Modelling financial time series with switching state space models

The deficiencies of stationary models applied to financial time series are well documented. A special form of non-stationarity, where the underlying generator switches between (approximately) stationary regimes, seems particularly appropriate for financial markets. We use a dynamic switching (modelled by a hidden Markov model) combined with a linear dynamical system in a hybrid switching state space model (SSSM) and discuss the practical details of training such models with a variational EM algorithm due to [Ghahramani and Hilton,1998]. The performance of the SSSM is evaluated on several financial data sets and it is shown to improve on a number of existing benchmark methods.

Hidden state models for time series

Amongst all the objectives in the study of time series, uncovering the dynamic law of its generation is probably the most important. When the underlying dynamics are not available, time series modelling consists of developing a model which best explains a sequence of observations. In this thesis, we consider hidden space models for analysing and describing time series. We first provide an introduction to the principal concepts of hidden state models and draw an analogy between hidden Markov models and state space models. Central ideas such as hidden state inference or parameter estimation are reviewed in detail. A key part of multivariate time series analysis is identifying the delay between different variables. We present a novel approach for time delay estimating in a non-stationary environment. The technique makes use of hidden Markov models and we demonstrate its application for estimating a crucial parameter in the oil industry. We then focus on hybrid models that we call dynamical local models. These models combine and generalise hidden Markov models and state space models. Probabilistic inference is unfortunately computationally intractable and we show how to make use of variational techniques for approximating the posterior distribution over the hidden state variables. Experimental simulations on synthetic and real-world data demonstrate the application of dynamical local models for segmenting a time series into regimes and providing predictive distributions.

The Effect of Spatial Scale on Predicting Time Series: A Study on Epidemiological System Identification

A susceptible-infective-recovered (SIR) epidemiological model based on probabilistic cellular automaton (PCA) is employed for simulating the temporal evolution of the registered cases of chickenpox in Arizona, USA, between 1994 and 2004. At each time step, every individual is in one of the states S, I, or R. The parameters of this model are the probabilities of each individual (each cell forming the PCA lattice ) passing from a state to another state. Here, the values of these probabilities are identified by using a genetic algorithm. If nonrealistic values are allowed to the parameters, the predictions present better agreement with the historical series than if they are forced to present realistic values. A discussion about how the size of the PCA lattice affects the quality of the model predictions is presented. Copyright (C) 2009 L. H. A. Monteiro et al.

Relating MODIS vegetation index time-series with structure, light absorption and stem production of fast-growing Eucalyptus plantations

By allowing the estimation of forest structural and biophysical characteristics at different temporal and spatial scales, remote sensing may contribute to our understanding and monitoring of planted forests. Here, we studied 9-year time-series of the Normalized Difference Vegetation Index (NDVI) from the Moderate Resolution Imaging Spectroradiometer (MODIS) on a network of 16 stands in fast-growing Eucalyptus plantations in Sao Paulo State, Brazil. We aimed to examine the relationships between NDVI time-series spanning entire rotations and stand structural characteristics (volume, dominant height, mean annual increment) in these simple forest ecosystems. Our second objective was to examine spatial and temporal variations of light use efficiency for wood production, by comparing time-series of Absorbed Photosynthetically Active Radiation (APAR) with inventory data. Relationships were calibrated between the NDVI and the fractions of intercepted diffuse and direct radiation, using hemispherical photographs taken on the studied stands at two seasons. APAR was calculated from the NDVI time-series using these relationships. Stem volume and dominant height were strongly correlated with summed NDVI values between planting date and inventory date. Stand productivity was correlated with mean NDVI values. APAR during the first 2 years of growth was variable between stands and was well correlated with stem wood production (r(2) = 0.78). In contrast, APAR during the following years was less variable and not significantly correlated with stem biomass increments. Production of wood per unit of absorbed light varied with stand age and with site index. In our study, a better site index was accompanied both by increased APAR during the first 2 years of growth and by higher light use efficiency for stem wood production during the whole rotation. Implications for simple process-based modelling are discussed. (C) 2009 Elsevier B.V. All rights reserved.

Predictability of music descriptor time series and its application to cover song detection

Intuitively, music has both predictable and unpredictable components. In this work we assess this qualitative statement in a quantitative way using common time series models fitted to state-of-the-art music descriptors. These descriptors cover different musical facets and are extracted from a large collection of real audio recordings comprising a variety of musical genres. Our findings show that music descriptor time series exhibit a certain predictability not only for short time intervals, but also for mid-term and relatively long intervals. This fact is observed independently of the descriptor, musical facet and time series model we consider. Moreover, we show that our findings are not only of theoretical relevance but can also have practical impact. To this end we demonstrate that music predictability at relatively long time intervals can be exploited in a real-world application, namely the automatic identification of cover songs (i.e. different renditions or versions of the same musical piece). Importantly, this prediction strategy yields a parameter-free approach for cover song identification that is substantially faster, allows for reduced computational storage and still maintains highly competitive accuracies when compared to state-of-the-art systems.

Estimating Attractor Dimension on the Nonlinear Pendulum Time Series

Chaotic dynamical systems exhibit trajectories in their phase space that converges to a strange attractor. The strangeness of the chaotic attractor is associated with its dimension in which instance it is described by a noninteger dimension. This contribution presents an overview of the main definitions of dimension discussing their evaluation from time series employing the correlation and the generalized dimension. The investigation is applied to the nonlinear pendulum where signals are generated by numerical integration of the mathematical model, selecting a single variable of the system as a time series. In order to simulate experimental data sets, a random noise is introduced in the time series. State space reconstruction and the determination of attractor dimensions are carried out regarding periodic and chaotic signals. Results obtained from time series analyses are compared with a reference value obtained from the analysis of mathematical model, estimating noise sensitivity. This procedure allows one to identify the best techniques to be applied in the analysis of experimental data.

Parameter identification in time series models

Time series analysis can be categorized into three different approaches: classical, Box-Jenkins, and State space. Classical approach makes a basement for the analysis and Box-Jenkins approach is an improvement of the classical approach and deals with stationary time series. State space approach allows time variant factors and covers up a broader area of time series analysis. This thesis focuses on parameter identifiablity of different parameter estimation methods such as LSQ, Yule-Walker, MLE which are used in the above time series analysis approaches. Also the Kalman filter method and smoothing techniques are integrated with the state space approach and MLE method to estimate parameters allowing them to change over time. Parameter estimation is carried out by repeating estimation and integrating with MCMC and inspect how well different estimation methods can identify the optimal model parameters. Identification is performed in probabilistic and general senses and compare the results in order to study and represent identifiability more informative way.

Probabilistic evaluation of time series models : a comparison of several approaches

Several methods are examined which allow to produce forecasts for time series in the form of probability assignments. The necessary concepts are presented, addressing questions such as how to assess the performance of a probabilistic forecast. A particular class of models, cluster weighted models (CWMs), is given particular attention. CWMs, originally proposed for deterministic forecasts, can be employed for probabilistic forecasting with little modification. Two examples are presented. The first involves estimating the state of (numerically simulated) dynamical systems from noise corrupted measurements, a problem also known as filtering. There is an optimal solution to this problem, called the optimal filter, to which the considered time series models are compared. (The optimal filter requires the dynamical equations to be known.) In the second example, we aim at forecasting the chaotic oscillations of an experimental bronze spring system. Both examples demonstrate that the considered time series models, and especially the CWMs, provide useful probabilistic information about the underlying dynamical relations. In particular, they provide more than just an approximation to the conditional mean.

Forecasting economic and financial time series with non-linear models

In this paper we discuss the current state-of-the-art in estimating, evaluating, and selecting among non-linear forecasting models for economic and financial time series. We review theoretical and empirical issues, including predictive density, interval and point evaluation and model selection, loss functions, data-mining, and aggregation. In addition, we argue that although the evidence in favor of constructing forecasts using non-linear models is rather sparse, there is reason to be optimistic. However, much remains to be done. Finally, we outline a variety of topics for future research, and discuss a number of areas which have received considerable attention in the recent literature, but where many questions remain.

Time-series-based maximization of distributed wind power generation integration

Energy policies and technological progress in the development of wind turbines have made wind power the fastest growing renewable power source worldwide. The inherent variability of this resource requires special attention when analyzing the impacts of high penetration on the distribution network. A time-series steady-state analysis is proposed that assesses technical issues such as energy export, losses, and short-circuit levels. A multiobjective programming approach based on the nondominated sorting genetic algorithm (NSGA) is applied in order to find configurations that maximize the integration of distributed wind power generation (DWPG) while satisfying voltage and thermal limits. The approach has been applied to a medium voltage distribution network considering hourly demand and wind profiles for part of the U.K. The Pareto optimal solutions obtained highlight the drawbacks of using a single demand and generation scenario, and indicate the importance of appropriate substation voltage settings for maximizing the connection of MPG.

Evaluation of physiologic complexity in time series using generalized sample entropy and surrogate data analysis

Complexity in time series is an intriguing feature of living dynamical systems, with potential use for identification of system state. Although various methods have been proposed for measuring physiologic complexity, uncorrelated time series are often assigned high values of complexity, errouneously classifying them as a complex physiological signals. Here, we propose and discuss a method for complex system analysis based on generalized statistical formalism and surrogate time series. Sample entropy (SampEn) was rewritten inspired in Tsallis generalized entropy, as function of q parameter (qSampEn). qSDiff curves were calculated, which consist of differences between original and surrogate series qSampEn. We evaluated qSDiff for 125 real heart rate variability (HRV) dynamics, divided into groups of 70 healthy, 44 congestive heart failure (CHF), and 11 atrial fibrillation (AF) subjects, and for simulated series of stochastic and chaotic process. The evaluations showed that, for nonperiodic signals, qSDiff curves have a maximum point (qSDiff(max)) for q not equal 1. Values of q where the maximum point occurs and where qSDiff is zero were also evaluated. Only qSDiff(max) values were capable of distinguish HRV groups (p-values 5.10 x 10(-3); 1.11 x 10(-7), and 5.50 x 10(-7) for healthy vs. CHF, healthy vs. AF, and CHF vs. AF, respectively), consistently with the concept of physiologic complexity, and suggests a potential use for chaotic system analysis. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4758815]

Stochastic simulation of time-series models combined with geostatistics to predict water-table scenarios in a Guarani Aquifer System outcrop area, Brazil

Stochastic methods based on time-series modeling combined with geostatistics can be useful tools to describe the variability of water-table levels in time and space and to account for uncertainty. Monitoring water-level networks can give information about the dynamic of the aquifer domain in both dimensions. Time-series modeling is an elegant way to treat monitoring data without the complexity of physical mechanistic models. Time-series model predictions can be interpolated spatially, with the spatial differences in water-table dynamics determined by the spatial variation in the system properties and the temporal variation driven by the dynamics of the inputs into the system. An integration of stochastic methods is presented, based on time-series modeling and geostatistics as a framework to predict water levels for decision making in groundwater management and land-use planning. The methodology is applied in a case study in a Guarani Aquifer System (GAS) outcrop area located in the southeastern part of Brazil. Communication of results in a clear and understandable form, via simulated scenarios, is discussed as an alternative, when translating scientific knowledge into applications of stochastic hydrogeology in large aquifers with limited monitoring network coverage like the GAS.

Solar-Terrestrial Signal Record in Tree Ring Width Time Series from Brazil

This work investigates the behavior of the sunspot number and Southern Oscillation Index (SOI) signal recorded in the tree ring time series for three different locations in Brazil: Humaita in Amaznia State, Porto Ferreira in So Paulo State, and Passo Fundo in Rio Grande do Sul State, using wavelet and cross-wavelet analysis techniques. The wavelet spectra of tree ring time series showed signs of 11 and 22 years, possibly related to the solar activity, and periods of 2-8 years, possibly related to El Nio events. The cross-wavelet spectra for all tree ring time series from Brazil present a significant response to the 11-year solar cycle in the time interval between 1921 to after 1981. These tree ring time series still have a response to the second harmonic of the solar cycle (5.5 years), but in different time intervals. The cross-wavelet maps also showed that the relationship between the SOI x tree ring time series is more intense, for oscillation in the range of 4-8 years.