Non-linear density dependence in time series is not evidence of non-logistic growth

Time series of population density are often used to seek deviations from logistic regulation by testing for a non-linear decline in per capita growth rate with density. Here I show that this method fails when the interval between observations is not matched by the timing of density impacts on growth. Time series overestimate instantaneous density impacts at low density and underestimate them at high density. More generally, logistic growth produces a deterministically decelerating decline in per capita growth with density if the interval between measures of population size exceeds any lag in density response. Deceleration arises independently out of stochastic density fluctuations, and under-compensating regulation. These multiple influences lead to the conclusion that sequential density estimates provide insufficient information on their own to reveal the identity of non-logistic growth processes. They can yield estimates of density compensation, however, which may suggest time lags in density dependence. Analysis of an empirical time series illustrates the issues.     

Selecting EEG components using time series analysis in brain death diagnosis

In diagnosis of brain death for human organ transplant, EEG (electroencephalogram) must be flat to conclude the patient’s brain death but it has been reported that the flat EEG test is sometimes difficult due to artifacts such as the contamination from the power supply and ECG (electrocardiogram, the signal from the heartbeat). ICA (independent component analysis) is an effective signal processing method that can separate such artifacts from the EEG signals. Applying ICA to EEG channels, we obtain several separated components among which some correspond to the brain activities while others contain artifacts. This paper aims at automatic selection of the separated components based on time series analysis. In the flat EEG test in brain death diagnosis, such automatic component selection is helpful.     

Statistical modeling,forecasting and time series analysis of birch phenology in Montreal,Canada

The aim of this study was to analyse birch pollen time series observed in Montreal (Canada) in order to understand the link between inter-annual variability of phenology and environmental factors and to build predictive models for the upcoming pollen season. Modeling phenology is challenging, especially in Canada, where phenological observations are rare. Nevertheless, understanding phenology is required for scientific applications (e.g. inputs to numerical models of pollen dispersion) but also to help allergy sufferers to better prepare their medication and avoidance strategies before the start of the pollen season. We used multivariate statistical regression to analyse and predict phenology. The predictors were drawn from a large basin (over 60) of potential environmental predictors including meteorological data and global climatic indices such NAO (North Atlantic Oscillation index) and ENSO/MEI (Multivariate Enso Index). Results of this paper are summarized as follows: (1) an accurate forecast for the upcoming season starting date of the birch pollen season was obtained (showing low bias and total forecast error of about 4 days in Montreal), (2) NAO and ENSO/MEI indices were found to be well correlated (i.e. 44% of the variance explained) with birch phenology, (3) a long-term trend of 2.6 days per decade (p < 0.1) towards longer season duration was found for the length of the birch pollen season in Montreal. Finally, perturbations of the quasi-biennial cycle of birch were observed in the pollen data during the pollen season following the Great Ice Storm of 1998 which affected south-eastern Canada.     

Measuring the directionality of coupling: phase versus state space dynamics and application to EEG time series

Measuring the directionality of coupling between dynamical systems is one of the challenging problems in nonlinear time series analysis. We investigate the relative merit of two approaches to assess directionality, one based on phase dynamics modeling and one based on state space topography. We analyze unidirectionally coupled model systems to investigate the ability of the two approaches to detect driver-responder relationships and discuss certain problems and pitfalls. In addition we apply both approaches to the intracranial electroencephalogram (EEG) recorded from one epilepsy patient during the seizure-free interval to demonstrate the general suitability of directionality measures to reflect the pathological interaction of the epileptic focus with other brain areas.     

Statistical modelling and forecasting annual sugarcane production in India: Using various time series models

This paper proposes a comparison of various time series forecasting models to forecast annual data on sugarcane production over 63 years from 1960 to 2022. In this research, the Mean Forecast Model, the Naive Model, the Simple Exponential Smoothing Model, Holt's model, and the Autoregressive Integrated Moving Average time series models have all been used to make effective and accurate predictions for sugarcane. Different scale-dependent error forecasting techniques and residual analysis have been used to examine the forecasting accuracy of these time series models. SE of Residuals, Root Mean Squared Error (RMSE), Mean Absolute Error (MAE) and Akaike's Information Criterion (AIC) are used to analyse the forecast's accuracy. The best model has been selected based on the predictions with the lowest value, according to the three-performance metrics of RMSE, MAE, and AIC. The estimated sugarcane production shows an increasing trend for the next 10 years and is projected to be 37,763.38 million tonnes in the year 2032. Further, empirical results support the plan and execution of viable strategies to advance sugarcane production in India to fulfil the utilisation need of the increasing population and further improve food security.     

The estimation of the Kolmogorov entropy from a time series and its limitations when performed on EEG

A method to estimate a lower bound of the Kolmogorov entropy—the so calledK ₂-entropy—from a time series is presented which avoids use of the generalized correlation integral. The influence of the norm is studied. The method is demonstrated on some standard examples. The entropy of the attractor apparent in the EEG of the foetal sheep is estimated and the results are compared with results obtained from synthesized data featuring some basic properties of EEG. This gives an insight into the limitations of the procedure.     

Detecting determinism in short time series, with an application to the analysis of a stationary EEG recording

We have developed a new method for detecting determinism in a short time series and used this method to examine whether a stationary EEG is deterministic or stochastic. The method is based on the observation that the trajectory of a time series generated from a differentiable dynamical system behaves smoothly in an embedded phase space. The angles between two successive directional vectors in the trajectory reconstructed from a time series at a minimum embedding dimension were calculated as a function of time. We measured the irregularity of the angle variations obtained from the time series using second-order difference plots and central tendency measures, and compared these values with those from surrogate data. The ability of the proposed method to distinguish between chaotic and stochastic dynamics is demonstrated through a number of simulated time series, including data from Lorenz, R?ssler, and Van der Pol attractors, high-dimensional equations, and 1/f noise. We then applied this method to the analysis of stationary segments of EEG recordings consisting of 750 data points (6-s segments) from five normal subjects. The stationary EEG segments were not found to exhibit deterministic components. This method can be used to analyze determinism in short time series, such as those from physiological recordings, that can be modeled using differentiable dynamical processes.     

Tracking and forecasting ecosystem interactions in real time

Evidence shows that species interactions are not constant but change as the ecosystem shifts to new states. Although controlled experiments and model investigations demonstrate how nonlinear interactions can arise in principle, empirical tools to track and predict them in nature are lacking. Here we present a practical method, using available time-series data, to measure and forecast changing interactions in real systems, and identify the underlying mechanisms. The method is illustrated with model data from a marine mesocosm experiment and limnologic field data from Sparkling Lake, WI, USA. From simple to complex, these examples demonstrate the feasibility of quantifying, predicting and understanding state-dependent, nonlinear interactions as they occur in situ and in real time—a requirement for managing resources in a nonlinear, non-equilibrium world.     

Determination of the trend of incidence of cutaneous leishmaniasis in Kerman province 2014-2020 and forecasting until 2023. A time series study

IntroductionCutaneous leishmaniasis (CL) is currently a health problem in several parts of Iran, particularly Kerman. This study was conducted to determine the incidence and trend of CL in Kerman during 2014–2020 and its forecast up to 2023. The effects of meteorological variables on incidence was also evaluated.Materials and methods4993 definite cases of CL recorded from January 2014 to December 2020 by the Vice-Chancellor for Health at Kerman University of Medical Sciences were entered. Meteorological variables were obtained from the national meteorological site. The time series SARIMA methods were used to evaluate the effects of meteorological variables on CL.ResultsMonthly rainfall at the lag 0 (β = -0.507, 95% confidence interval:-0.955,-0.058) and monthly sunny hours at the lag 0 (β = -0.214, 95% confidence interval:-0.308,-0.119) negatively associated with the incidence of CL. Based on the Akaike information criterion (AIC) the multivariable model (AIC = 613) was more suitable than univariable model (AIC = 690.66) to estimate the trend and forecast the incidence up to 36 months.ConclusionThe decreasing pattern of CL in Kerman province highlights the success of preventive, diagnostic and therapeutic interventions during the recent years. However, due to endemicity of disease, extension and continuation of such interventions especially before and during the time periods with higher incidence is essential.     

Determining the degree of chaos from analysis of ISI time series in the nervous system: a comparison between correlation dimension and nonlinear forecasting methods

Two different chaotic time series analysis methods – the correlation dimension and nonlinear forecasting – are introduced and then used to process the interspike intervals (ISI) of the action potential trains propagated along a single nerve fiber of the anesthetized rat. From the results, the conclusion is drawn that compared with the correlation dimension, nonlinear forecasting is more efficient and robust for chaotic ISI time series analysis in a noisy environment. Moreover, the evolution of the correlation coefficient curves calculated from nonlinear forecasting can qualitatively give a better reflection of the unpredictability of the system's future behavior and is in good agreement with the values of the largest Lyapunov exponent that quantitatively measures the degree of chaos. Received: 19 November 1996 / Accepted in revised form: 15 September 1997