirical Applications --- p.24 / Chapter 2.4.1 --- AR model --- p.25 / Chapter 2.4.2 --- GARCH model --- p.27 / Chapter 2.5 --- Conclusion --- p.29 / Chapter 3 --- Multivariate Density Forecast Evaluation: Smooth Test Approach --- p.39 / Chapter 3.1 --- Introduction --- p.39 / Chapter 3.2 --- Exponential Transformation for Multi-dimension Reduction --- p.47 / Chapter 3.3 --- The Smooth Test --- p.56 / Chapter 3.4 --- The Data-Driven Smooth Test Statistic --- p.66 / Chapter 3.4.1 --- Selection of K --- p.66 / Chapter 3.4.2 --- Choosing p of the Portmanteau based test --- p.69 / Chapter 3.5 --- Monte Carlo Simulations --- p.70 / Chapter 3.5.1 --- Multivariate normal and Student’s t distributions --- p.71 / Chapter 3.5.2 --- VAR(1) model --- p.74 / Chapter 3.5.3 --- Multivariate GARCH(1,1) Model --- p.78 / Chapter 3.6 --- Density Forecast Evaluation of the DCC-GARCH Model in Density Forecast of Spot-Future returns and International Equity Markets --- p.80 / Chapter 3.7 --- Conclusion --- p.87 / Chapter 4 --- Stick-Breaking Bayesian Change-Point VAR Model with Stochastic Search Variable Selection --- p.111 / Chapter 4.1 --- Introduction --- p.111 / Chapter 4.2 --- The Bayesian Change-Point VAR Model --- p.116 / Chapter 4.3 --- The Stick-breaking Process Prior --- p.120 / Chapter 4.4 --- Stochastic Search Variable Selection (SSVS) --- p.121 / Chapter 4.4.1 --- Priors on Φ[subscript j] = vec(Φ[subscript j]) = --- p.122 / Chapter 4.4.2 --- Prior on Σ[subscript j] --- p.123 / Chapter 4.5 --- The Gibbs Sampler and a Monte Carlo Simulation --- p.123 / Chapter 4.5.1 --- The posteriors of ΦΣ[subscript j] and Σ[subscript j] --- p.123 / Chapter 4.5.2 --- MCMC Inference for SB Change-Point Model: A Gibbs Sampler --- p.126 / Chapter 4.5.3 --- A Monte Carlo Experiment --- p.128 / Chapter 4.6 --- Application to Daily Hedge Fund Return --- p.130 / Chapter 4.6.1 --- Hedge Funds Composite Indices --- p.132 / Chapter 4.6.2 --- Single Strategy Hedge Funds Indices --- p.135 / Chapter 4.7 --- Conclusion --- p.138 / Chapter A --- Derivation and Proof --- p.166 / Chapter A.1 --- Derivation of the distribution of (Z₁ - EZ₁) x (Z₂ - EZ₂) --- p.166 / Chapter A.2 --- Derivation of limiting distribution of the smooth test statistic without parameter estimation uncertainty ( θ = θ₀) --- p.168 / Chapter A.3 --- Proof of Theorem 2 --- p.170 / Chapter A.4 --- Proof of Theorem 3 --- p.172 / Chapter A.5 --- Proof of Theorem 4 --- p.174 / Chapter A.6 --- Proof of Theorem 5 --- p.175 / Bibliography --- p.176