Instrumental Variable Identification of Dynamic Variance Decompositions

Macroeconomists increasingly use external sources of exogenous variation for causal inference. However, unless such external instruments (proxies) capture the underlying shock without measurement error, existing methods are silent on the importance of that shock for macroeconomic fluctuations. We show that, in a general moving average model with external instruments, variance decompositions for the instrumented shock are interval-identified, with informative bounds. Various additional restrictions guarantee point identification of both variance and historical decompositions. Unlike SVAR analysis, our methods do not require invertibility. Applied to U.S. data, they give a tight upper bound on the importance of monetary shocks for inflation dynamics

Linearization Methods in Time Series Analysis

In this dissertation, we propose a set of computationally efficient methods based on approximating/representing nonlinear processes by linear ones, so-called linearization. Firstly, a linearization method is introduced for estimating the multiple frequencies in sinusoidal processes. It utilizes a regularized autoregressive (AR) approximation, which can be regarded as a "large p - small n" approach in a time series context. An appealing property of regularized AR is that it avoids a model selection step and allows for an efficient updating of the frequency estimates whenever new observations are obtained. The theoretical analysis shows that the regularized AR frequency estimates are consistent and asymptotically normally distributed. Secondly, a sieve bootstrap scheme is proposed using the linear representation of generalized autoregressive conditional heteroscedastic (GARCH) models to construct prediction intervals (PIs) for the returns and volatilities. Our method is simple, fast and distribution-free, while providing sharp and well-calibrated PIs. A similar linear bootstrap scheme can also be used for diagnostic testing. Thirdly, we introduce a robust lagrange multiplier (LM) test, which utilizes either the bootstrap or permutation procedure to obtain critical values, for detecting GARCH effects. We justify that both bootstrap and permutation LM tests are consistent. Intensive numerical studies indicate that the proposed resampling algorithms significantly improve the size and power of the LM test in both skewed and heavy-tailed processes. Moreover, fourthly, we introduce a nonparametric trend test in the presence of GARCH effects (NT-GARCH) based on heteroscedastic ANOVA. Our empirical evidence show that NT-GARCH can effectively detect non-monotonic trends under GARCH, especially in the presence of irregular seasonal components. We suggest to apply the bootstrap procedure for both selecting the window length and finding critical values. The newly proposed methods are illustrated by applications to astronomical data, to foreign currency exchange rates as well as to water and air pollution data. Finally, the dissertation is concluded by an outlook on further extensions of linearization methods, e.g., in model order selection and change point detection

Implementation and Application of Statistical Methods in Research, Manufacturing Technology and Quality Control

Práce se zabývá možnostmi použití moderních statistických postupů se zaměřením na robustní metody. Vybrané postupy jsou analyzovány a aplikovány na častých problémech z praxe v českém průmyslu a technologii. Studovaná témata, metody a algoritmy jsou voleny tak, aby byla přínosem v reálných aplikacích ve srovnání s používanými klasickými metodami. Použitelnost a účinnost algoritmů je ověřena a demonstrována na reálných studiích a problémech z výzkumného prostředí českých průmyslových subjektů. V práci je poukázáno na nevyužitý potenciál současné teoreticko-matematické a výpočetní kapacity a nových přístupů k chápání statistických modelů a metod. Výsledkem práce je rovněž původní vývojové prostředí s programovacím jazykem DARWin (Data Analysis Robot for Windows) pro intenzivní využití efektivních numerických postupů pro získávání informací z dat. Práce je impulsem pro širší využití robustních a numericky, nebo výpočetně náročnějších metod, jako jsou neuronové sítě, pro modelování procesů a kontrolu kvality.This thesis deals with modern statistical approaches and their application aimed at robust methods and neural network modelling. Selected methods are analyzed and applied on frequent practical problems in czech industry and technology. Topics and methods are to be benificial in real applications compared to currently used classical methods. Applicability and effectivity of the algorithms is verified and demonstrated on real studies and problems in czech industrial and research bodies. The great and unexploited potential of modern theoretical and computational capacity and the potential of new approaces to statistical modelling and methods. A significant result of this thesis is also an environment for software application development for data analysis with own programming language DARWin (Data Analysis Robot for Windows) for implemenation of effective numerical algorithms for extaction information from data. The thesis should be an incentive for boarder use of robust and computationally intensive methods as neural networks for modelling processes, quality control and generally better understanding of nature.

Rapid identification of oil contaminated soils using visible near infrared diffuse reflectance spectroscopy

Initially, 46 petroleum contaminated and non-contaminated soil samples were collected and scanned using visible near-infrared diffuse reflectance spectroscopy (VisNIR DRS) at three combinations of moisture content and pretreatment. The VisNIR spectra of soil samples were used to predict total petroleum hydrocarbon (TPH) content using partial least squares (PLS) regression and boosted regression tree (BRT) models. The field-moist intact scan proved best for predicting TPH content with a validation r2 of 0.64 and relative percent difference (RPD) of 1.70. Those 46 samples were used to calibrate a penalized spline (PS) model. Subsequently, the PS model was used to predict soil TPH content for 128 soil samples collected over an 80 ha study site. An exponential semivariogram using PS predictions revealed strong spatial dependence among soil TPH [r2 = 0.76, range = 52 m, nugget = 0.001 (log10 mg kg-1)2, and sill 1.044 (log10 mg kg-1)2]. An ordinary block kriging map produced from the data showed that TPH distribution matched the expected TPH variability of the study site. Another study used DRS to measure reflectance patterns of 68 artificially constructed samples with different clay content, organic carbon levels, petroleum types, and different levels of contamination per type. Both first derivative of reflectance and discrete wavelet transformations were used to preprocess the spectra. Principal component analysis (PCA) was applied for qualitative VisNIR discrimination of variable soil types, organic carbon levels, petroleum types, and concentration levels. Soil types were separated with 100% accuracy, and organic carbon levels were separated with 96% accuracy by linear discriminant analysis. The support vector machine produced 82% classification accuracy for organic carbon levels by repeated random splitting of the whole dataset. However, spectral absorptions for each petroleum hydrocarbon overlapped with each other and could not be separated with any classification scheme when contaminations were mixed. Wavelet-based multiple linear regression performed best for predicting petroleum amount with the highest residual prediction deviation (RPD) of 3.97. While using the first derivative of reflectance spectra, PS regression performed better (RPD = 3.3) than the PLS (RPD= 2.5) model. Specific calibrations considering additional soil physicochemical variability are recommended to produce improved predictions

Various Statistical Inferences for High-dimensional Time Series: Bootstrap, Homogeneity Pursuit and Autocovariance Test

This thesis aims to study various statistical inferences for high-dimensional data, especially high-dimensional time series, including sieve bootstrap, homogeneity pursuit, and an equivalence test for spiked eigenvalues of autocovariance matrix. The primary techniques used in this thesis are novel dimension-reduction methods developed from factor models and principal component analysis (PCA). Chapter 2 proposes a novel sieve bootstrap method for high-dimensional time series and applies it to sparse functional time series where the actual observations are not dense, and pre-smoothing is misleading. Chapter 3 introduces an iterative complement-clustering principal component analysis (CPCA) to study high-dimensional data with group structures, where both homogeneity and sub-homogeneity (group-specific information) can be identified and estimated. Lastly, Chapter 4 proposes a novel test statistic named the autocovariance test to compare the spiked eigenvalues of the autocovariance matrices for two high-dimensional time series. In all chapters, dimension-reduction methods are applied for novel statistical inferences. In particular, Chapters 2 and 4 focus on the spiked eigenstructure of autocovariance matrix and use factors to capture the temporal dependence of the high-dimensional time series. Meanwhile, Chapter 3 aims to simultaneously estimate homogeneity and sub-homogeneity, which form a more complicated spiked eigenstructure of the covariance matrix, despite that the group-specific information is relatively weak compared with the homogeneity and traditional PCA fails to capture it. The theoretical and asymptotic results of all three statistical inferences are provided in each chapter, respectively, where the numerical evidence on the finite-sample performance for each method is also discussed. Finally, these three statistical inferences are applied on particulate matter concentration data, stock return data, and age-specific mortality data for multiple countries, respectively, to provide valid statistical inferences

NONPARAMETRIC IDENTIFICATION AND ESTIMATION OF STOCHASTIC FRONTIER MODELS

This dissertation studies nonparametric identication and estimation of stochastic frontiermodels. It is composed of three chapters. The rst chapter investigates the identication and estimation of a cross sectional stochastic frontier model with Laplacian errors and unknown variance, which is built on a nonparametric density deconvolution strategy. Chapter two studies a zero-ineciency stochastic frontier model utilizing a penalized sieve estimator, which allows flexible function forms and arbitrary distributions of ineciency. The third chapter explores identication and estimation of a nonparametric panel stochastic frontier model based on Kotlarski\u27s Lemma and moments derived from conditional characteristic functions

Forecasting: theory and practice

Forecasting has always been in the forefront of decision making and planning. The uncertainty that surrounds the future is both exciting and challenging, with individuals and organisations seeking to minimise risks and maximise utilities. The lack of a free-lunch theorem implies the need for a diverse set of forecasting methods to tackle an array of applications. This unique article provides a non-systematic review of the theory and the practice of forecasting. We offer a wide range of theoretical, state-of-the-art models, methods, principles, and approaches to prepare, produce, organise, and evaluate forecasts. We then demonstrate how such theoretical concepts are applied in a variety of real-life contexts, including operations, economics, finance, energy, environment, and social good. We do not claim that this review is an exhaustive list of methods and applications. The list was compiled based on the expertise and interests of the authors. However, we wish that our encyclopedic presentation will offer a point of reference for the rich work that has been undertaken over the last decades, with some key insights for the future of the forecasting theory and practice