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Popular models for time series of count data are integer-valued autoregressive (INAR) models, for which the literature mainly deals with parametric estimation. In this regard, a semiparametric estimation approach is a remarkable exception which allows for estimation of the INAR models without any parametric assumption on the innovation distribution. However, for small sample sizes, the estimation performance of this semiparametric estimation approach may be inferior. Therefore, to improve the estimation accuracy, we propose a penalized version of the semiparametric estimation approach, which exploits the fact that the innovation distribution is often considered to be smooth, i.e. two consecutive entries of the PMF differ only slightly from each other. This is the case, for example, in the frequently used INAR models with Poisson, negative binomially or geometrically distributed innovations. For the data-driven selection of the penalization parameter, we propose two algorithms and evaluate their performance. In Monte Carlo simulations, we illustrate the superiority of the proposed penalized estimation approach and argue that a combination of penalized and unpenalized estimation approaches results in overall best INAR model fits.

For univariate stationary and centered time series ( X t ) t ∈ Z , Akaike’s identity links the inverse of the Yule–Walker matrix Γ ( p ) = E ( X X ′ ) , where X = ( X t − 1 , … , X t − p ) ′ , to the corresponding finite predictor coefficients. It reads as a Cholesky-type factorization Γ ( p ) − 1 = L ( p ) ′ Σ ( p ) − 1 L ( p ) , where L ( p ) is lower-triangular and Σ ( p ) − 1 is diagonal. Whereas this Cholesky-type factorization exists whenever Γ ( p ) is positive definite, Akaike derived a meaningful interpretation of L ( p ) and Σ ( p ) − 1 in terms of finite predictor coefficients. It is useful in many applications and is particularly crucial to derive asymptotic theory for Berk’s spectral density estimator. We investigate the validity of a bona fide extension of Akaike’s identity to univariate stationary random fields ( X t ) t ∈ Z d . An analogue of Akaike’s result is shown to hold true if and only if the corresponding Yule–Walker matrix Γ ( p ) is Toeplitz. This condition turns out to be very restrictive and rules out commonly used unilateral autoregressive models in Z d (such as half-plane or quarter-plane fits in Z 2 ). Instead, we prove that the corresponding Cholesky-type factorization Γ ( p ) − 1 = L ( p ) ′ Σ ( p ) − 1 L ( p ) for random fields does establish a link to a different, but practically less relevant sequence of so-called reshaping past projection coefficients.

In recent years, the use of dynamic networks became increasingly popular. An important task is to identify differences at particular time points, e.g. for online monitoring, change-point detection or testing procedures. Due to the complexity of network data, the statistical analysis is challenging. Therefore, it is usually a main step to characterize the networks by one or few scalar-valued metrics at each time point. As the reduction to such metrics can result in information loss, the understanding of their behaviour in various change scenarios is crucial. However, existing studies commonly use specific data examples and do not give any deeper theoretical insights of the general performances. In this paper, we propose a categorization of different types of changes which can occur in network data. We analyze the suitability and limitations of common network metrics in such situations and give comprehensive explanations of their behaviour. This leads to a well-founded advice of which metrics to use in various application scenarios. Our findings are underlined by an extensive simulation study and some real-world data which involve both time-dependent and independent setups for online monitoring.

Wir stellen in diesem Aufsatz ein Modell interdisziplinarer Zusammenarbeit zwischen Kommunikationswissenschaft und Methodenwissenschaft (hier: Statistik) vor. Dabeisteht die Frage im Mittelpunkt, wie sich die Kollaboration grundverschiedener Disziplinen uber einen langeren Zeitraum verstetigen lasst. Der agilen Entwicklung von Forschungssoftware, die die fachubergreifende Zusammenarbeit strukturiert, kann hierbei eine zentrale Rolle zukommen. Sie ermoglicht zwei Ebenen der Zusammenarbeit mit verschiedenen Zeithorizonten: auf der einen werden zeitlich begrenzte Projekte umgesetzt, auf der anderen die langerfristige Zusammenarbeit organisiert. Wechselnde Team-Konstellationen und Hierarchien ermoglichen kontinuierlichen Wissensaustausch, die verwendete Programmiersprache ist Grundlage fur die Entstehung einer facherubergreifenden Kommunikation und die Orientierung auf ein gemeinsames Produkt schafft eine Kultur der gemeinsamen Verantwortlichkeit. Um die theoretischen Reflexionen an der Forschungspraxis zu spiegeln, greifen die Autor*innen auf ihre Erfahrungen im Kontext des Dortmund Center fur datenbasierte Medien-Analyse (kurz: DoCMA) zuruck. DoCMA ist deswegen als Fallbeispiel relevant, da Struktur und Organisation hier auf die Erfordernisse der agilen Entwicklung offener Forschungssoftware ausgerichtet wurden.

Summary We discuss Poisson reduced-rank models for low-dimensional summaries of high-dimensional Poisson vectors that allow inference on the location of individuals in a low-dimensional space. We show that under weak dependence conditions, which allow for certain correlations between the Poisson random variables, the locations can be consistently estimated using Poisson maximum likelihood estimation. Moreover, we develop consistent rules for determining the dimension of the location from the discrete data. Our main motivation for studying Poisson reduced-rank models arises from applications to political text data, where word counts in a political document are modelled by Poisson random variables. We apply our method to party manifesto data taken from German political parties across seven federal elections following German reunification, to make statistical inferences on the multi-dimensional evolution of party positions.

For understanding large text corpora, a widely used method is Latent Dirichlet Allocation (LDA). The topic assignments from LDA usually rely on a (random) initialization such that the outcome is also to some extent random. In particular, replicated runs on the same text data lead to different results such that the LDA is not fully reproducible. This instability of the LDA approach is often neglected in practice, where text data analysis is commonly based only on a single LDA run. We propose a new method called LDAPrototype for selecting the most representative run from a set of replicated LDA runs on the same dataset. We improve the reliability of conclusions drawn from LDA results, since replications of LDAPrototype are more similar to each other than replications of single LDA runs, or even as models selected by perplexity or NPMI. For this purpose, we propose a reliability score based on a new tailored model similarity measure S-CLOP. For the quantification of topic similarities, we compare a thresholded version of the Jaccard coefficient to cosine similarity, Jensen-Shannon divergence and Rank Biased Overlap. Our results of an application to six real datasets consisting of newspaper articles or tweets show that the reproducibility of LDA results using LDAPrototype increases, and so does the reliability of empirical findings based on topic modeling. Overall, the new approach is justified in view of its application, comprehensibility, easy implementation and computational feasibility. The algorithm’s concept is generalizable to other topic modeling procedures with topics characterized by word distributions.

In this paper, we propose a kernel-type estimator for the local characteristic function of locally stationary processes. Under weak moment conditions, we prove joint asymptotic normality for local empirical characteristic functions. For time-varying linear processes, we establish a central limit theorem under the assumption of finite absolute first moments of the process. Additionally, we prove weak convergence of the local empirical characteristic process. We apply our asymptotic results to parameter estimation. Furthermore, by extending the notion of distance correlation of Szekely, Rizzo and Bakirov (2007) to locally stationary processes, we are able to provide asymptotic theory for local empirical distance correlations. Finally, we provide a simulation study on minimum distance estimation for a-stable distributions and illustrate the pairwise dependence structure over time of log returns of German stock prices via local empirical distance correlations.

Mertens and Ravn (2013) estimate impulse response functions (IRFs) from income tax changes in a structural vector autoregression (SVAR) by using narrative accounts of tax liability changes as proxy variables. To produce confidence intervals for their IRFs, they use a residual-based wild bootstrap, which has subsequently become popular in the proxy SVAR literature. We argue that their wild bootstrap is not valid, producing confidence intervals that are much too small. Using a residual-based moving block bootstrap that is proven to be asymptotically valid, we reestimate confidence intervals for Mertens and Ravn’s (2013) IRFs and find no statistically significant effects of tax changes on output, labor, and investment. (JEL E23, E62, H24, H25, H31, H32)

Integer-valued autoregressive (INAR) processes form a very useful class of processes suitable to model time series of counts. Several practically relevant estimators based on INAR data are known to...

In the extreme value analysis of stationary regularly varying time series, tail array sums form a broad class of statistics suitable to analyze their extremal behavior. This class includes for example, the Hill estimator or estimators of the extremogram and the tail dependence coefficient. General asymptotic theory for tail array sums has been developed by Rootzen et al. (Ann. Appl. Probab. 8 (1998) 868–885) under mixing conditions and in Kulik et al. (Stochastic Process. Appl. 129 (2019) 4209–4238) for functions of geometrically ergodic Markov chains. A more general framework of cluster functionals is presented in Drees and Rootzen (Ann. Statist. 38 (2010) 2145–2186). However, the resulting limiting distributions turn out to be very complex and cumbersome to estimate as they usually depend on the whole extremal dependence structure of the time series. Hence, a suitable bootstrap procedure is desired, but available bootstrap consistency results for tail array sums are scarce. In this paper, following Drees (Drees (2015)), we consider a multiplier block bootstrap to estimate the limiting distribution of tail array sums. We prove that, conditionally on the data, an appropriately constructed multiplier block bootstrap statistic converges to the correct limiting distribution. Interestingly, in contrast, it turns out that an apparently natural, but naive application of the multiplier block bootstrap scheme does not yield the correct limit. In simulations, we provide numerical evidence of our theoretical findings and illustrate the superiority of the proposed multiplier block bootstrap over some obvious competitors. The proposed bootstrap scheme proves to be computationally efficient in comparison to other approaches.

Latent Dirichlet Allocation (LDA) is one of the most popular topic models employed for the analysis of large text data. When applied repeatedly to the same text corpus, LDA leads to different results. To address this issue, several methods have been proposed. In this paper, instead of dealing with this methodological source of algorithmic uncertainty, we assess the aleatoric uncertainty of the text generating process itself. For this task, we use a direct LDA-model approach to quantify the uncertainty due to the random process of text generation and propose three different bootstrap approaches to resample texts. These allow to construct uncertainty intervals of topic proportions for single texts as well as for text corpora over time. We discuss the differences of the uncertainty intervals derived from the three bootstrap approaches and the direct approach for single texts and for aggregations of texts. We present the results of an application of the proposed methods to an example corpus consisting of all published articles in a German daily quality newspaper of one full year and investigate the effect of different sample sizes to the uncertainty intervals.

The serial dependence of categorical data is commonly described using Markovian models. Such models are very flexible, but they can suffer from a huge number of parameters if the state space or the model order becomes large. To address the problem of a large number of model parameters, the class of (new) discrete autoregressive moving-average (NDARMA) models has been proposed as a parsimonious alternative to Markov models. However, NDARMA models do not allow any negative model parameters, which might be a severe drawback in practical applications. In particular, this model class cannot capture any negative serial correlation. For the special case of binary data, we propose an extension of the NDARMA model class that allows for negative model parameters, and, hence, autocorrelations leading to the considerably larger and more flexible model class of generalized binary ARMA (gbARMA) processes. We provide stationary conditions, give the stationary solution, and derive stochastic properties of gbARMA processes. For the purely autoregressive case, classical Yule&ndash, Walker equations hold that facilitate parameter estimation of gbAR models. Yule&ndash, Walker type equations are also derived for gbARMA processes.

Statistik befasst sich mit Daten, und Daten bestehen aus Zahlen. So denken die meisten Menschen aus dem Bauch heraus. Aber als Folge der IT-Revolution gerieten auch ganz andere Dinge in den Fokus der Wissenschaft Statistik, darunter auch Texte. Die werden zwar schon seit vielen Jahrhunderten in grosen Mengen von verschiedensten Quellen erzeugt. Aber erst seit Kurzem ermoglicht die zunehmende Digitalisierung von Texten und die damit einhergehende Verfugbarkeit von Texten in grosen Textsammlungen, die in den Textdaten enthaltene Information strukturiert und automatisiert zu analysieren. Die Statistik liefert hierfur viele hilfreiche Methoden, sowohl zur Verarbeitung der Daten als auch fur die Interpretation bei inhaltlichen Fragen.

Many random phenomena in the environmental and geophysical sciences are functions of both space and time; these are usually called spatio-temporal processes. Typically, the spatio-temporal process is observed over discrete equidistant time and at irregularly spaced locations in space. One important aim is to develop statistical models based on what is observed. While doing so a commonly used assumption is that the underlying spatio-temporal process is stationary. If this assumption does not hold, then either the mean or the covariance function is misspecified. This can, for example, lead to inaccurate predictions. In this article we propose a test for spatio-temporal stationarity. The test is based on the dichotomy that Fourier transforms of stochastic processes are near uncorrelated if the process is second-order stationary but correlated if the process is second-order nonstationary. Using this as motivation, a discrete Fourier transform for spatio-temporal data over discrete equidistant times but on irregularly spaced spatial locations is defined. Two statistics which measure the degree of correlation in the discrete Fourier transforms are proposed. These statistics are used to test for spatio-temporal stationarity. It is shown that the same statistics can also be adapted to test for the one-way stationarity (either spatial or temporal stationarity). The proposed methodology is illustrated with a small simulation study.

For core financial market activities like risk management and asset pricing, it appears to be crucial to investigate the “connectedness” among financial institutions. In times of economic crises, a suitable measure of connectedness can provide valuable insights of financial markets and helps to understand how institutions influence each other. In particular, depending on contractual obligations between financial institutions, the financial distress at a bank with large systemic impact is likely to cause also distress at other institutions. In the literature, the latter phenomenon is generally tagged by ’contagion’ and can eventually result in severe economic crises. The purpose of this paper is to investigate the connectedness among German financial institutions during the global financial crisis 2007-2009, where the authors focus particularly on 2008 and its height in September 2008 with the bankruptcy of Lehman Brothers. They make use of the definition of connectedness, as it was recently proposed by Diebold and Yilmaz (2014). Their approach relies on analyzing multiple time series of volatilities by a vector autoregressive (VAR) model and a generalized forecast error variance decompositions. It provides several meaningful measures of connectedness and allows for static (average), as well as dynamic (daily time-varying) analyses. The authors show that the connectedness in Germany can be described well by the model. Keywords: сonnectedness, contagion, generalized variance decomposition, networks, spillover effects. JEL Classification: C32, C58, G32, G33

This article is motivated by several articles that propose statistical inference where the independence of wavelet coefficients for both short- as well as long-range dependent time series is assumed. We focus on the sample variance and investigate the influence of the dependence between wavelet coefficients and this statistic. To this end, we derive asymptotic distributional properties of the sample variance for a time series that is synthesized, ignoring some or all dependence between wavelet coefficients. We show that the second-order properties differ from the those of the true time series whose wavelet coefficients have the same marginal distribution except in the independent Gaussian case. This holds true even if the dependency is correct within each level and only the dependence between levels is ignored. In the case of sample autocovariances and sample autocorrelations at lag one, we indicate that first-order properties are erroneous. In a second step, we investigate several nonparametric b...

We derive a framework for asymptotically valid inference in stable vector autoregressive (VAR) models with conditional heteroskedasticity of unknown form. We prove a joint central limit theorem for the VAR slope parameter and innovation covariance parameter estimators and address bootstrap inference as well. Our results are important for correct inference on VAR statistics that depend both on the VAR slope and the variance parameters as e.g. in structural impulse response functions (IRFs). We also show that wild and pairwise bootstrap schemes fail in the presence of conditional heteroskedasticity if inference on (functions) of the unconditional variance parameters is of interest because they do not correctly replicate the relevant fourth moments' structure of the error terms. In contrast, the residual-based moving block bootstrap results in asymptotically valid inference. We illustrate the practical implications of our theoretical results by providing simulation evidence on the finite sample properties of different inference methods for IRFs. Our results point out that estimation uncertainty may increase dramatically in the presence of conditional heteroskedasticity. Moreover, most inference methods are likely to understate the true estimation uncertainty substantially in finite samples.

We consider Poisson reduced rank models where parameters depend on time. Our main motivation comes from studies in comparative politics where one wants to locate party positions in a certain political space. For this purpose, several empirical methods have been proposed using text as data sources. As the data structure of texts is quite complex, its analysis to extract information is generally a difficult task. Furthermore, political texts usually contain a large number of words such that a simultaneous analysis of word counts becomes challenging. In this paper, we consider Poisson models for each word count simultaneously and provide a statistical method suitable to analyze political text data. We consider a novel model which allows the political lexicon to change over time and develop an estimation procedure based on LASSO and fused LASSO penalization techniques to address high-dimensionality via significant dimension reduction. This model gives insights into the potentially changing use of words by left and right-wing parties over time. The procedure allows to identify automatically those words having a discriminating effect between party positions. To address the dependence structure of word counts over time, we propose integer-valued time series processes to implement a suitable bootstrap method for constructing confidence intervals for the model parameters. We apply our approach to party manifesto data from German parties over seven federal elections after German reunification. The approach does not require any a priori information nor expert knowledge to process the data.

It is well known that the discrete Fourier transforms (DFT) of a second order stationary time series between two distinct Fourier frequencies are asymptotically uncorrelated. In contrast for a large class of second order nonstationary time series, including locally stationary time series, this property does not hold. In this paper these starkly differing properties are used to define a global test for stationarity based on the DFT of a vector time series. It is shown that the test statistic under the null of stationarity asymptotically has a chi-squared distribution, whereas under the alternative of local stationarity asymptotically it has a noncentral chi-squared distribution. Further, if the time series is Gaussian and stationary, the test statistic is pivotal. However, in many econometric applications, the assumption of Gaussianity can be too strong, but under weaker conditions the test statistic involves an unknown variance that is extremely difficult to directly estimate from the data. To overcome this issue, a scheme to estimate the unknown variance, based on the stationary bootstrap, is proposed. The properties of the stationary bootstrap under both stationarity and nonstationarity are derived. These results are used to show consistency of the bootstrap estimator under stationarity and to derive the power of the test under nonstationarity. The method is illustrated with some simulations. The test is also used to test for stationarity of FTSE 100 and DAX 30 stock indexes from January 2011-December 2012.