Getting Started with Particle Metropolis-Hastings for Inference in Nonlinear Dynamical Models

This tutorial provides a gentle introduction to the particle Metropolis-Hastings (PMH) algorithm for parameter inference in nonlinear state-space models together with a software implementation in the statistical programming language R. We employ a step-by-step approach to develop an implementation of the PMH algorithm (and the particle filter within) together with the reader. This final implementation is also available as the package pmhtutorial in the CRAN repository. Throughout the tutorial, we provide some intuition as to how the algorithm operates and discuss some solutions to problems that might occur in practice. To illustrate the use of PMH, we consider parameter inference in a linear Gaussian state-space model with synthetic data and a nonlinear stochastic volatility model with real-world data.Comment: 41 pages, 7 figures. In press for Journal of Statistical Software. Source code for R, Python and MATLAB available at: https://github.com/compops/pmh-tutoria

Dynamic Spatial Autoregressive Models with Time-varying Spatial Weighting Matrices

We propose a new spatio-temporal model with time-varying spatial weighting matrices, by allowing for a general parameterization of the spatial matrix. The filtering procedure of the time-varying unknown parameters is performed using the information contained in the score of the conditional distribution of the observables. We provide conditions for the stationarity and ergodicity of the filtered sequence of the spatial matrices as well as for the consistency and asymptotic normality of the maximum likelihood estimator (MLE). An extensive Monte Carlo simulation study to investigate the finite sample properties of the maximum likelihood estimator is also reported. We finally analyze the association between eight European countries' perceived risk, suggesting that the economically strong countries have their perceived risk increased due to their spatial connection with the economically weaker countries, and we investigate the evolution of the spatial connection between the house prices in different areas of the UK, identifying periods when the usually adopted sparse weighting matrix is not sufficient to describe the underlying spatial process

Tail behaviour analysis and robust regression meets modern methodologies

Diese Arbeit stellt Modelle und Methoden vor, die für robuste Statistiken und ihre Anwendungen in verschiedenen Bereichen entwickelt wurden. Kapitel 2 stellt einen neuartigen Partitionierungs-Clustering-Algorithmus vor, der auf Expectiles basiert. Der Algorithmus bildet Cluster, die sich an das Endverhalten der Clusterverteilungen anpassen und sie dadurch robuster machen. Das Kapitel stellt feste Tau-Clustering- und adaptive Tau-Clustering-Schemata und ihre Anwendungen im Kryptowährungsmarkt und in der Bildsegmentierung vor. In Kapitel 3 wird ein faktorerweitertes dynamisches Modell vorgeschlagen, um das Tail-Verhalten hochdimensionaler Zeitreihen zu analysieren. Dieses Modell extrahiert latente Faktoren, die durch Extremereignisse verursacht werden, und untersucht ihre Wechselwirkung mit makroökonomischen Variablen mithilfe des VAR-Modells. Diese Methodik ermöglicht Impuls-Antwort-Analysen, Out-of-Sample-Vorhersagen und die Untersuchung von Netzwerkeffekten. Die empirische Studie stellt den signifikanten Einfluss von durch finanzielle Extremereignisse bedingten Faktoren auf makroökonomische Variablen während verschiedener Wirtschaftsperioden dar. Kapitel 4 ist eine Pilotanalyse zu Non Fungible Tokens (NFTs), insbesondere CryptoPunks. Der Autor untersucht die Clusterbildung zwischen digitalen Assets mithilfe verschiedener Visualisierungstechniken. Die durch CNN- und UMAP-Regression identifizierten Cluster werden mit Preisen und Merkmalen von CryptoPunks in Verbindung gebracht. Kapitel 5 stellt die Konstruktion eines Preisindex namens Digital Art Index (DAI) für den NFT-Kunstmarkt vor. Der Index wird mithilfe hedonischer Regression in Kombination mit robusten Schätzern für die Top-10-Liquid-NFT-Kunstsammlungen erstellt. Es schlägt innovative Verfahren vor, nämlich Huberisierung und DCS-t-Filterung, um abweichende Preisbeobachtungen zu verarbeiten und einen robusten Index zu erstellen. Darüber hinaus werden Preisdeterminanten des NFT-Marktes analysiert.This thesis provides models and methodologies developed on robust statistics and their applications in various domains. Chapter 2 presents a novel partitioning clustering algorithm based on expectiles. The algorithm forms clusters that adapt to the tail behavior of the cluster distributions, making them more robust. The chapter introduces fixed tau-clustering and adaptive tau-clustering schemes and their applications in crypto-currency market and image segmentation. In Chapter 3 a factor augmented dynamic model is proposed to analyse tail behavior of high-dimensional time series. This model extracts latent factors driven by tail events and examines their interaction with macroeconomic variables using VAR model. This methodology enables impulse-response analysis, out-of-sample predictions, and the study of network effects. The empirical study presents significant impact of financial tail event driven factors on macroeconomic variables during different economic periods. Chapter 4 is a pilot analysis on Non Fungible Tokens (NFTs) specifically CryptoPunks. The author investigates clustering among digital assets using various visualization techniques. The clusters identified through regression CNN and UMAP are associated with prices and traits of CryptoPunks. Chapter 5 introduces the construction of a price index called the Digital Art Index (DAI) for the NFT art market. The index is created using hedonic regression combined with robust estimators on the top 10 liquid NFT art collections. It proposes innovative procedures, namely Huberization and DCS-t filtering, to handle outlying price observations and create a robust index. Furthermore, it analyzes price determinants of the NFT market

Empirical Studies on Financial Stability and Natural Capital

This dissertation develops and applies empirical methods to find policy-relevant answers regarding financial stability and network effects, predicting food insecurity risks, and understanding the financial relevance of natural capital. Chapter 2 proposes a dynamic network effect (DNE) model to study network effects, which refer to entities affecting their neighbors due to the proximity to each other. The smooth marginalized particle filter (SMPF) is shown to be a well-suited estimator in Monte Carlo simulations. Chapter 3 applies the DNE model to explain contagion among the largest Eurozone banks. Supervisory asset holding data allow the construction of a bank business model similarity network. The associated time-varying network effects help resolve the credit spread puzzle, especially during turbulent times. Chapter 4 proposes a stochastic framework to forecast food insecurity risks using LASSO variable selection, a panel vector-autoregression and Bayesian priors to incorporate expert opinions. The model is stochastic and can inform vulnerability and risk assessments. Chapter 5 asks how 1% growth in natural capital affects a country’s government bond yields. Comparisons across countries lead to problematic insights, due to the ingrained income bias. Instead, within-country comparisons over the recent past, estimated using interactive fixed-effects, are unaffected by the bias and show that renewable natural capital tend to lower borrowing costs

Kalman Filter vs Alternative Modeling Techniques and Applied Investment Strategies

This thesis examines the efficacy of alternative modeling techniques to predict stock market returns modeled with time-varying coefficients with the goal of developing and implementing a trading strategy that yields excess returns. First, we determine the modeling technique with the smallest forecast error using historical predictors: the differenced dividend-price ratio, lagged S&P 500 returns, and the change in implied volatility. The candidate modeling techniques include both constant and recursive ordinary least squares (OLS) regression methods and diverges from previous return forecast literature with the comparison of a state-space model (SSM) cast as a VAR(1) process to each OLS technique. The state-space model is found to be the superior modeling technique with the smallest RMSE 3.76% and greatest out-of-sample of 2.62% using delta VIX as the forecasting variable. Second, we demonstrate economic significance, using 1) monthly stock return forecasts in a market timing strategy, and 2) daily price forecasts in a simulated live pairs trading strategy taking into account implementation shortfall. In both trading strategies, the state-space model Kalman filter significantly outperforms the alternative OLS modeling techniques with an annualized total return of 21.64% in the market timing strategy and an annualized total return of 13.21% unlevered in the pairs trading strategy

Untangling hotel industry’s inefficiency: An SFA approach applied to a renowned Portuguese hotel chain

The present paper explores the technical efficiency of four hotels from Teixeira Duarte Group - a renowned Portuguese hotel chain. An efficiency ranking is established from these four hotel units located in Portugal using Stochastic Frontier Analysis. This methodology allows to discriminate between measurement error and systematic inefficiencies in the estimation process enabling to investigate the main inefficiency causes. Several suggestions concerning efficiency improvement are undertaken for each hotel studied.info:eu-repo/semantics/publishedVersio

Essays on Modern Econometrics and Machine Learning

Diese Dissertation behandelt verschiedene Aspekte moderner Ökonometrie und Machine Learnings. Kapitel 2 stellt einen neuen Schätzer für die Regressionsparameter in einem Paneldatenmodell mit interaktiven festen Effekten vor. Eine Besonderheit unserer Methode ist die Modellierung der factor loadings durch nichtparametrische Funktionen. Wir zeigen die root-NT-Konvergenz sowie die asymptotische Normalverteilung unseres Schätzers. Kapitel 3 betrachtet die rekursive Schätzung von Quantilen mit Hilfe des stochastic gradient descent (SGD) Algorithmus mit Polyak-Ruppert Mittelwertbildung. Der Algorithmus ist rechnerisch und Speicher-effizient verglichen mit herkömmlichen Schätzmethoden. Unser Fokus ist die Untersuchung des nichtasymptotischen Verhaltens, indem wir eine exponentielle Wahrscheinlichkeitsungleichung zeigen. In Kapitel 4 stellen wir eine neue Methode zur Kalibrierung von conditional Value-at-Risk (CoVaR) basierend auf Quantilregression mittels Neural Networks vor. Wir modellieren systemische Spillovereffekte in einem Netzwerk von systemrelevanten Finanzinstituten. Eine Out-of-Sample Analyse zeigt eine klare Verbesserung im Vergleich zu einer linearen Grundspezifikation. Im Vergleich mit bestehenden Risikomaßen eröffnet unsere Methode eine neue Perspektive auf systemisches Risiko. In Kapitel 5 modellieren wir die gemeinsame Dynamik von Kryptowährungen in einem nicht-stationären Kontext. Um eine Analyse in einem dynamischen Rahmen zu ermöglichen, stellen wir eine neue vector error correction model (VECM) Spezifikation vor, die wir COINtensity VECM nennen.This thesis focuses on different aspects of the union of modern econometrics and machine learning. Chapter 2 considers a new estimator of the regression parameters in a panel data model with unobservable interactive fixed effects. A distinctive feature of the proposed approach is to model the factor loadings as a nonparametric function. We show that our estimator is root-NT-consistent and asymptotically normal, as well that it reaches the semiparametric efficiency bound under the assumption of i.i.d. errors. Chapter 3 is concerned with the recursive estimation of quantiles using the stochastic gradient descent (SGD) algorithm with Polyak-Ruppert averaging. The algorithm offers a computationally and memory efficient alternative to the usual empirical estimator. Our focus is on studying the nonasymptotic behavior by providing exponentially decreasing tail probability bounds under minimal assumptions. In Chapter 4 we propose a novel approach to calibrate the conditional value-at-risk (CoVaR) of financial institutions based on neural network quantile regression. We model systemic risk spillover effects in a network context across banks by considering the marginal effects of the quantile regression procedure. An out-of-sample analysis shows great performance compared to a linear baseline specification, signifying the importance that nonlinearity plays for modelling systemic risk. A comparison to existing network-based risk measures reveals that our approach offers a new perspective on systemic risk. In Chapter 5 we aim to model the joint dynamics of cryptocurrencies in a nonstationary setting. In particular, we analyze the role of cointegration relationships within a large system of cryptocurrencies in a vector error correction model (VECM) framework. To enable analysis in a dynamic setting, we propose the COINtensity VECM, a nonlinear VECM specification accounting for a varying system-wide cointegration exposure

Panel data models with long-range dependence

This thesis comprises of three chapters that study panel data models with long-range dependence. The first chapter is a coauthored paper with Prof. Carlos Velasco. We consider large N; T panel data models with fixed effects, common factors allowing cross-section dependence, and persistent data and shocks, which are assumed fractionally integrated. In a basic setup, the main interest is on the fractional parameter of the idiosyncratic component, which is estimated in first differences after factor removal by projection on the cross-section average. The pooled conditional-sum-of-squares estimate is √NT consistent but the normal asymptotic distribution might not be centered, requiring the time series dimension to grow faster than the cross-section size for correction. Generalizing the basic setup to include covariates and heterogeneous parameters, we propose individual and common-correlation estimates for the slope parameters, while error memory parameters are estimated from regression residuals. The two parameter estimates are √T consistent and asymptotically normal and mutually uncorrelated, irrespective of possible cointegration among idiosyncratic components. A study of small-sample performance and an empirical application to realized volatility persistence are included. The second chapter extends the first chapter. In this paper, a general dynamic panel data model is considered that incorporates individual and interactive fixed effects and possibly correlated innovations. The model accommodates general stationary or nonstationary long-range dependence through interactive fixed effects and innovations, removing the necessity to perform a priori unitroot or stationarity testing. Moreover, persistence in innovations and interactive fixed effects allows for cointegration; innovations can also have vector-autoregressive dynamics; deterministic trends can be nested. Estimations are performed using conditional-sum-of-squares criteria based on projected series by which latent characteristics are proxied. Resulting estimates are consistent and asymptotically normal at parametric rates. A simulation study provides reliability on the estimation method. The method is then applied to the long-run relationship between debt and GDP. The third and final chapter of the thesis is a coauthored paper with Prof. Abderrahim Taamouti. In this paper, a parametric portfolio policy function is considered that incorporates common stock volatility dynamics to optimally determine portfolio weights. Reducing dimension of the traditional portfolio selection problem signifficantly, only a number of policy parameters corresponding to first- and second-order characteristics are estimated based on a standard methodof- moments technique. The method, allowing for the calculation of portfolio weight and return statistics, is illustrated with an empirical application to 30 U.S. industries to study the economic activity before and after the recent financial crisis.Financial support from the Spanish Plan Nacional de I+D+I (ECO2012-31748), Spanish Ministerio de Ciencia e Innovacion grant ECO2010-19357 and Consolider-2010.Estimation of fractionally integrated panel data models with fixed effects and cross-section dependence / Yunus Emre Ergemen, Carlos Velasco Gómez. -- System estimation of panel data models under long-range dependence. -- Parametric portfolio policies with common volatility dynamics / Yunus Emre Ergemen, Abderrahim TaamoutiPrograma Oficial de Doctorado en EconomíaPresidente: Jesús Gonzalo Muñoz; Secretario: Pilar Poncela; Vocal: Javier Huald