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The purpose of this paper is to demonstrate new properties of continuous‐ and discrete‐time dynamical systems.

First, definitions of two types of spatial symmetry are introduced. These are used as definitions, which, along with existing knowledge show that it is possible to identify properties of dynamical systems that were previously unknown.

The main result of the paper is a new theorem regarding new properties of continuous‐ and discrete‐time dynamical systems.

The present study provides a starting point for further research on the differences between continuous‐ and discrete‐time dynamical systems. This work builds on the definition of spatial symmetry.

The theorem proved in this paper and the new properties of dynamical systems can be used to introduce new methods of approximating continuous‐time dynamical systems by discrete‐time dynamical systems and vice versa. Such approaches can also be helpful in constructing chaotic sources to model noise.

This paper offers contributions to the broader discussion of differences between continuous‐ and discrete‐time dynamical systems. In particular, the paper supports the statement that many discrete‐time processes cannot be embedded into continuous ones.

The topic of volatility measurement and estimation is central to financial and more generally time-series econometrics. In this chapter, we begin by surveying models of volatility, both discrete and continuous, and then we summarize some selected empirical findings from the literature. In particular, in the first sections of this chapter, we discuss important developments in volatility models, with focus on time-varying and stochastic volatility as well as nonparametric volatility estimation. The models discussed share the common feature that volatilities are unobserved and belong to the class of missing variables. We then provide empirical evidence on “small” and “large” jumps from the perspective of their contribution to overall realized variation, using high-frequency price return data on 25 stocks in the DOW 30. Our “small” and “large” jump variations are constructed at three truncation levels, using extant methodology of Barndorff-Nielsen and Shephard (2006), Andersen, Bollerslev, and Diebold (2007), and Aït-Sahalia and Jacod (2009a, 2009b, 2009c). Evidence of jumps is found in around 22.8% of the days during the 1993–2000 period, much higher than the corresponding figure of 9.4% during the 2001–2008 period. Although the overall role of jumps is lessening, the role of large jumps has not decreased, and indeed, the relative role of large jumps, as a proportion of overall jumps, has actually increased in the 2000s.

This paper aims to develop a methodology to accurately and timely measure movements in housing markets by constructing a continuously estimated house price index.

The continuous index, which is extracted from an additive model that includes the temporal and the locational effects as smooth functions, can be interpreted as an extension of the classical hedonic time-dummy method. The methodology is applied to housing sales from Sydney, Australia, between 2001 and 2011, and compared to three types of discrete indexes.

Discrete indexes turn out to approach the continuously estimated index with decreasing period lengths but eventually become wiggly and unreliable because of fewer observations per period. The continuous index, in contrast, is stable, has favourable robustness properties and is more objective in several ways.

The resulting index tracks movements in the housing market precisely and in “real-time” and is hence suited for monitoring and assessing housing markets. Because turbulence in housing markets is often a harbinger of financial crises, such monitoring tools support policymakers and investors in tailoring their decisions and reactions. Additionally, the index can be evaluated arbitrarily frequently and therefore is well suited for use in property derivatives.

The purpose of this paper is to improve the transient response and the inter‐sample behavior of a model reference adaptive control system by an appropriate selection of the fractional order hold (FROH) gain β and the multirate gains used in the control reconstruction signal through a fully freely chosen reference model even when the continuous plant possesses unstable zeros.

A multiestimation adaptive control scheme for linear time‐invariant continuous‐time plant with unknown parameters is presented. The set of discrete adaptive models is calculated from a different combination of the correcting gain β in a FROH and the set of gains to reconstruct the plant input under multirate sampling with fast input sampling. Then the scheme selects online the model with the best continuous‐time tracking performance which includes a measure of the inter‐sample ripple, which is improved. The estimated discrete unstable zeros are avoided through an appropriate design of the multirate gains so that the reference model might be freely chosen with no constraints on potential unstable zeros.

The scheme is able to select online the discretization model with the best continuous‐time tracking performance without an appropriate initialization.

The switching mechanism among the different models should maintain in operation the active discretization model at least for a minimum residence time in order to guarantee closed‐loop stability. The inter‐sample behavior is improved, but it is not always completely removed.

The transient response and the inter‐sample behavior are improved by using this multiestimation‐based discrete controller compared with a single estimation‐based one. The implementation of discrete controllers makes it easier and cheaper to implement and also more reliable than continuous‐time controllers.

The main innovation of the paper compared with previous background work is that the reference output is supplied by a stable continuous transfer function. Then the scheme is able to partly regulate the continuous‐time tracking error while the controller is essentially discrete‐time and operated by a FROH in general.

In this chapter, the authors consider the role of time for research in occupational stress and well-being. First, temporal issues in studying occupational health longitudinally, focusing in particular on the role of time lags and their implications for observed results (e.g., effect detectability), analyses (e.g., handling unequal durations between measurement occasions), and interpretation (e.g., result generalizability, theoretical revision) were discussed. Then, time-based assumptions when modeling lagged effects in occupational health research, providing a focused review of how research has handled (or ignored) these assumptions in the past, and the relative benefits and drawbacks of these approaches were discussed. Finally, recommendations for readers, an accessible tutorial (including example data and code), and discussion of a new structural equation modeling technique, continuous time structural equation modeling, that can “handle” time in longitudinal studies of occupational health were provided.

To provide an overview of how a number of frequently used smoothing‐based forecasting techniques can be modelled for use in dynamic analysis of production‐inventory systems.

The smoothing techniques are modelled using transfer functions and state space representation. Basic control theory is used for analysing the dynamic properties.

A set of expressions are derived for the smoothing techniques and dynamic properties are identified.

Dynamic properties are important in many applications. It is shown that the different smoothing techniques can have very different influences on the dynamic behaviour and therefore should be considered as a factor when smoothing parameters are decided on.

Dynamic behaviour of production‐inventory systems can be analysed using control theory based on, e.g. transfer functions or state space models. In this paper a set of models for five common smoothing techniques are analysed and their respective dynamic properties are highlighted.

The traditional audit paradigm is outdated in the real time economy. Innovation of the traditional audit process is necessary to support real time assurance. Practitioners and academics are exploring continuous auditing as a potential successor to the traditional audit paradigm. Using technology and automation, continuous auditing methodology enhances the efficiency and effectiveness of the audit process to support real time assurance. This paper defines how continuous auditing methodology introduces innovation to practice in seven dimensions and proposes a four-stage paradigm to advance future research. In addition, we formulate a set of methodological propositions concerning the future of assurance for practitioners and academic researchers.

This study proposes targeted modernization of the Department of Defense (DoD's) Joint Forces Ammunition Logistics information system by implementing the optimized innovative information technology open architecture design and integrating Radio Frequency Identification Device data technologies and real-time optimization and control mechanisms as the critical technology components of the solution. The innovative information technology, which pursues the focused logistics, will be deployed in 36 months at the estimated cost of $568 million in constant dollars. We estimate that the Systems, Applications, Products (SAP)-based enterprise integration solution that the Army currently pursues will cost another $1.5 billion through the year 2014; however, it is unlikely to deliver the intended technical capabilities.

We investigate the return and volatility spillovers from major UK banks to Financial Times Stock Exchange 100 (FTSE 100) index using Gaussian estimation and continuous time models as well as discrete time multivariate GARCH (MGARCH) modelling approaches. Using daily, weekly and monthly data over the period December 1999–December 2010, which includes the recent 2007–2009 global financial crisis, empirical estimates of uni- and/or bi-directional return and volatility spillovers are provided. The bivariate MGARCH results reveal strong return spillovers from the FTSE to the banks, and no return spillover from the latter to the FTSE. Nevertheless, strong bi-directional volatility transmission is verified. The continuous time analysis provides mixed evidence of feedback effects over the different models.

The purpose of this paper is to consider a discrete‐time, Markov, regime‐switching, affine term‐structure model for valuing bonds and other interest rate securities. The proposed model incorporates the impact of structural changes in (macro)‐economic conditions on interest‐rate dynamics. The market in the proposed model is, in general, incomplete. A modified version of the Esscher transform, namely, a double Esscher transform, is used to specify a price kernel so that both market and economic risks are taken into account.

The market in the proposed model is, in general, incomplete. A modified version of the Esscher transform, namely, a double Esscher transform, is used to specify a price kernel so that both market and economic risks are taken into account.

The authors derive a simple way to give exponential affine forms of bond prices using backward induction. The authors also consider a continuous‐time extension of the model and derive exponential affine forms of bond prices using the concept of stochastic flows.

The methods and results presented in the paper are new.