Multiple Lags Research Articles

Bayesian Dynamical Systems Modelling in the Social Sciences

Data arising from social systems is often highly complex, involving non-linear relationships between the macro-level variables that characterize these systems. We present a method for analyzing this type of longitudinal or panel data using differential equations. We identify the best non-linear functions that capture interactions between variables, employing Bayes factor to decide how many interaction terms should be included in the model. This method punishes overly complicated models and identifies models with the most explanatory power. We illustrate our approach on the classic example of relating democracy and economic growth, identifying non-linear relationships between these two variables. We show how multiple variables and variable lags can be accounted for and provide a toolbox in R to implement our approach.

Trajectories of Life Satisfaction: Positive Feedback Loops May Explain Why Life Satisfaction Changes in Multi-Year Waves, Rather than Oscillating Around a Set-Point

Long term panel data enable researchers to construct Life Satisfaction (LS) trajectories for individuals over time. In this paper we analyse the trajectories of respondents in the German Socio-Economic Panel who recorded their LS for 20 consecutive years in 1991-2010. Previous research has shown that at least a quarter of these respondents recorded substantial long term changes in LS (Headey, Muffels and Wagner, 2010, 2012). In this paper, bar charts of LS trajectories, and subsequent statistical analysis, show that respondents tend to spend multiple consecutive years either above and/or below their own 20-year mean level of LS. These results are contrary to set-point theory which views LS as stable, except for short term fluctuations due to major life events. In the later part of the paper we attempt to explain multi-year/medium term changes in LS. We estimate structural equation models with two-way causation between LS and variables usually treated as causes of LS, including health, frequency of physical exercise, frequency of social activities/social participation, and satisfaction with work and leisure. The results are interpreted as showing positive feedback loops between these variables and LS, such that gains and losses of LS tend to be reinforced over time. The models are based on a modified concept of ‘Granger-causation’ (Granger, 1969). The main intuition behind Granger-causation is that if x can be shown to be statistically significantly related to y in a model which includes multiple lags of y, then it can be inferred that x is one cause of y.

Joint Cycle Frequencies and Lags Utilization in Cyclostationary Feature Spectrum Sensing

Cognitive radio (CR) systems require awareness of spectrum occupancy in order to operate without causing harmful interference to primary users (PUs). Cyclostationary feature detection (CFD) is a preferred method for spectrum sensing under low signal-to-noise ratio (SNR) or/and noise uncertainty scenarios. To determine the presence, or otherwise, of PU signals, conventional CFD schemes tend to use test statistics over, either, multiple cycle frequencies for a fixed lag set, or, multiple lags for a fixed cycle frequency. This paper proposes a new method that jointly utilizes cycle frequencies and lags to produce more reliable test statistics. As the optimal way to apply this joint utilization requires prior knowledge of the 4th-order cyclic cumulant, which can be challenging to obtain, an alternative sub-optimal scheme independent of this cumulant knowledge will also be provided. It will be shown that, in the low SNR region, where it is most critical for CR applications, the proposed sub-optimal scheme can lead to similar detection performances as the optimal maximum likelihood technique. It will also be demonstrated that, compared to multi-cycle-frequency detection with selection combining, equal gain combining, or maximum ratio combining, the proposed provide superior performance.

An optimization problem for infinite order distributed parabolic systems with multiple time-varying lags

In this paper, the optimal boundary control problem for (n×n) infinite order distributed parabolic systems, with boundary conditions involving multiple time-varying lags is considered. Constraints on controls are imposed. Necessary and sufficient optimality conditions for the Neumann problem with the quadratic performance functional are derived.

A fractional model for robust fractional order Smith predictor

In this paper, we propose to use a fractional order model to predict the process output in Smith predictor. The parameters of the model are determined by minimizing the error between its output and one of the processes using a genetic algorithm. After determining the model’s parameters, a fractional PID controller is proposed to improve the controlled system performances. The parameters of the controller are also determined in an optimal way by minimizing the position error taking into account the sensitivity and the complementary sensitivity conditions. Applications on a dead time and multiple lags processes have been performed, where the simulation results show that the proposed Smith predictor enhance the closed loop control system.

On Cyclostationarity Based Spectrum Sensing Under Uncertain Gaussian Noise

Detection of cyclostationary primary user (PU) signals in colored Gaussian noise for cognitive radio systems is considered based on looking for single or multiple cycle frequencies at single or multiple time lags in the cyclic autocorrelation function (CAF) of the noisy PU signal. We explicitly exploit the knowledge that under the null hypothesis of PU signal absent, the measurements originate from possible colored Gaussian noise with unknown correlation function. Our formulation allows us to simplify the spectrum sensing detector and obviates the need for estimating an unwieldy covariance matrix needed in some prior works. We consider both single and multiple antenna receivers, and both nonconjugate and conjugate CAFs. A performance analysis of the proposed detector is carried out. Supporting simulation examples are provided to demonstrate the efficacy of the proposed approaches and to compare them with some existing approaches. Our proposed approaches are computationally cheaper than the Dandawate-Giannakis and related approaches while having quite similar detection performance for a given false alarm rate.

A Kaleidoscopic Study of Pricing Performance of Stochastic Volatility Option Pricing Models: Evidence from Recent Indian Economic Turbulence

A whole host of researchers have modeled volatility as a non-constant stochastic process, based on the principle that volatility follows a stochastic process whose parameters are not directly observable in the market. The objective of this research paper is to empirically investigate the forecasting performance of three most dominant models of this species namely, Hull-White (1988), Heston�s (1993), and Heston-Nandi GARCH (2000) option pricing model. These three models have been collaterally compared and contrasted against Black-Scholes and market for pricing S&P CNX Nifty 50 index option of India. The Hull-White model not only warrants a range of stochastic volatility specifications but also incorporates correlation of volatility of asset return and its price changes. The closed form Heston�s (1993) model explicitly and elaborately communicates non-lognormal distribution of the assets return, leverage effect, and mean-reverting property of volatility. The model of Heston-Nandi, also in closed form, successfully incorporates variance of asset returns as a range of GARCH process. It strongly permits correlation between returns of the spot asset and variance and also technically accepts multiple lags in the dynamics of the GARCH process. To decide, determine, and delineate the effectiveness of stochastic models against the Black-Scholes and market, the current paper adopts a structured approach of relative error price, viz., percentage mean error (PME) and mean absolute percentage error (MAPE). The most turbulent period of the Indian economy � January 1, 2008 to December 31, 2008 — was considered appropriate for testiing the suggested model. It was a testing time for the Indian economy as well as a critical period questioning the sustainability of all financial products/models and challenging their fundamental platform depicted as equity market. How to safeguard investors� faith and at least protect their investments if not multiply returns in the face of such financial hardships remained a burning question for all thinkers and experts on the subject. Data pertaining to the specific period of such drastic disturbance was analysed with the help of the proposed models. After rigorous churning of specific data taken across various models, the Heston model was found to outperform and surpass other models.

Transfer Entropy for Coupled Autoregressive Processes

A method is shown for computing transfer entropy over multiple time lags for coupled autoregressive processes using formulas for the differential entropy of multivariate Gaussian processes. Two examples are provided: (1) a first-order filtered noise process whose state is measured with additive noise, and (2) two first-order coupled processes each of which is driven by white process noise. We found that, for the first example, increasing the first-order AR coefficient while keeping the correlation coefficient between filtered and measured process fixed, transfer entropy increased since the entropy of the measured process was itself increased. For the second example, the minimum correlation coefficient occurs when the process noise variances match. It was seen that matching of these variances results in minimum information flow, expressed as the sum of transfer entropies in both directions. Without a match, the transfer entropy is larger in the direction away from the process having the larger process noise. Fixing the process noise variances, transfer entropies in both directions increase with the coupling strength. Finally, we note that the method can be generally employed to compute other information theoretic quantities as well.

An Efficient Multiple Lags Selection Method for Cyclostationary Feature Based Spectrum-Sensing

The principle of cognitive radio (CR) systems is to utilize the licensed spectrum when their interference to primary users (PUs) can be maintained below a certain threshold. Thus, to successfully coexist, cognitive users must have awareness of PUs presence in the vicinity. As most communication signals exhibit statistical periodicities, cyclostationary feature detection (CFD) can be used to perform the task of sensing the spectrum for PUs presence. A second-order statistical approach is most widely used to perform CFD in which a set of lags should be chosen for statistical testing. The optimal method for choosing multiple lags requires knowledge of the 4th-order cyclic cumulant of PUs' signals, which can be a burden in practice. In this letter, we present a new idea for lag set selection with which avoids the mentioned 4th-order cumulant burden. The results, verified via analysis and simulation, show that the performance of the proposed method is comparable to the optimal one in the low signal to-noise ratio region where it is most critical for CR applications.

Risk stratification of cardiac autonomic neuropathy based on multi-lag Tone–Entropy

Cardiac autonomic neuropathy (CAN) is an irreversible condition affecting the autonomic nervous system, which leads to abnormal functioning of the visceral organs and affects critical body functions such as blood pressure, heart rate and kidney filtration. This study presents multi-lag Tone-Entropy (T-E) analysis of heart rate variability (HRV) at multiple lags as a screening tool for CAN. A total of 41 ECG recordings were acquired from diabetic subjects with definite CAN (CAN+) and without CAN (CAN-) and analyzed. Tone and entropy values of each patient were calculated for different beat sequence lengths (len: 50-900) and lags (m: 1-8). The CAN- group was found to have a lower mean tone value compared to that of CAN+ group for all m and len, whereas the mean entropy value was higher in CAN- than that in CAN+ group. Leave-one-out (LOO) cross-validation tests using a quadratic discriminant (QD) classifier were applied to investigate the performance of multi-lag T-E features. We obtained 100 % accuracy for tone and entropy with len = 250 and m = {2, 3} settings, which is better than the performance of T-E technique based on lag m = 1. The results demonstrate the usefulness of multi-lag T-E analysis over single lag analysis in CAN diagnosis for risk stratification and highlight the change in autonomic nervous system modulation of the heart rate associated with cardiac autonomic neuropathy.

The rain–runoff response of tropical humid forest ecosystems to use and reforestation in the Western Ghats of India

summary The effects of forest degradation and use and establishment of tree-plantations on degraded or modified forest ecosystems at multi-decadal time-scales using tree-plantations on the streamflow response are less studied in the humid tropics when compared to deforestation and forest conversion to agriculture. In the Western Ghats of India (Uttar Kannada, Karnataka State), a previous soil hydraulic conductivity survey linked with rain IDF (intensity–duration–frequency) had suggested a greater occurrence of infiltration-excess overland within the degraded forest and reforested areas and thus potentially higher streamflow (Bonell et al., 2010). We further tested these predictions in Uttar Kannada by establishing experimental basins ranging from 7 to 23 ha across three ecosystems, (1) remnant tropical evergreen Forest (NF), (2) heavily-used former evergreen forest which now has been converted to tree savanna, known as degraded forest (DF) and (3) exotic Acacia plantations (AC, Acacia auriculiformis) on degraded former forest land. In total, 11 basins were instrumented (3 NF, 4 AC and 4 DF) in two geomorphological zones, i.e., Coastal and Up-Ghat (Malnaad) and at three sites (one Coastal, two Up-Ghat). The rainfall–streamflow observations collected (at daily and also at a 36 min time resolutions in the Coastal basins) over a 2–3 year period (2003–2005) were analysed. In both the Coastal and Up-Ghat basins, the double mass curves showed during the rainy season a consistent trend in favour of more proportion of streamflow in the rank order DF > AC > NF. These double mass curves provide strong evidence that overland flow is progressively becomes a more dominant stormflow pathway. Across all sites, NF converted 28.4 ± 6.41 stdev% of rainfall into total streamflow in comparison to 32.7 ± 6.97stdev% in AC and 45.3 ± 9.61stdev% in DF. Further support for the above trends emerges from the quickflow ratio QF/Q for the Coastal basins. There are much higher values for both the DF and AC land covers, and their rank order DF > AC > NF. The quickflow response ratio QF/P is also the highest for the DF basin, and along with the QF/Q ratio, can exceed 90%. The corresponding delayed flow response ratios, QD/P clearly show the largest QD yields as a proportion of event precipitation from the Forest (NF1). The application of linear model supported these differences (e.g. 10–36% difference between NF and DF, p < 0.001) in the storm hydrologic response of the Coastal basins. The exception was QF/P where there was a higher uncertainty connected with interbasin mean differences. Cross-correlation plots for rain–streamflow and corresponding lag regression models for three storm events in the Coastal basins suggested the existence of alternative stormflow pathways with multiple lags with peaks between � 12 and 24 h in NF, compared to respective bimodal peaks at � 1 and 16 h in AC and � 1 and 12 h in DF. The long time lags for NF are suggestive of deep subsurface stormflow and groundwater as the contributing sources to the storm hydrograph. The short time lags in DF and AC are indicative of overland flow and so ‘memory’ of the previous degraded land cover is retained in AC as supported by previous hydraulic conductivity data. As potential and actual evapotranspiration is likely to be depressed during the monsoon, differences in streamflow and run-off responses between land-cover types is largely attributed to differences in soil infiltration and hydrologic pathways. Enhancing infiltration and reducing run-off in managed ecosystems should be explored in the terms of the context of other ecosystem services and biodiversity.

Polycyclic aromatic hydrocarbon exposure and wheeze in a cohort of children with asthma in Fresno, CA

Polycyclic aromatic hydrocarbons (PAHs) are found widely in the ambient air and result from combustion of various fuels and industrial processes. PAHs have been associated with adverse human health effects such as cognitive development, childhood IQ, and respiratory health. The Fresno Asthmatic Children's Environment Study enrolled 315 children aged 6-11 years with asthma in Fresno, CA and followed the cohort from 2000 to 2008. Subjects were evaluated for asthma symptoms in up to three 14-day panels per year. Detailed ambient pollutant concentrations were collected from a central site and outdoor pollutants were measured at 83 homes for at least one 5-day period. Measurements of particle-bound PAHs were used with land-use regression models to estimate individual exposures to PAHs with 4-, 5-, or 6-member rings (PAH456) and phenanthrene for the cohort (approximately 22,000 individual daily estimates). We used a cross-validation-based algorithm for model fitting and a generalized estimated equation approach to account for repeated measures. Multiple lags and moving averages of PAH exposure were associated with increased wheeze for each of the three types of PAH exposure estimates. The odds ratios for asthmatics exposed to PAHs (ng/m(3)) ranged from 1.01 (95% CI, 1.00-1.02) to 1.10 (95% CI, 1.04-1.17). This trend for increased wheeze persisted among all PAHs measured. Phenanthrene was found to have a higher relative impact on wheeze. These data provide further evidence that PAHs contribute to asthma morbidity.

Extensive use of no-tillage in grain growing regions of Australia

The shift to agricultural systems involving no-tillage from those based on multiple cultivations has required decades and is ongoing. This paper examines the enabling factors for the adoption of no-tillage cropping systems including the demand-induced innovation by farmers and agricultural engineers, enabling agronomic technologies such as herbicides and crop disease resistance, extension processes, and economic influences. The first section draws upon existing studies from grain producing regions to demonstrate the multiple dimensions and lags involved in achieving such a major change in agricultural practice. In the second section, we identify and quantify the major agronomic and socio-economic drivers of no-tillage adoption rates in Australia. Analysis of data collected from 1170 grain growers across 19 Australian grain growing regions is used to characterise current no-tillage adoption by regions and the its extent of use. Cumulative adoption curves show that the proportion of farmers using at least some no-tillage has started to plateau near 90% in several regions, while in others, a much lower proportion of farmers have adopted or expect to adopt in the medium term future. Many Australian growers use some no-tillage but maintain a high degree of flexibility in their approach to soil disturbance and respond to economic and seasonal drivers. The results suggest that the same extension and diffusion processes that have led to the current high adoption by farmers in some regions may not lead to further adoption of no-tillage in all regions. Soil erosion, for example, was an important motivating factor early in the development of no-tillage but is not found to be a major factor differentiating adopters and non-adopters in the later stages of technology diffusion. Increasingly, the constraint to more extensive use of no-tillage is the extent of use by existing adopters. Factors relating to disease risks and weed management are identified as important. The long and knowledge intensive innovation process for no-tillage systems has led to remarkable changes in agricultural landscapes. It is an ongoing process that continues in later-adopting regions and in sustaining extensive use.

Detection and Mitigation of Second-Trip Echo in Polarimetric Weather Radar Employing Random Phase Coding

This study presents a new identification and mitigation scheme of second trip contamination for pulsed Doppler polarimetric weather radars with the ability of random phase coding. This scheme can be easily implemented in a magnetron radar without any hardware changes. For relatively weak contamination, identification and mitigation are based on a multilag processing method, which uses multiple lags of both the auto- and cross-correlation functions to estimate radar moments. For relatively strong contamination, instantaneous phase variations of horizontal and vertical polarization channels are combined into a simple fuzzy-logic scheme to complete the identification. Data from the C-band OU-PRIME radar are used to demonstrate the effectiveness of the proposed scheme for identification and mitigation of second-trip echoes.

High-frequency analysis of the complex linkage between soil CO2 fluxes, photosynthesis and environmental variables

High-frequency soil CO(2) flux data are valuable for providing new insights into the processes of soil CO(2) production. A record of hourly soil CO(2) fluxes from a semi-arid ponderosa pine stand was spatially and temporally deconstructed in attempts to determine if variation could be explained by logical drivers using (i) CO(2) production depths, (ii) relationships and lags between fluxes and soil temperatures, or (iii) the role of canopy assimilation in soil CO(2) flux variation. Relationships between temperature and soil fluxes were difficult to establish at the hourly scale because diel cycles of soil fluxes varied seasonally, with the peak of flux rates occurring later in the day as soil water content decreased. Using a simple heat transport/gas diffusion model to estimate the time and depth of CO(2) flux production, we determined that the variation in diel soil CO(2) flux patterns could not be explained by changes in diffusion rates or production from deeper soil profiles. We tested for the effect of gross ecosystem productivity (GEP) by minimizing soil flux covariance with temperature and moisture using only data from discrete bins of environmental conditions (±1 °C soil temperature at multiple depths, precipitation-free periods and stable soil moisture). Gross ecosystem productivity was identified as a possible driver of variability at the hourly scale during the growing season, with multiple lags between ~5, 15 and 23 days. Additionally, the chamber-specific lags between GEP and soil CO(2) fluxes appeared to relate to combined path length for carbon flow (top of tree to chamber center). In this sparse and heterogeneous forested system, the potential link between CO(2) assimilation and soil CO(2) flux may be quite variable both temporally and spatially. For model applications, it is important to note that soil CO(2) fluxes are influenced by many biophysical factors, which may confound or obscure relationships with logical environmental drivers and act at multiple temporal and spatial scales; therefore, caution is needed when attributing soil CO(2) fluxes to covariates like temperature, moisture and GEP.

Closed-Form Real Single-Tone Frequency Estimator Based on Phase Compensation of Multiple Correlation Lags

A new frequency estimator for a single real-valued sinusoid signal in white noise is proposed. The new estimator uses the Pisarenko Harmonic Decomposer (PHD) estimator to get a coarse frequency estimate and then makes use of multiple correlation lags to obtain an adjustment term. For the limited-length single sinusoid, its correlation has the same frequency as itself but with a non-zero phase. We propose to use Taylor series to expand the correlation at the PHD coarse estimated frequency with amplitude and phase of the correlation into consideration. Simulation results show that this new method improves the estimation performance of the PHD estimator. Moreover, when compared with other existing estimator, the mean square frequency error of the proposed method is closer to the Cramer-Rao Lower Bound (CRLB) for certain SNR range.

Computational fixed-point theory for differential delay equations with multiple time lags

We introduce a general computational fixed-point method to prove existence of periodic solutions of differential delay equations with multiple time lags. The idea of such a method is to compute numerical approximations of periodic solutions using Newtonʼs method applied on a finite dimensional projection, to derive a set of analytic estimates to bound the truncation error term and finally to use this explicit information to verify computationally the hypotheses of a contraction mapping theorem in a given Banach space. The fixed point so obtained gives us the desired periodic solution. We provide two applications. The first one is a proof of coexistence of three periodic solutions for a given delay equation with two time lags, and the second one provides rigorous computations of several nontrivial periodic solutions for a delay equation with three time lags.

Exploiting periodicity to extract the atrial activity in atrial arrhythmias

Atrial fibrillation disorders are one of the main arrhythmias of the elderly. The atrial and ventricular activities are decoupled during an atrial fibrillation episode, and very rapid and irregular waves replace the usual atrial P-wave in a normal sinus rhythm electrocardiogram (ECG). The estimation of these wavelets is a must for clinical analysis. We propose a new approach to this problem focused on the quasiperiodicity of these wavelets. Atrial activity is characterized by a main atrial rhythm in the interval 3-12 Hz. It enables us to establish the problem as the separation of the original sources from the instantaneous linear combination of them recorded in the ECG or the extraction of only the atrial component exploiting the quasiperiodic feature of the atrial signal. This methodology implies the previous estimation of such main atrial period. We present two algorithms that separate and extract the atrial rhythm starting from a prior estimation of the main atrial frequency. The first one is an algebraic method based on the maximization of a cost function that measures the periodicity. The other one is an adaptive algorithm that exploits the decorrelation of the atrial and other signals diagonalizing the correlation matrices at multiple lags of the period of atrial activity. The algorithms are applied successfully to synthetic and real data. In simulated ECGs, the average correlation index obtained was 0.811 and 0.847, respectively. In real ECGs, the accuracy of the results was validated using spectral and temporal parameters. The average peak frequency and spectral concentration obtained were 5.550 and 5.554 Hz and 56.3 and 54.4%, respectively, and the kurtosis was 0.266 and 0.695. For validation purposes, we compared the proposed algorithms with established methods, obtaining better results for simulated and real registers.

A closed-form expanded autocorrelation method for frequency estimation of a sinusoid

A closed-form expanded autocorrelation method for real single-tone frequency estimation is proposed. Firstly, the modified covariance (MC) method based on multiple autocorrelation lags is applied to provide a coarse frequency estimate. Then, a closed-form adjustment term based on a least square cost function is derived to get the fine frequency estimate. Simulation results show that the performance of the proposed algorithm, when compared with several existing closed-form time-domain estimators, is closer to the Cramer–Rao bound (CRB). Moreover, the proposed method has lower computation complexity than other autocorrelation-based approaches, which also use multiple autocorrelation lags.

Endogenous business cycle propagation and the persistence problem: The role of labor-market frictions

Contrasting sharply with a recent trend in DSGE modeling, we propose a business cycle model where frictions and shocks are chosen with parsimony. The model emphasizes a few labor-market frictions and shocks to monetary policy and technology. The model, estimated from U.S. quarterly postwar data, accounts well for important differences in the serial correlation of the growth rates of aggregate quantities, the size of aggregate fluctuations and key comovements, including the correlation between hours and labor productivity. Despite its simplicity, the model offers an answer to the persistence problem ( Chari et al., 2000) that does not rely on multiple frictions and adjustment lags or ad hoc backward-looking components. We conclude modern DSGE models need not embed large batteries of frictions and shocks to account for the salient features of postwar business cycles.