Empirical mode decomposition: a novel technique for the study of tremor time series

Tremor is a clinical feature characterized by oscillations of a part of the body. The detection and study of tremor is an important step in investigations seeking to explain underlying control strategies of the central nervous system under natural (or physiological) and pathological conditions. It is well established that tremorous activity is composed of deterministic and stochastic components. For this reason, the use of digital signal processing techniques (DSP) which take into account the nonlinearity and nonstationarity of such signals may bring new information into the signal analysis which is often obscured by traditional linear techniques (e.g. Fourier analysis). In this context, this paper introduces the application of the empirical mode decomposition (EMD) and Hilbert spectrum (HS), which are relatively new DSP techniques for the analysis of nonlinear and nonstationary time-series, for the study of tremor. Our results, obtained from the analysis of experimental signals collected from 31 patients with different neurological conditions, showed that the EMD could automatically decompose acquired signals into basic components, called intrinsic mode functions (IMFs), representing tremorous and voluntary activity. The identification of a physical meaning for IMFs in the context of tremor analysis suggests an alternative and new way of detecting tremorous activity. These results may be relevant for those applications requiring automatic detection of tremor. Furthermore, the energy of IMFs was visualized as a function of time and frequency by means of the HS. This analysis showed that the variation of energy of tremorous and voluntary activity could be distinguished and characterized on the HS. Such results may be relevant for those applications aiming to identify neurological disorders. In general, both the HS and EMD demonstrated to be very useful to perform objective analysis of any kind of tremor and can therefore be potentially used to perform functional assessment.

Bayesian model averaging and identification of structural breaks in time series

Bayesian Model Averaging (BMA) is used for testing for multiple break points in univariate series using conjugate normal-gamma priors. This approach can test for the number of structural breaks and produce posterior probabilities for a break at each point in time. Results are averaged over specifications including: stationary; stationary around trend and unit root models, each containing different types and number of breaks and different lag lengths. The procedures are used to test for structural breaks on 14 annual macroeconomic series and 11 natural resource price series. The results indicate that there are structural breaks in all of the natural resource series and most of the macroeconomic series. Many of the series had multiple breaks. Our findings regarding the existence of unit roots, having allowed for structural breaks in the data, are largely consistent with previous work.

Periodic time series modeling of environmental proxy records with guaranteed positive growth rate estimation

Identifying a periodic time-series model from environmental records, without imposing the positivity of the growth rate, does not necessarily respect the time order of the data observations. Consequently, subsequent observations, sampled in the environmental archive, can be inversed on the time axis, resulting in a non-physical signal model. In this paper an optimization technique with linear constraints on the signal model parameters is proposed that prevents time inversions. The activation conditions for this constrained optimization are based upon the physical constraint of the growth rate, namely, that it cannot take values smaller than zero. The actual constraints are defined for polynomials and first-order splines as basis functions for the nonlinear contribution in the distance-time relationship. The method is compared with an existing method that eliminates the time inversions, and its noise sensitivity is tested by means of Monte Carlo simulations. Finally, the usefulness of the method is demonstrated on the measurements of the vessel density, in a mangrove tree, Rhizophora mucronata, and the measurement of Mg/Ca ratios, in a bivalve, Mytilus trossulus.

Spatial disaggregation and intensity correction of TRMM-based rainfall time series for hydrological applications in dryland catchments

A novel approach is presented for combining spatial and temporal detail from newly available TRMM-based data sets to derive hourly rainfall intensities at 1-km spatial resolution for hydrological modelling applications. Time series of rainfall intensities derived from 3-hourly 0.25° TRMM 3B42 data are merged with a 1-km gridded rainfall climatology based on TRMM 2B31 data to account for the sub-grid spatial distribution of rainfall intensities within coarse-scale 0.25° grid cells. The method is implemented for two dryland catchments in Tunisia and Senegal, and validated against gauge data. The outcomes of the validation show that the spatially disaggregated and intensity corrected TRMM time series more closely approximate ground-based measurements than non-corrected data. The method introduced here enables the generation of rainfall intensity time series with realistic temporal and spatial detail for dynamic modelling of runoff and infiltration processes that are especially important to water resource management in arid regions.

"Oft expectation fails": a time-series analysis of construction starts in the London office market

Expectations of future market conditions are generally acknowledged to be crucial for the development decision and hence for shaping the built environment. This empirical study of the Central London office market from 1987 to 2009 tests for evidence of adaptive and naive expectations. Applying VAR models and a recursive OLS regression with one-step forecasts, we find evidence of adaptive and naïve, rather than rational expectations of developers. Although the magnitude of the errors and the length of time lags vary over time and development cycles, the results confirm that developers’ decisions are explained to a large extent by contemporaneous and past conditions in both London submarkets. The corollary of this finding is that developers may be able to generate excess profits by exploiting market inefficiencies but this may be hindered in practice by the long periods necessary for planning and construction of the asset. More generally, the results of this study suggest that real estate cycles are largely generated endogenously rather than being the result of unexpected exogenous shocks.

EMD: A novel technique for the study of tremor time series

This paper introduces the Hilbert Analysis (HA), which is a novel digital signal processing technique, for the investigation of tremor. The HA is formed by two complementary tools, i.e. the Empirical Mode Decomposition (EMD) and the Hilbert Spectrum (HS). In this work we show that the EMD can automatically detect and isolate tremulous and voluntary movements from experimental signals collected from 31 patients with different conditions. Our results also suggest that the tremor may be described by a new class of mathematical functions defined in the HA framework. In a further study, the HS was employed for visualization of the energy activities of signals. This tool introduces the concept of instantaneous frequency in the field of tremor. In addition, it could provide, in a time-frequency-energy plot, a clear visualization of local activities of tremor energy over the time. The HA demonstrated to be very useful to perform objective measurements of any kind of tremor and can therefore be used to perform functional assessment.

Application of EMD as a novel technique for the study of tremor time series

This paper introduces the Hilbert Analysis (HA), which is a novel digital signal processing technique, for the investigation of tremor. The HA is formed by two complementary tools, i.e. the Empirical Mode Decomposition (EMD) and the Hilbert Spectrum (HS). In this work we show that the EMD can automatically detect and isolate tremulous and voluntary movements from experimental signals collected from 31 patients with different conditions. Our results also suggest that the tremor may be described by a new class of mathematical functions defined in the HA framework. In a further study, the HS was employed for visualization of the energy activities of signals. This tool introduces the concept of instantaneous frequency in the field of tremor. In addition, it could provide, in a time-frequency energy plot, a clear visualization of local activities of tremor energy over the time. The HA demonstrated to be very useful to perform objective measurements of any kind of tremor and can therefore be used to perform functional assessment.

Reconstruction of gusty wind speed time series from autonomous data logger records

The collection of wind speed time series by means of digital data loggers occurs in many domains, including civil engineering, environmental sciences and wind turbine technology. Since averaging intervals are often significantly larger than typical system time scales, the information lost has to be recovered in order to reconstruct the true dynamics of the system. In the present work we present a simple algorithm capable of generating a real-time wind speed time series from data logger records containing the average, maximum, and minimum values of the wind speed in a fixed interval, as well as the standard deviation. The signal is generated from a generalized random Fourier series. The spectrum can be matched to any desired theoretical or measured frequency distribution. Extreme values are specified through a postprocessing step based on the concept of constrained simulation. Applications of the algorithm to 10-min wind speed records logged at a test site at 60 m height above the ground show that the recorded 10-min values can be reproduced by the simulated time series to a high degree of accuracy.

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.

Decline and recovery of total column ozone using a multimodel time series analysis

Simulations of 15 coupled chemistry climate models, for the period 1960–2100, are presented. The models include a detailed stratosphere, as well as including a realistic representation of the tropospheric climate. The simulations assume a consistent set of changing greenhouse gas concentrations, as well as temporally varying chlorofluorocarbon concentrations in accordance with observations for the past and expectations for the future. The ozone results are analyzed using a nonparametric additive statistical model. Comparisons are made with observations for the recent past, and the recovery of ozone, indicated by a return to 1960 and 1980 values, is investigated as a function of latitude. Although chlorine amounts are simulated to return to 1980 values by about 2050, with only weak latitudinal variations, column ozone amounts recover at different rates due to the influence of greenhouse gas changes. In the tropics, simulated peak ozone amounts occur by about 2050 and thereafter total ozone column declines. Consequently, simulated ozone does not recover to values which existed prior to the early 1980s. The results also show a distinct hemispheric asymmetry, with recovery to 1980 values in the Northern Hemisphere extratropics ahead of the chlorine return by about 20 years. In the Southern Hemisphere midlatitudes, ozone is simulated to return to 1980 levels only 10 years ahead of chlorine. In the Antarctic, annually averaged ozone recovers at about the same rate as chlorine in high latitudes and hence does not return to 1960s values until the last decade of the simulations.

A time-series method to identify and correct range sidelobes in meteorological radar data

The use of pulse compression techniques to improve the sensitivity of meteorological radars has become increasingly common in recent years. An unavoidable side-effect of such techniques is the formation of ‘range sidelobes’ which lead to spreading of information across several range gates. These artefacts are particularly troublesome in regions where there is a sharp gradient in the power backscattered to the antenna as a function of range. In this article we present a simple method for identifying and correcting range sidelobe artefacts. We make use of the fact that meteorological targets produce an echo which fluctuates at random, and that this echo, like a fingerprint, is unique to each range gate. By cross-correlating the echo time series from pairs of gates therefore we can identify whether information from one gate has spread into another, and hence flag regions of contamination. In addition we show that the correlation coefficients contain quantitative information about the fraction of power leaked from one range gate to another, and we propose a simple algorithm to correct the corrupted reflectivity profile.