Structural Time Series Models and the Kalman Filter: a concise review

The continued increase in availability of economic data in recent years and, more impor- tantly, the possibility to construct larger frequency time series, have fostered the use (and development) of statistical and econometric techniques to treat them more accurately. This paper presents an exposition of structural time series models by which a time series can be decomposed as the sum of a trend, seasonal and irregular components. In addition to a detailled analysis of univariate speci?cations we also address the SUTSE multivariate case and the issue of cointegration. Finally, the recursive estimation and smoothing by means of the Kalman ?lter algorithm is described taking into account its di¤erent stages, from initialisation to parameter?s estimation. JEL codes: C10, C22, C32

Near-Rational Exuberance

We study how the use of judgement or “add-factors” in macroeconomic forecasting may disturb the set of equilibrium outcomes when agents learn using recursive methods. We isolate conditions under which new phenomena, which we call exuberance equilibria, can exist in standard macroeconomic environments. Examples include a simple asset pricing model and the New Keynesian monetary policy framework. Inclusion of judgement in forecasts can lead to self-fulfilling fluctuations, but without the requirement that the underlying rational expectations equilibrium is locally indeterminate. We suggest ways in which policymakers might avoid unintended outcomes by adjusting policy to minimize the risk of exuberance equilibria

Near-rational exuberance

We study how the use of judgement or "add-factors" in macroeconomic forecasting may disturb the set of equilibrium outcomes when agents learn using recursive methods. We isolate conditions under which new phenomena, which we call exuberance equilibria, can exist in standard macroeconomic environments. Examples include a simple asset pricing model and the New Keynesian monetary policy framework. Inclusion of judgement in forecasts can lead to self-fulfilling fluctuations, but without the requirement that the underlying rational expectations equilibrium is locally indeterminate. We suggest ways in which policymakers might avoid unintended outcomes by adjusting policy to minimize the risk of exuberance equilibria.Monetary policy ; Macroeconomics

Forecasting VARMA processes using VAR models and subspace-based state space models

VAR modelling is a frequent technique in econometrics for linear processes. VAR modelling offers some desirable features such as relatively simple procedures for model specification (order selection) and the possibility of obtaining quick non-iterative maximum likelihood estimates of the system parameters. However, if the process under study follows a finite-order VARMA structure, it cannot be equivalently represented by any finite-order VAR model. On the other hand, a finite-order state space model can represent a finite-order VARMA process exactly, and, for state-space modelling, subspace algorithms allow for quick and non-iterative estimates of the system parameters, as well as for simple specification procedures. Given the previous facts, we check in this paper whether subspace-based state space models provide better forecasts than VAR models when working with VARMA data generating processes. In a simulation study we generate samples from different VARMA data generating processes, obtain VAR-based and state-space-based models for each generating process and compare the predictive power of the obtained models. Different specification and estimation algorithms are considered; in particular, within the subspace family, the CCA (Canonical Correlation Analysis) algorithm is the selected option to obtain state-space models. Our results indicate that when the MA parameter of an ARMA process is close to 1, the CCA state space models are likely to provide better forecasts than the AR models. We also conduct a practical comparison (for two cointegrated economic time series) of the predictive power of Johansen restricted-VAR (VEC) models with the predictive power of state space models obtained by the CCA subspace algorithm, including a density forecasting analysis.subspace algorithms; VAR; forecasting; cointegration; Johansen; CCA

On the identification and parametric modelling of offshore dynamic systems

This thesis describes an investigation into the analysis methods arising from identification aspects of the theory of dynamic systems with application to full-scale offshore monitoring and marine environmental data including target spectra. Based on the input and output of the dynamic system, the System Identification (SI) techniques are used first to identify the model type and then to estimate the model parameters. This work also gives an understanding of how to obtain a meaningful matching between the target (power spectra or time series data sets) and SI models with minimal loss of information. The SI techniques, namely. Autoregressive (AR), Moving Average (MA) and Autoregressive Moving Average (ARMA) algorithms are formulated in the frequency domain and also in the time domain. The above models can only be economically applicable provided the model order is low in the sense that it is computationally efficient and the lower order model can most appropriately represent the offshore time series records or the target spectra. For this purpose, the orders of the above SI models are optimally selected by Least Squares Error, Akaike Information Criterion and Minimum Description Length methods. A novel model order reduction technique is established to obtain the reduced order ARMA model. At first estimations of higher order AR coefficients are determined using modified Yule-Walker equations and then the first and second order real modes and their energies are determined. Considering only the higher energy modes, the AR part of the reduced order ARMA model is obtained. The MA part of the reduced order ARMA model is determined based on partial fraction and recursive methods. This model order reduction technique can remove the spurious noise modes which are present in the time series data. Therefore, firstly using an initial optimal AR model and then a model order reduction technique, the time series data or target spectrum can be reduced to a few parameters which are the coefficients of the reduced order ARMA model. The above univariate SI models and model order reduction techniques are successfully applied for marine environmental and structural monitoring data, including ocean waves, semi-submersible heave motions, monohull crane vessel motions and theoretical (Pierson- Moskowitz and JONSWAP) spectra. Univariate SI models are developed based on the assumption that the offshore dynamic systems are stationary random processes. For nonstationary processes, such as, measurements of combined sea waves and swells, or coupled responses of offshore structures with short period and long period motions, the time series are modelled by the Autoregressive Integrated Moving Average algorithms. The multivariate autoregressive (MAR) algorithm is developed to reduce the time series wave data sets into MAR model parameters. The MAR algorithms are described by feedback weighting coefficients matrices and the driving noise vector. These are obtained based on the estimation of the partial correlation of the time series data sets. Here the appropriate model order is selected based on auto and cross correlations and multivariate Akaike information criterion methods. These algorithms are applied to estimate MAR power spectral density spectra and then phase and coherence spectra of two time series wave data sets collected at a North Sea location. The estimation of MAR power spectral densities are compared with spectral estimates computed from a two variable fast Fourier transform, which show good agreement

Accurate portfolio risk-return structure modelling

Markowitz's modem portfolio theory has played a vital role in investment portfolio management, which is constantly pushing the development on volatility models. Particularly, the stochastic volatility model which reveals the dynamics of conditional volatility. Financial time series and volatility models has become one of the hot spots in operations research. In this thesis, one of the areas we explore is the theoretical formulation of the optimal portfolio selection problem under Ito calculus framework. Particularly, a stochastic variation calculus problem, i.e., seeking the optimal stochastic volatility diffusion family for facilitating the best portfolio selection identified under the continuous-time stochastic optimal control theoretical settings. One of the properties this study examines is the left-shifting role of the GARCH(1, 1) (General Autoregressive Conditional Heteroskedastic) model's efficient frontier. This study considers many instances where the left shifting superior behaviour of the GARCH(1, 1) is observed. One such instance is when GARCH(1, 1) is compared within the volatility modelling extensions of the GARCH environ in a single index framework. This study will demonstrate the persistence of the superiority of the G ARCH ( 1, 1) frontier within a multiple and single index context of modem portfolio theory. Many portfolio optimization models are investigated, particularly the Markowitz model and the Sharpe Multiple and Single index models. Includes bibliographical references (p. 313-323)

Comparative review of methods for stability monitoring in electrical power systems and vibrating structures

This study provides a review of methods used for stability monitoring in two different fields, electrical power systems and vibration analysis, with the aim of increasing awareness of and highlighting opportunities for cross-fertilisation. The nature of the problems that require stability monitoring in both fields are discussed here as well as the approaches that have been taken. The review of power systems methods is presented in two parts: methods for ambient or normal operation and methods for transient or post-fault operation. Similarly, the review of methods for vibration analysis is presented in two parts: methods for stationary or linear time-invariant data and methods for non-stationary or non-linear time-variant data. Some observations and comments are made regarding methods that have already been applied in both fields including recommendations for the use of different sets of algorithms that have not been utilised to date. Additionally, methods that have been applied to vibration analysis and have potential for power systems stability monitoring are discussed and recommended. � 2010 The Institution of Engineering and Technology

Estimation of Autoregressive Parameters from Noisy Observations Using Iterated Covariance Updates

Estimating the parameters of the autoregressive (AR) random process is a problem that has been well-studied. In many applications, only noisy measurements of AR process are available. The effect of the additive noise is that the system can be modeled as an AR model with colored noise, even when the measurement noise is white, where the correlation matrix depends on the AR parameters. Because of the correlation, it is expedient to compute using multiple stacked observations. Performing a weighted least-squares estimation of the AR parameters using an inverse covariance weighting can provide significantly better parameter estimates, with improvement increasing with the stack depth. The estimation algorithm is essentially a vector RLS adaptive filter, with time-varying covariance matrix. Different ways of estimating the unknown covariance are presented, as well as a method to estimate the variances of the AR and observation noise. The notation is extended to vector autoregressive (VAR) processes. Simulation results demonstrate performance improvements in coefficient error and in spectrum estimation

Dynamic modeling of mean-reverting spreads for statistical arbitrage

Statistical arbitrage strategies, such as pairs trading and its generalizations, rely on the construction of mean-reverting spreads enjoying a certain degree of predictability. Gaussian linear state-space processes have recently been proposed as a model for such spreads under the assumption that the observed process is a noisy realization of some hidden states. Real-time estimation of the unobserved spread process can reveal temporary market inefficiencies which can then be exploited to generate excess returns. Building on previous work, we embrace the state-space framework for modeling spread processes and extend this methodology along three different directions. First, we introduce time-dependency in the model parameters, which allows for quick adaptation to changes in the data generating process. Second, we provide an on-line estimation algorithm that can be constantly run in real-time. Being computationally fast, the algorithm is particularly suitable for building aggressive trading strategies based on high-frequency data and may be used as a monitoring device for mean-reversion. Finally, our framework naturally provides informative uncertainty measures of all the estimated parameters. Experimental results based on Monte Carlo simulations and historical equity data are discussed, including a co-integration relationship involving two exchange-traded funds.Comment: 34 pages, 6 figures. Submitte