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.

Real-time multi-model decadal climate predictions

We present the first climate prediction of the coming decade made with multiple models, initialized with prior observations. This prediction accrues from an international activity to exchange decadal predictions in near real-time, in order to assess differences and similarities, provide a consensus view to prevent over-confidence in forecasts from any single model, and establish current collective capability. We stress that the forecast is experimental, since the skill of the multi-model system is as yet unknown. Nevertheless, the forecast systems used here are based on models that have undergone rigorous evaluation and individually have been evaluated for forecast skill. Moreover, it is important to publish forecasts to enable open evaluation, and to provide a focus on climate change in the coming decade. Initialized forecasts of the year 2011 agree well with observations, with a pattern correlation of 0.62 compared to 0.31 for uninitialized projections. In particular, the forecast correctly predicted La Niña in the Pacific, and warm conditions in the north Atlantic and USA. A similar pattern is predicted for 2012 but with a weaker La Niña. Indices of Atlantic multi-decadal variability and Pacific decadal variability show no signal beyond climatology after 2015, while temperature in the Niño3 region is predicted to warm slightly by about 0.5 °C over the coming decade. However, uncertainties are large for individual years and initialization has little impact beyond the first 4 years in most regions. Relative to uninitialized forecasts, initialized forecasts are significantly warmer in the north Atlantic sub-polar gyre and cooler in the north Pacific throughout the decade. They are also significantly cooler in the global average and over most land and ocean regions out to several years ahead. However, in the absence of volcanic eruptions, global temperature is predicted to continue to rise, with each year from 2013 onwards having a 50 % chance of exceeding the current observed record. Verification of these forecasts will provide an important opportunity to test the performance of models and our understanding and knowledge of the drivers of climate change.

Assessing levels of uncertainty in recent temperature time series

We examine to what degree we can expect to obtain accurate temperature trends for the last two decades near the surface and in the lower troposphere. We compare temperatures obtained from surface observations and radiosondes as well as satellite-based measurements from the Microwave Soundings Units (MSU), which have been adjusted for orbital decay and non-linear instrument-body effects, and reanalyses from the European Centre for Medium-Range Weather Forecasts (ERA) and the National Centre for Environmental Prediction (NCEP). In regions with abundant conventional data coverage, where the MSU has no major influence on the reanalysis, temperature anomalies obtained from microwave sounders, radiosondes and from both reanalyses agree reasonably. Where coverage is insufficient, in particular over the tropical oceans, large differences are found between the MSU and either reanalysis. These differences apparently relate to changes in the satellite data availability and to differing satellite retrieval methodologies, to which both reanalyses are quite sensitive over the oceans. For NCEP, this results from the use of raw radiances directly incorporated into the analysis, which make the reanalysis sensitive to changes in the underlying algorithms, e.g. those introduced in August 1992. For ERA, the bias-correction of the one-dimensional variational analysis may introduce an error when the satellite relative to which the correction is calculated is biased itself or when radiances change on a time scale longer than a couple of months, e.g. due to orbit decay. ERA inhomogeneities are apparent in April 1985, October/November 1986 and April 1989. These dates can be identified with the replacements of satellites. It is possible that a negative bias in the sea surface temperatures (SSTs) used in the reanalyses may have been introduced over the period of the satellite record. This could have resulted from a decrease in the number of ship measurements, a concomitant increase in the importance of satellite-derived SSTs, and a likely cold bias in the latter. Alternately, a warm bias in SSTs could have been caused by an increase in the percentage of buoy measurements (relative to deeper ship intake measurements) in the tropical Pacific. No indications for uncorrected inhomogeneities of land surface temperatures could be found. Near-surface temperatures have biases in the boundary layer in both reanalyses, presumably due to the incorrect treatment of snow cover. The increase of near-surface compared to lower tropospheric temperatures in the last two decades may be due to a combination of several factors, including high-latitude near-surface winter warming due to an enhanced NAO and upper-tropospheric cooling due to stratospheric ozone decrease.

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.

Medieval foreign exchange: a time series analysis

This chapter applies rigorous statistical analysis to existing datasets of medieval exchange rates quoted in merchants’ letters sent from Barcelona, Bruges and Venice between 1380 and 1310, which survive in the archive of Francesco di Marco Datini of Prato. First, it tests the exchange rates for stationarity. Second, it uses regression analysis to examine the seasonality of exchange rates at the three financial centres and compares them against contemporary descriptions by the merchant Giovanni di Antonio da Uzzano. Third, it tests for structural breaks in the exchange rate series.

The cyclical relations between traded property stock prices and aggregate time-series

This paper examines the cyclical regularities of macroeconomic, financial and property market aggregates in relation to the property stock price cycle in the UK. The Hodrick Prescott filter is employed to fit a long-term trend to the raw data, and to derive the short-term cycles of each series. It is found that the cycles of consumer expenditure, total consumption per capita, the dividend yield and the long-term bond yield are moderately correlated, and mainly coincident, with the property price cycle. There is also evidence that the nominal and real Treasury Bill rates and the interest rate spread lead this cycle by one or two quarters, and therefore that these series can be considered leading indicators of property stock prices. This study recommends that macroeconomic and financial variables can provide useful information to explain and potentially to forecast movements of property-backed stock returns in the UK.

Testing for unit roots in bounded time series

Many key economic and financial series are bounded either by construction or through policy controls. Conventional unit root tests are potentially unreliable in the presence of bounds, since they tend to over-reject the null hypothesis of a unit root, even asymptotically. So far, very little work has been undertaken to develop unit root tests which can be applied to bounded time series. In this paper we address this gap in the literature by proposing unit root tests which are valid in the presence of bounds. We present new augmented Dickey–Fuller type tests as well as new versions of the modified ‘M’ tests developed by Ng and Perron [Ng, S., Perron, P., 2001. LAG length selection and the construction of unit root tests with good size and power. Econometrica 69, 1519–1554] and demonstrate how these tests, combined with a simulation-based method to retrieve the relevant critical values, make it possible to control size asymptotically. A Monte Carlo study suggests that the proposed tests perform well in finite samples. Moreover, the tests outperform the Phillips–Perron type tests originally proposed in Cavaliere [Cavaliere, G., 2005. Limited time series with a unit root. Econometric Theory 21, 907–945]. An illustrative application to U.S. interest rate data is provided

Combined use of satellite estimates and rain gauge observations to generate high-quality historical rainfall time series over Ethiopia

Climate data are used in a number of applications including climate risk management and adaptation to climate change. However, the availability of climate data, particularly throughout rural Africa, is very limited. Available weather stations are unevenly distributed and mainly located along main roads in cities and towns. This imposes severe limitations to the availability of climate information and services for the rural community where, arguably, these services are needed most. Weather station data also suffer from gaps in the time series. Satellite proxies, particularly satellite rainfall estimate, have been used as alternatives because of their availability even over remote parts of the world. However, satellite rainfall estimates also suffer from a number of critical shortcomings that include heterogeneous time series, short time period of observation, and poor accuracy particularly at higher temporal and spatial resolutions. An attempt is made here to alleviate these problems by combining station measurements with the complete spatial coverage of satellite rainfall estimates. Rain gauge observations are merged with a locally calibrated version of the TAMSAT satellite rainfall estimates to produce over 30-years (1983-todate) of rainfall estimates over Ethiopia at a spatial resolution of 10 km and a ten-daily time scale. This involves quality control of rain gauge data, generating locally calibrated version of the TAMSAT rainfall estimates, and combining these with rain gauge observations from national station network. The infrared-only satellite rainfall estimates produced using a relatively simple TAMSAT algorithm performed as good as or even better than other satellite rainfall products that use passive microwave inputs and more sophisticated algorithms. There is no substantial difference between the gridded-gauge and combined gauge-satellite products over the test area in Ethiopia having a dense station network; however, the combined product exhibits better quality over parts of the country where stations are sparsely distributed.

The 30-year TAMSAT African rainfall climatology and time-series (TARCAT) dataset

African societies are dependent on rainfall for agricultural and other water-dependent activities, yet rainfall is extremely variable in both space and time and reoccurring water shocks, such as drought, can have considerable social and economic impacts. To help improve our knowledge of the rainfall climate, we have constructed a 30-year (1983–2012), temporally consistent rainfall dataset for Africa known as TARCAT (TAMSAT African Rainfall Climatology And Time-series) using archived Meteosat thermal infra-red (TIR) imagery, calibrated against rain gauge records collated from numerous African agencies. TARCAT has been produced at 10-day (dekad) scale at a spatial resolution of 0.0375°. An intercomparison of TARCAT from 1983 to 2010 with six long-term precipitation datasets indicates that TARCAT replicates the spatial and seasonal rainfall patterns and interannual variability well, with correlation coefficients of 0.85 and 0.70 with the Climate Research Unit (CRU) and Global Precipitation Climatology Centre (GPCC) gridded-gauge analyses respectively in the interannual variability of the Africa-wide mean monthly rainfall. The design of the algorithm for drought monitoring leads to TARCAT underestimating the Africa-wide mean annual rainfall on average by −0.37 mm day−1 (21%) compared to other datasets. As the TARCAT rainfall estimates are historically calibrated across large climatically homogeneous regions, the data can provide users with robust estimates of climate related risk, even in regions where gauge records are inconsistent in time.

Real-time factor model forecasting and the effects of instability

Factor forecasting models are shown to deliver real-time gains over autoregressive models for US real activity variables during the recent period, but are less successful for nominal variables. The gains are largely due to the Financial Crisis period, and are primarily at the shortest (one quarter ahead) horizon. Excluding the pre-Great Moderation years from the factor forecasting model estimation period (but not from the data used to extract factors) results in a marked fillip in factor model forecast accuracy, but does the same for the AR model forecasts. The relative performance of the factor models compared to the AR models is largely unaffected by whether the exercise is in real time or is pseudo out-of-sample.

Extracting planetary waves from geomagnetic time series using Empirical Mode Decomposition

Empirical Mode Decomposition is presented as an alternative to traditional analysis methods to decompose geomagnetic time series into spectral components. Important comments on the algorithm and its variations will be given. Using this technique, planetary wave modes of 5-, 10-, and 16-day mean periods can be extracted from magnetic field components of three different stations in Germany. In a second step, the amplitude modulation functions of these wave modes can be shown to contain significant contribution from solar cycle variation through correlation with smoothed sunspot numbers. Additionally, the data indicate connections with geomagnetic jerk occurrences, supported by a second set of data providing reconstructed near-Earth magnetic field for 150 years. Usually attributed to internal dynamo processes within the Earth's outer core, the question of who is impacting whom will be briefly discussed here.