Linear Detrending Research Articles

Defining the Intra-subject Variability of Whole-lung CT Densitometry in Two Lung Cancer Screening Trials

To define a statistically based variation of individual whole-lung densitometry above which a real increase of pulmonary extent can be suspected in lung cancer screening trials. Baseline and 3-month follow-up low-dose computed tomography (LDCT) examinations of 131 smokers or former smokers recruited in the ITALUNG (32 subjects) and MILD (99 subjects) trials were compared using for each data set two different image processing tools for whole-lung densitometry. Both trials were approved by institutional review boards, and written informed consent was obtained from all participants. Assuming that no change of emphysema extent can occur in a 3-month interval, the Bland and Altman method was used to assess the agreement between baseline and follow-up LDCT examinations for lung volume, 15th percentile (Perc15) of lung density and Perc15 corrected for lung volume by application of a linear detrend on log-transformed data. Similar results were obtained in each data set using two different image processing tools. In the ITALUNG cohort the 95% limits of agreement (LoA) interval of volume corrected Perc15 was -9.7 to 10.7% using image processing method 1 and -10.3 to 11.5% using image processing method 2. In the MILD cohort, the 95% LoA interval of volume corrected Perc15 was -14.7 to 17.3% with both image processing methods. In the two considered lung cancer screening settings a range of 9.7-14.7% decrease of volume corrected Perc15 represents a statistically defined threshold to suspect a real increase of emphysema extent in serial LDCT examinations.

Test of diurnal and semidiurnal tidal analysis of temperatures from SABER-like sampling of a realistic global model, CMAM-DAS

Abstract. Because the TIMED satellite orbit precesses slowly in local time, 3 degrees (12 min) per day, thus apparently covering all local times at low and mid latitudes in 2 months when ascending and descending nodes are included, there is a potential for determining migrating and non-migrating tides from temperatures. Many papers have been written on the subject, but none have taken a realistic model atmosphere with high time resolution and tested tidal analysis. The present paper contains results from a tidal analysis of a SABER-sampled global model, the Canadian Middle Atmosphere (data assimilated) Model, CMAM-DAS, which has hourly values, and compares these with analysis using the full model. Fits to 60 d intervals at the equator show reasonable agreement between full and SABER-sampled data analysis for mean, diurnal and semidiurnal tides, with or without inclusion of a linear detrend term. At 50° N where there is irregular coverage of local times, there are serious disagreements in all parameters except the background mean, and detrending has a significant effect.

Multifractal moving average analysis and test of multifractal model with tuned correlations

We address two common major problems in the study of time series characterizing fluctuations in complex systems: multifractal analysis and multifractal modeling. Specifically, we introduce a multi-fractal centered moving average (MF-CMA) analysis, which is computationally easier but equivalently performing compared with the well-established multi-fractal detrended fluctuation analysis (MF-DFA) with linear detrending. In addition, we study in detail a generalized binomial multi-fractal model (GB-MFM) to conveniently and reliably generate multifractal surrogate data with arbitrary singularity strengths and arbitrary long-term persistence. We use the data generated by this model as well as realistic, by construction monofractal data series with crossovers and trends to test and compare the multifractal analysis methods and discuss finite-size effects as well as limitations due to spurious multifractality.

New method to measure and improve consistency of baroreflex sensitivity values

Baroreflex sensitivity (BRS) is an important prognostic index in cardiovascular diseases, however, its use is complicated by different methods difficult to compare and standardize, often providing conflicting results. We tested whether the simple ratio of RR interval to systolic blood pressure global variabilities (assessed by standard deviations) is a reliable measure of BRS, by measuring the agreement with six established methods. In addition, we tested whether high-pass filtering of data, by removing slow non-baroreflex-mediated fluctuations, could improve the agreement between different BRS methods. In 1,409 subjects, we compared 6 established methods (derived by cross-spectral and sequence analysis) and the new method, supine and in response to tilting (1,175 subjects). Data were analyzed after linear detrending, high-pass filtering at 0.025 and 0.05Hz. Although all seven methods showed a general agreement, the new method consistently showed the lowest distance from the median of the remaining methods (0.04±0.06ms/mmHg over 2,584 files, p<0.05 with respect to the second best method). High-pass filtering improved (p<0.001) the agreement between methods without reducing the sensitivity to changes induced by tilting. Only the new method could provide estimates in all 2,584 files tested. The new method intercepts the mean information of all other methods better than any other method, hence providing a simple, easy to standardize (no mathematical constraints) and yet robust and reliable BRS estimate. High-pass filtering markedly improves the agreement of all methods, without loss of sensitivity, and could be routinely used in clinical trials, to provide comparable BRS estimates.

Linear Detrending Subsequence Matching in Time-Series Databases

Each time-series has its own linear trend, the directionality of a timeseries, and removing the linear trend is crucial to get the more intuitive matching results. Supporting the linear detrending in subsequence matching is a challenging problem due to a huge number of possible subsequences. In this paper we define this problem the linear detrending subsequence matching and propose its efficient index-based solution. To this end, we first present a notion of LD-windows (LD means linear detrending), which is obtained as follows: we eliminate the linear trend from a subsequence rather than each window itself and obtain LD-windows by dividing the subsequence into windows. Using the LD-windows we then present a lower bounding theorem for the index-based matching solution and formally prove its correctness. Based on the lower bounding theorem, we next propose the index building and subsequence matching algorithms for linear detrending subsequence matching.We finally show the superiority of our index-based solution through extensive experiments.

Estimation of DSGE models when the data are persistent

Dynamic stochastic general equilibrium (DSGE) models are often solved and estimated under specific assumptions as to whether the exogenous variables are difference or trend stationary. However, even mild departures of the data generating process from these assumptions can severely bias the estimates of the model parameters. This paper proposes new estimators that do not require researchers to take a stand on whether shocks have permanent or transitory effects. These procedures have two key features. First, the same filter is applied to both the data and the model variables. Second, the filtered variables are stationary when evaluated at the true parameter vector. The estimators are approximately normally distributed not only when the shocks are mildly persistent, but also when they have near or exact unit roots. Simulations show that these robust estimators perform well especially when the shocks are highly persistent yet stationary. In such cases, linear detrending and first differencing are shown to yield biased or imprecise estimates.

Estimation of DSGE Models When the Data are Persistent

Dynamic Stochastic General Equilibrium (DSGE) models are often solved and estimated under specific assumptions as to whether the exogenous variables are difference or trend stationary. However, even mild departures of the data generating process from these assumptions can severely bias the estimates of the model parameters. This paper proposes new estimators that do not require researchers to take a stand on whether shocks have permanent or transitory effects. These procedures have two key features. First, the same filter is applied to both the data and the model variables. Second, the filtered variables are stationary when evaluated at the true parameter vector. The estimators are approximately normally distributed not only when the shocks are mildly persistent, but also when they have near or exact unit roots. Simulations show that these robust estimators perform well especially when the shocks are highly persistent yet stationary. In such cases, linear detrending and first differencing are shown to yield biased or imprecise estimates.

Estimation procedures affect the center of pressure frequency analysis

Even though frequency analysis of body sway is widely applied in clinical studies, the lack of standardized procedures concerning power spectrum estimation may provide unreliable descriptors. Stabilometric tests were applied to 35 subjects (20-51 years, 54-95 kg, 1.6-1.9 m) and the power spectral density function was estimated for the anterior-posterior center of pressure time series. The median frequency was compared between power spectra estimated according to signal partitioning, sampling rate, test duration, and detrending methods. The median frequency reliability for different test durations was assessed using the intraclass correlation coefficient. When increasing number of segments, shortening test duration or applying linear detrending, the median frequency values increased significantly up to 137%. Even the shortest test duration provided reliable estimates as observed with the intraclass coefficient (0.74-0.89 confidence interval for a single 20-s test). Clinical assessment of balance may benefit from a standardized protocol for center of pressure spectral analysis that provides an adequate relationship between resolution and variance. An algorithm to estimate center of pressure power density spectrum is also proposed.

Monetary Policy Estimation in Real Time: Forward-Looking Taylor Rules without Forward-Looking Data

I propose a methodology for estimating forward-looking Taylor rules in real time when forward-looking real-time central bank data is unavailable. The methodology consists of choosing appropriate models to closely replicate U.S. Greenbook forecasts, and then applying these models to Canada, Germany, and the U.K. The results show that the Greenbook output gap series is well described by rolling window linear detrending, while Greenbook inflation forecasts can be closely replicated using Bayesian model averaging over Autoregressive Distributed Lag models in inflation and the GDP growth rate. German and U.S. Taylor rules are characterized by inflation coefficients increasing with the forecast horizon and a positive output gap response. The U.K. and Canada interest rate reaction functions achieve maximum inflation response at middle-term horizons of about 1/2 years and the output gap coefficient is insignificant

Drift in Posturography Systems Equipped With a Piezoelectric Force Platform: Analysis and Numerical Compensation

Piezoelectric force platforms are electronic instruments widely used for posturography in movement analysis laboratories. As is well known, drift affects piezoelectric transducers; therefore, the accuracy of piezoelectric measurement systems should be periodically checked. The objectives of this paper were as follows: (1) to detect the occurrence of drift in the posturographic signals derived from a piezoelectric force plate (FP) using an easy-to-use standard procedure; (2) to determine the impact on drift itself of two clinically relevant factors: applied load [for values related to children/adolescent weights (range 49-588 N)] and test duration; and (3) to suggest numerical solutions, if any, to compensate for drift effects. Drift in piezoelectric FPs is essentially caused by leakage currents and/or poor insulation resistances. Moreover, it may be considered as a low-frequency event affecting the accuracy of standing posture descriptive parameters. The measurement system outputs available to the end user, namely ground reaction force (GRF) components and center of pressure (CoP) sway, were analyzed both in the time and frequency domains. According to the obtained results, it was possible to demonstrate that drift significantly affects the signals of the posturography system under study and that it can be assessed by the analysis of the GRF and CoP component values. As it exhibits a constant rate versus time, drift can be well approximated by a linear regression line. The main results are represented by the independence of drift rate from applied load and test duration and by finding that drift can relevantly affect CoP evaluation for test duration that is equal or longer than 1 min when the applied load is less than 245 N (which could be the case for children and young slim adolescents). High-pass numeric filtering with a cutoff frequency of 0.15 Hz and linear detrending can compensate drift in the presented case.

Robustness of proxy‐based climate field reconstruction methods

We present results from continued investigations into the fidelity of covariance‐based climate field reconstruction (CFR) approaches used in proxy‐based climate reconstruction. Our experiments employ synthetic “pseudoproxy” data derived from simulations of forced climate changes over the past millennium. Using networks of these pseudoproxy data, we investigate the sensitivity of CFR performance to signal‐to‐noise ratios, the noise spectrum, the spatial sampling of pseudoproxy locations, the statistical representation of predictors used, and the diagnostic used to quantify reconstruction skill. Our results reinforce previous conclusions that CFR methods, correctly implemented and applied to suitable networks of proxy data, should yield reliable reconstructions of past climate histories within estimated uncertainties. Our results also demonstrate the deleterious impact of a linear detrending procedure performed recently in certain CFR studies and illustrate flaws in some previously proposed metrics of reconstruction skill.

The energy balance experiment EBEX-2000. Part II: Intercomparison of eddy-covariance sensors and post-field data processing methods

The eddy-covariance method is the primary way of measuring turbulent fluxes directly. Many investigators have found that these flux measurements often do not satisfy a fundamental criterion—closure of the surface energy balance. This study investigates to what extent the eddy-covariance measurement technology can be made responsible for this deficiency, in particular the effects of instrumentation or of the post-field data processing. Therefore, current eddy-covariance sensors and several post-field data processing methods were compared. The differences in methodology resulted in deviations of 10% for the sensible heat flux and of 15% for the latent heat flux for an averaging time of 30 min. These disparities were mostly due to different sensor separation corrections and a linear detrending of the data. The impact of different instrumentation on the resulting heat flux estimates was significantly higher. Large deviations from the reference system of up to 50% were found for some sensor combinations. However, very good measurement quality was found for a CSAT3 sonic together with a KH20 krypton hygrometer and also for a UW sonic together with a KH20. If these systems are well calibrated and maintained, an accuracy of better than 5% can be achieved for 30-min values of sensible and latent heat flux measurements. The results from the sonic anemometers Gill Solent-HS, ATI-K, Metek USA-1, and R.M. Young 81000 showed more or less larger deviations from the reference system. The LI-COR LI-7500 open-path H2O/CO2 gas analyser in the test was one of the first serial numbers of this sensor type and had technical problems regarding direct solar radiation sensitivity and signal delay. These problems are known by the manufacturer and improvements of the sensor have since been made.

Spatial representativeness of single tower measurements and the imbalance problem with eddy-covariance fluxes: results of a large-eddy simulation study

A large-eddy simulation (LES) study is presented that investigates the spatial variability of temporal eddy covariance fluxes and the systematic underestimation of representative fluxes linked to them. It extends a prior numerical study by performing high resolution simulations that allow for virtual measurements down to 20 m in a convective boundary layer, so that conditions for small tower measurement sites can be analysed. It accounts for different convective regimes as the wind speed and the near-surface heat flux are varied. Moreover, it is the first LES imbalance study that extends to the stable boundary layer. It reveals shortcomings of single site measurements and the necessity of using horizontally-distributed observation networks. The imbalances in the convective case are attributed to a locally non-vanishing mean vertical advection due to turbulent organised structures (TOS). The strength of the TOS and thus the imbalance magnitude depends on height, the horizontal mean wind and the convection type. Contrary to the results of a prior study, TOS cannot generally be responsible for large energy imbalances: at low observation heights (corresponding to small towers and near-surface energy balance stations) the TOS related imbalances are generally about one order of magnitude smaller than those in field experiments. However, TOS may cause large imbalances at large towers not only in the case of cellular convection and low wind speeds, as found in the previous study, but also in the case of roll convection at large wind speeds. In the stably stratified boundary layer for all observation heights neither TOS nor significant imbalances are observed. Attempting to reduce imbalances in convective situations by applying the conventional linear detrending method increases the systematic flux underestimation. Thus, a new filter method is proposed.

A Study on the Electroencephalographic Characteristics at Each Anesthetic Steps

Background: Bispectrum and bicoherence analysis that is the frequency domain methods of EEG analysis was examined to elucidate the correlation with the depth of anesthesia. Methods: 25 patients under the gynecological surgery were studied. EEG was surveyed by PhysioLab 400. Analysis of EEG was done according to the progress of anesthesia, normal state before anesthesia, before incision of skin, operation 1, operation 2, awake and post-anesthesia. EEG is applied to filtering of signal, base line correction, linear detrend removal to get more reliable analysis. The appearance rate of bispectrum peaks are calculated by bispectrum operation. And bicoherences are calculated by bispectrum and power spectrum of AR model. Results: In awaking state of patient in pre-anesthesia and post anesthesia, appearance rate of bispectral coupling was observed that a strong appearance rate was represented in all area (0-35 Hz). During the anesthesia, the low frequency area (3-15 Hz) revealed a strong appearance. Also the 2D map of a appearance rate is divided into four sections for more objectivity. Of four sections Bipara#4 is considered that the best parameter which showed progress of anesthesia (P

Weather Derivative Pricing and the Detrending of Meteorological Data: Three Alternative Representations of Damped Linear Detrending

It is often desirable to remove the trends from historical meteorological data prior to using that data for the pricing of weather derivatives. In previous articles we have introduced the method of damped linear detrending and argued that it is an effective way to remove trends when the trends are approximately linear. In this article we show that damped linear detrending can be interpreted in three different ways: as a mixture of the linear and flat-line models, as a linear model with the trend slope reduced, and as a linear model with reverse extrapolation.

Weather Derivative Pricing and the Year-ahead Forecasting of Surface Air Temperature: An Empirical Evaluation of Damped Linear Detrending

The pricing of temperature derivatives is often based on statistical methods that predict the surface air temperature a year in advance. We perform an empirical comparison of three simple methods for such year-ahead temperature forecasting and draw clear conclusions about their relative merits. The three methods we consider are the standard flat-line and best-fit linear detrending methods and the recently introduced damped linear detrending method.

Closed Form Expressions for the Uncertainty from Linear Detrending, and the Pricing of Weather Derivatives

Weather derivative pricing is often based on a statistical analysis of past weather data. Such data may be non-stationary, and detrending methods can be used to attempt to remove the non-stationarity in the mean. The performance of different methods can be compared by considering aspects of the distribution of errors in the predictions they make. In this paper we derive closed-form expressions for the mean error, error variance and mean square error for flat line and linear trend models in the case where the real trend is linear.

POWGRAF2: a program for graphical spectral analysis in cyclostratigraphy

Spectral analysis is a widely used statistical tool in cyclostratigraphy. The aim is to detect hidden periodicities in noisy temporal (or spatial) series derived from stratigraphic sequences at outcrops or boreholes. A graphical program to assist the geologist with the spectral analysis is presented in this paper. The program follows a sequential approach to spectral analysis in which the automatic graphical displays of the results guide the user through the analysis. Features of the program are the imputation of missing data, linear drift detrending, selection of white noise or red noise from the correlogram, possibility of evolutive spectral analysis (spectrogram), and a variety of spectral estimators and confidence bands for the power spectrum estimates consistent with the selected model for the underlying noise (red or white). The analysis is enhanced by graphical screens with the original series, detrended series, experimental correlogram, theoretical model of an AR(1) correlogram fitted to the series, confidence bands for the estimated correlogram, estimated power spectrum, underlying white or red noise spectrum and 90%, 95% and 99% upper confidence bands for the estimated power spectrum. The performance of the program is illustrated using a well-known time series of δ 18O at site 607 of the Deep Sea Drilling Project.

POWGRAF2: a program for graphical spectral analysis in cyclostratigraphy*1

Spectral analysis is a widely used statistical tool in cyclostratigraphy. The aim is to detect hidden periodicities in noisy temporal (or spatial) series derived from stratigraphic sequences at outcrops or boreholes. A graphical program to assist the geologist with the spectral analysis is presented in this paper. The program follows a sequential approach to spectral analysis in which the automatic graphical displays of the results guide the user through the analysis. Features of the program are the imputation of missing data, linear drift detrending, selection of white noise or red noise from the correlogram, possibility of evolutive spectral analysis (spectrogram), and a variety of spectral estimators and confidence bands for the power spectrum estimates consistent with the selected model for the underlying noise (red or white). The analysis is enhanced by graphical screens with the original series, detrended series, experimental correlogram, theoretical model of an AR(1) correlogram fitted to the series, confidence bands for the estimated correlogram, estimated power spectrum, underlying white or red noise spectrum and 90%, 95% and 99% upper confidence bands for the estimated power spectrum. The performance of the program is illustrated using a well-known time series of δ 18 O at site 607 of the Deep Sea Drilling Project.

A Study of the Use of EEG Analysis to Evaluate the Depth of Anesthesia Using Bispectrum Analysis Method

Background: In this study, a distribute characteristics on the bispectral coupling of EEG were examined according to the depth of anesthesia by using bispectum analysis a type of nonlinear signal processing. Methods: 25 patients during the general anesthesia were studied. In the preprocess, base line correction and linear detrend was used. During the awakening state, preoperatively and postoperatively, appearance rate of bispectral coupling was observed that a strong appearance rate was represented in major frequency zone such as (15, 15) Hz but weak appearance rate investigated in the other minor frequency zone. Whilst anesthetized, a strong appearance rate revealed the low frequency range below (10, 10) Hz and a weak appearance rate viewed in the other frequency range. As such was compared with the delta ratio and spectrum edge frequency (SEF). Results: The delta ratio showed significantly lower values at induction (3.60 0.98) and during the maintenance (5.0P1.74) of anaesthesia than preoperatively (10.30 2.44) and postoperatively (13.03 2.29)(P 1.22) and postoperatively (12.20 L 1.53) than preoperatively (22.50 1.75) and at the induction (22.40 1.18) of anesthesia(P