Manfred Deistler

• TU Wien

The “retrieval from mixed frequency sampling” approach based on blocking—described e.g., in Anderson et al. (Econom Theory 32:793–826, 2016a)—is concerned with retrieving an underlying high frequency model from mixed frequency observations. In this paper, we investigate parameter-identifiability in the Johansen (Likelihood-based inference in cointe...

Factor Sequences are stochastic double sequences $(y_{it}: i \in \mathbb N, t \in \mathbb Z)$ indexed in time and cross-section which have a so called factor structure. The name was coined by Forni et al. 2001, who introduced dynamic factor sequences. We show the difference between dynamic factor sequences and static factor sequences which are the...

A survey is provided dealing with the formulation of modelling problems for dynamic factor models, and the various algorithm possibilities for solving these modelling problems. Emphasis is placed on understanding requirements for the handling of errors, noting the relevance of the proposed application of the model, be it for example prediction or b...

In many areas the dependence structure between variables, in particular, univariate component processes, is of special interest. For instance, often the question arises whether there exist causal relationships. The topic of this chapter is the discussion of the so-called Granger causality. This concept has received great attention in econometrics—b...

The computation of “good” predictions and a quantitative analysis of the prediction quality are among the most important applications of time series analysis. Prediction in general is concerned with approximating a future process variable by a function of the observed values up to the present time. Here, we discuss a special prediction problem, nam...

Linear state-space systems, like ARMA systems, are models for stationary processes, more precisely for the class of stationary processes with rational spectral density. ARMA models and state-space models (with white noise as input) represent the same class of stationary processes. State-space systems became particularly popular through the work of...

In this chapter we will show that every stationary process can be approximated by a sum of harmonic oscillations with random and uncorrelated amplitudes. The limit of these sums leads to an integral representation, the so called spectral representation of stationary processes. This spectral representation is a generalization of the Fourier represen...

In many applications, the observed variables can be divided into variables which are to be explained by a model, called endogenous variables or outputs, and observed variables which influence the endogenous variables without being influenced by them. The latter variables are called exogenous variables or observed inputs. They provide important info...

In finance data one often observes so-called volatility clustering, i.e. periods with relatively high volatility and periods with low volatility occur. This is an indication that the (conditional) variance is dependent on past observations. The most common models for the conditional variance are (G)ARCH models and stochastic volatility (SV) models....

In this chapter, we discuss so-called autoregressive processes, i.e. stationary solutions \((x_t)\) of difference equations of the form $$ x_{t}=a_{1}x_{t-1}+\cdots +a_{p}x_{t-p}+\epsilon _{t},\,\,\forall t\in \mathbb {Z}$$where \((\epsilon _{t})\) is white noise. AR models are probably the most widely used class of models for practical application...

In this chapter, we deal with linear dynamic factor models and related topics, such as dynamic principal component analysis (dynamic PCA). The main motivation for the use of such models is the so-called “curse of dimensionality” plaguing modeling of high-dimensional time series by “ordinary” multivariate AR or ARMA models. For instance, consider an...

This chapter introduces basic concepts such as time series, stationary process and covariance function. Subsequently, the time domain of a stationary process, which is a subspace of the Hilbert space of square integrable random variables, is presented. This Hilbert space approach allows for nice geometric interpretations and offers useful tools e.g...

ARMA (Autoregressive Moving Average) systems are difference equations of the form $$x_{t}=a_{1}x_{t-1}+\cdots +a_{p}x_{t-p}+\epsilon _{t}+b_{1}\epsilon _{t-1}+\cdots +b_{q}\epsilon _{t-q}, \forall t \in \mathbb {Z}$$where \((\epsilon _{t})\) is white noise. A stationary process \((x_t)\), which solves an ARMA system is called ARMA process. In a fir...

In this chapter, we consider linear, time-invariant, and generally dynamic transformations of stationary processes. Such transformations are also called (linear) filters or systems, where the original process is the input and the transformed process is the output. The most important application areas of such filters or systems are: These systems se...

The "REtrieval from MIxed Sampling" (REMIS) approach based on blocking developed in Anderson et al. (2016a) is concerned with retrieving an underlying high frequency model from mixed frequency observations. In this paper we investigate parameter-identifiability in the Johansen (1995) vector error correction model for mixed frequency data. We prove...

High-Dimensional Dynamic Factor Models are presented in detail: The main assumptions and their motivation, main results, illustrations by means of elementary examples. In particular, the role of singular ARMA models in the theory and applications of High-Dimensional Dynamic Factor Models is discussed. The emphasis is on model classes and their stru...

High-Dimensional Dynamic Factor Models are presented in detail: The main assumptions and their motivation, main results, illustrations by means of elementary examples. In particular, the role of singular ARMA models in the theory and applications of High-Dimensional Dynamic Factor Models is discussed.The emphasis of the paper is on model classes an...

Functional (un-)coupling (task-related change of functional connectivity) between different sites of the brain is a mechanism of general importance for cognitive processes. In Alzheimer's disease (AD), prior research identified diminished cortical connectivity as a hallmark of the disease. However, little is known about the relation between the amo...

In this paper we present a new estimation procedure named MF-IVL for VAR systems in the case of mixed-frequency data, where the data maybe, e.g., stock or flow data. The main idea of this new procedure is to project the slow components on the present and past fast ones in order to create instrumental variables. This procedure is shown to be generic...

Vector autoregressive moving average (VARMA) processes constitute a flexible class of linearly regular processes with a wide range of applications. In many cases VARMA models allow for a more parsimonious parametrization than vector autoregressive (VAR) models. However, compared to VAR processes the relation between internal parameters and external...

This article studies the sensitivity of Granger causality to the addition of noise, the introduction of subsampling, and the application of causal invertible filters to weakly stationary processes. Using canonical spectral factors and Wold decompositions, we give general conditions under which additive noise or filtering distorts Granger‐causal pro...

Recently, identifiability results for VAR systems in the context of mixed frequency data have been shown in a number of papers. These results have been extended to VARMA systems, where the MA order is smaller than or equal to the AR order. Here, it is shown that in the VMA case and in the VARMA case, where the MA order exceeds the AR order, results...

Analysis of nonlinear quantitative EEG (qEEG) markers describing complexity of signal in relation to severity of Alzheimer’s disease (AD) was the focal point of this study. In this study, 79 patients diagnosed with probable AD were recruited from the multi-centric Prospective Dementia Database Austria (PRODEM). EEG recordings were done with the sub...

We consider the cointegration properties of singular ARMA processes integrated of order one. Such processes are necessarily cointegrated as opposed to the regular case. We show that in the left coprime case the cointegrating space only depends upon the autoregressive polynomial at one.

This paper is concerned with the problem of identifiability of the parameters of a high frequency multivariate autoregressive model from mixed frequency time series data. We demonstrate identifiability for generic parameter values using the population second moments of the observations. In addition we display a constructive algorithm for the parame...

Alzheimer's Disease (AD) can take different courses: some patients remain relatively stable while others decline rapidly within a given period of time. Losing more than 3 Mini-Mental State Examination (MMSE) points in one year is classified as rapid cognitive decline (RCD). This study used neuropsychological test scores and quantitative EEG (QEEG)...

We analyzed the relation of several synchrony markers in the electroencephalogram (EEG) and Alzheimer's disease (AD) severity as measured by Mini-Mental State Examination (MMSE) scores. The study sample consisted of 79 subjects diagnosed with probable AD. All subjects were participants in the PRODEM-Austria study. Following a homogeneous protocol,...

This paper is concerned with the structure of multivariate AR and ARMA systems. The emphasis is on two “non-standard” cases: We deal with the structure of singular AR and ARMA systems which generate singular spectral densities and with identifiability of ARMA systems from mixed frequency data. In the mixed frequency case we show that, for the case...

This paper is concerned with estimation of the parameters of a high-frequency VAR model using mixed-frequency data, both for the stock and for the flow case. Extended Yule-Walker estimators and (Gaussian) maximum likelihood type estimators based on the EM algorithm are considered. Properties of these estimators are derived, partly analytically and...

We analyzed the relation between Alzheimer’s disease (AD) severity as measured by Mini-Mental State Examination (MMSE) scores and quantitative electroencephalographic (qEEG) markers that were derived from canonical correlation analysis. This allowed an investigation of EEG synchrony between groups of EEG channels. In this study, we applied the data...

Objective To investigate which single quantitative electro-encephalographic (QEEG) marker or which combination of markers correlates best with Alzheimer’s disease (AD) severity as measured by the Mini-Mental State Examination (MMSE). Methods We compared quantitative EEG markers for slowing (relative band powers), synchrony (coherence, canonical co...

Background: Quantitative electroencephalogram (qEEG) recorded during cognitive tasks has been shown to differentiate between patients with Alzheimer's disease (AD) and healthy individuals. However, the association between various qEEG markers recorded during mnestic paradigms and clinical measures of AD has not been studied in detail. Objective:...

We investigated the correlation of Alzheimer's disease (AD) severity as measured by the Mini-Mental State Examination (MMSE) to the signal complexity measures auto-mutual information, Shannon entropy and Tsallis entropy in 79 patients with probable AD from the multi-centric Prospective Dementia Database Austria (PRODEM). Using quadratic (linear) re...

Background : quantitative electroencephalogram (qEEG) recorded during cognitive tasks has been shown to differentiate between patients with Alzheimer’s disease (AD) and healthy individuals. However, the association between various qEEG markers recorded during mnestic paradigms and clinical measures of AD has not been studied in detail. Objective :...

Dementia caused by Alzheimer’s disease (AD) is worldwide one of the main medical and social challenges for the next years and decades. An automated analysis of changes in the electroencephalogram (EEG) of patients with AD may contribute to improving the quality of medical diagnoses. In this paper, measures based on uni- and multi-variate spectral d...

High-frequency oscillations (HFOs) are a reliable indicator for the epileptic seizure onset zone (SOZ) in ECoG recordings. We propose a novel method for the automatic detection of ictal HFOs in the ripple band (80-250Hz) based on CFAR matched sub-space filtering. This allows to track the early propagation of ictal HFOs, revealing initial and follow...

This paper is concerned with identifiability of an underlying high frequency multivariate stable singular AR system from mixed frequency observations. Such problems arise for instance in economics when some variables are observed monthly whereas others are observed quarterly. In particular, this paper studies stable singular AR systems where the co...

Motivated by problems of modeling high dimensional time series, this paper considers time-invariant, discrete-time linear systems which have a larger number of outputs than inputs, with the inputs being independent stationary white noise sequences. Moreover, different outputs are measured at different rates (in economic modeling, it is common that...

In this paper, we present a novel method for the identification of synchronization effects in multichannel electrocorticograms (ECoG). Based on autoregressive modeling, we define a dependency measure termed extrinsic-to-intrinsic power ratio (EIPR) which quantifies directed coupling effects in the time domain. Hereby, a dynamic input channel select...

Granger causality is a useful concept for studying causal relations in networks. However, numerical problems occur when applying the corresponding methodology to high-dimensional time series showing co-movement, e.g. EEG recordings or economic data. In order to deal with these shortcomings, we propose a novel method for the causal analysis of such...

This paper is concerned with identifiability of an underlying high frequency multivariate AR system from mixed frequency observations. Such problems arise for instance in economics when some variables are observed monthly whereas others are observed quarterly. If we have identifiability, the system and noise parameters and thus all second moments o...

This paper deals with autoregressive (AR) models of singular spectra, whose corresponding transfer function matrices can be expressed in a stable AR matrix fraction description [Formula: see text] with [Formula: see text] a tall constant matrix of full column rank and with the determinantal zeros of [Formula: see text] all stable, i.e. in [Formula:...

This paper presents a systematic study on the properties of blocked linear systems that have resulted from blocking discrete-time linear time invariant systems. The main idea is to explore the relationship between the blocked and the unblocked systems. Existing results are reviewed and a number of important new results are derived. Focus is given p...

In this paper we propose a novel segmentation method based on the relative frequency contributions of ictal multichannel ECoG data. Segments with predominant ϑ-activity are classified as epileptic. The seizure onset zone is determined by the temporal delay of the epileptic ϑ-activity (4-9Hz) on the different channels. We apply this methodology to t...

In this contribution we describe measures for dependence and causality between component processes in multivariate time series in a stationary context. Symmetric measures, such as the partial spectral coherence, as well as directed measures, such as the partial directed coherence and the conditional Granger causality index, are described and discus...

This paper studies properties of blocked systems resulting from blocking discrete linear systems with mixed frequency data. The focus is on the zeros of the blocked systems. We first establish results on the simpler single frequency case, where the unblocked linear systems have all data at the same frequency. In particular, an explicit relation bet...

A study is presented on solutions of the Yule‐Walker equations for singular AR processes that are stationary outputs of a given AR system. If the Yule-Walker equations admit more than one solution and the order of the AR system is no less than two, the solution set includes solutions which define unstable AR systems. The solution set also includes...

We consider the codifference and the normalized codifference function as dependence measures for stationary processes. Based on the empirical characteristic function, we propose estimators of the codifference and the normalized codifference function. We show consistency of the proposed estimators, where the underlying model is the ARMA with symmetr...

Introduction and problem statementRepresentations of linear systemsThe structure of state-space systemsThe structure of ARMA systemsThe realization of state-space systemsThe realization of ARMA systemsParametrizationEstimation of real-valued parametersDynamic specification

We consider Generalized Linear Dynamic Factor Models in a stationary context, where the latent variables and thus the static and dynamic factors are the sum of a linearly regular and a linearly singular stationary process and the noise process is linearly regular. The linearly singular component may be useful for modeling e.g. business cycles or se...

We deal with singular multivariate AR systems and the corresponding AR processes. An AR system is called singular if the variance of the white noise innovation is singular. AR processes are the stationary solutions of AR systems. In the singular case AR processes consist of a linearly regular and a linearly singular component. The corresponding Yul...

Transfer functions of linear, time-invariant finite-dimensional systems with more outputs than inputs, as arise in factor analysis (for example in econometrics), have, for state-variable descriptions with generic entries in the relevant matrices, no finite zeros. This paper gives a number of characterizations of such systems (and indeed square disc...

We consider generalized linear dynamic factor models. These models have been developed recently and they are used for high dimensional time series in order to overcome the “curse of dimensionality”. We present a structure theory with emphasis on the zeroless case, which is generic in the setting considered. Accordingly the latent variables are mode...

In this technical note, a framework for designing specially structured input sequences for non-parametric nonlinear system identification is presented so that interaction terms which describe interactions among variables can be identified separately. In a sense, the approach decomposes a general difficult nonlinear identification problem into a num...

1 Abstract In this paper, we extend Bai and Perron's (1998, Econometrica, pp.

This paper deals with autoregressive models of singular spectra. The starting point is the assumption that there is available a transfer function matrix W(q) expressible in the form D^-1(q)B for some tall constant matrix B of full column rank and with the determinantal zeros of D(q) all stable. It is shown that, even if this matrix fracti...

In factor analysis, which is used for example in econometrics, by definition the number of latent variables has to exceed the number of factor variables. The associated transfer function matrix has more rows than columns, and when the factor variables are independent zero mean white noise sequences and the transfer function matrix is stable, then t...

In this paper we assess a dependency measure for multivariate time series termed Extrinsic-to-Intrinsic-Power-Ratio (EIPR) using two different signal models. In a comparison with Partial Directed Coherence (PDC) we show that both measures correctly identify imposed couplings, but that limitations of the PDC do not affect EIPR. Moreover, EIPR is suc...

A condensed presentation of linear multivariate time series models, their identification and their use for forecasting is given. General stationary processes, ARMA and state space systems and linear dynamic factor models are described.

The aim of this contribution is to describe main features in the development of system identification, in the sense of modelling from time series data. Given the restrictions in space, such an effort is necessarely fragmentary. Clearly, subjective judgements cannot be avoided. System identification has been developed in a number of different scient...

In this paper, a framework for selecting input sequences is presented for non-parametric nonlinear system identification so that interaction terms can be identified separably. In a sense, the approach decomposes a general difficult high dimensional nonlinear identification problem into a number of problems that are lower dimensionable. Correspondin...

In this contribution we present a structure theory for generalized linear dynamic factor models. Generalized dynamic factor models have been proposed approximately a decade ago for modeling of high dimensional time series where the cross sectional dimension is of the same order of magnitude as the sample size. In these models the classical assumpti...

System identification is concerned with obtaining good models from data, i.e. with data driven modeling. In this contribution the aim is to explain and discuss ideas, general approaches and theories underlying identification of linear systems. Identification of linear systems is a nonlinear problem and is “prototypical” also for many parts of ident...

Factor models are used to condense high dimensional data consisting of many vari-ables into a much smaller number of factors. Here we present an introductory survey to factor models for time series, where the factors represent the comovement between the single time series. Principal component analysis, linear dynamic factor models with idiosyncrati...

This contribution is concerned with system identification, i.e., with data-driven modeling, for multivariate time series. Linear dynamic models in the framework of stationary processes are considered. After an introduction to stationary processes, two topics are treated: The first is identification of multivariate state space- and ARMA(X) systems,...

Time series analysis is concerned with the systematic approaches to extract information from time series, i.e. from observations ordered in time. Unlike in classical statistics of independent and identically distributed observations, not only the values of the observations, but also their ordering in time may contain information. Main questions in...

System identification is concerned with finding a good model from, in general, noisy data, i.e. with data driven modeling. Often the task of identification is so complex that it cannot be performed in a naive way with the naked eye. In addition many identification problems share common features. For these reasons methods and theories have been deve...

A data-driven approach for forecasting returns of asset prices is introduced. Special emphasis is given to data-driven specification and to dimension reduction. Specification is performed by a modified AIC, BIC-based An-algorithm. Quasi-static principal component analysis, quasi-static factor models with idiosyncratic errors and reduced rank regres...

In this paper we study a novel parametrization for state-space systems, namely separable least squares data driven local coordinates (slsDDLC). The parametrization by slsDDLC has recently been successfully applied to maximum likelihood estimation of linear dynamic systems. In a simulation study, the use of slsDDLC has led to numerical advantages in...

A new approach to the question of parametrizing state-space systems is considered. The approach consists of using input-normal state-space representations. These representations are unique up to an isometric state isomorphism. By decomposing the tangent space of the set of normalized controllable matrix pairs into the tangent space of the equivalen...

Apart from traditional identifiability analysis, questions of parameterization do not attain much attention in econometrics. In the linear dynamic case a major reason for this fact seems to be that mainly AR(X) models are used, where parameterization problems are simple. However, for ARMA(X) and state-space models, parameterization issues are impor...

The analysis of multivariate time series is an important issue in many research areas, such as economics, finance, signal processing and medicine. Multivariate time series are modeled jointly when the relation between the single time series or comovements are important. In general, the number of free parameters, which is a measure of the complexity...

Zeitlich ablaufende zufällige Vorgänge können durch stochastische Prozesse modelliert werden, insbesondere ist es in diesem Rahmen möglich, UnsicherheitüberUnsicherheit¨Unsicherheitüber die Zukunft zu beschreiben. Für stationäre Prozesse wurde bereits vor ca. 70 Jahren eine elegante Prognosetheo-rie von Kolmogorov [35] und Wiener [59] entwickelt. E...

In this paper we introduce two variants of a new parametrization for state–space systems which we will both call separable least squares data driven local co-ordinates (slsDDLC). SlsDDLC is obtained by modifying the parametrization by data driven local co-ordinates (DDLC). These modifications lead to analogous parametrizations, and we show how they...

In this paper, we study a novel parametrization for state-space systems, namely data driven local coordinates (DDLC) which have recently been introduced and applied. Even though DDLC has meanwhile become the default parametrization used in the system identification toolbox of the software package MATLAB, an analysis of properties of DDLC, which are...

deterministic interpretation of the Kalman #ltering formulas is given, using theprinc#RB of least squares estimation. The observed signal and the to-be-estimated signal are modeled as being generated as outputs of a #nite-dimensional linear system driven by an input disturbanc, Postulating that the observed signal is generated by the inputdisturban...

Der Aufsatz bietet eine Zusammenfassung der theoretischen Grundlagen der linearen Kleinst-Quadrate-Prognose im Kontext von stationären Prozessen, insbesondere im Zusammenhang von ARMA bzw. ARMAX Systemen. In einem ersten Schritt wird das Prognoseproblem unter der Voraussetzung, dass die zweiten Momente bekannt sind, behandelt. Da diese jedoch meist...

We describe a novel approach, called data driven local coordinates (DDLC), for parametrizing linear systems in state space form, and we analyze some of its properties which are relevant for, e.g., maximum likelihood estimation. In addition we describe how this idea can be used for a concentrated likelihood function, obtained by a least squares type...

In this paper we consider identification of static balanced flow systems. Static balanced flow systems are characterised by balancing equations and other physical laws governing the systems. These equations are used for improving estimates of flows and transfer coefficients, and we examine the structure of the equations in the case where in additio...

In this paper, the parametrization of state-space systems by data driven local coordinates as introduced by (McKelvey et al., 2003) is modified. This modification leads to an alternative analogous parametrization which can be used for a suitable concentrated likelihood-type criterion function, where the concentration step can be done by a generaliz...

Certain topological and geometrical properties of data driven local coordinates (DDLC) for state-space systems as introduced in (Wolodkin et al., 1997) and (McKelvey and Helmersson, 1999) are derived. First the special case of SISO systems with McMillan degree n ¥ 1 is discussed in order to provide some insights into the geometry of the DDLC constr...

This is the third supplementary volume to Kluwer's highly acclaimed twelve-volume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This...

This paper is concerned with the question of continuity of the mapping from observed time series to models. The behavioral framework is adopted to formalize a model identification problem in which the observed time series is decomposed into a part explained by a model and a remaining part which is ascribed to noise. The misfit between data and mode...