Nonlinear Time Series Approach Research Articles

Disentangling extrinsic from intrinsic factors in disease dynamics: a nonlinear time series approach with an application to cholera.

Alternative explanations for disease and other population cycles typically include extrinsic environmental drivers, such as climate variability, and intrinsic nonlinear dynamics resulting from feedbacks within the system, such as species interactions and density dependence. Because these different factors can interact in nonlinear systems and can give rise to oscillations whose frequencies differ from those of extrinsic drivers, it is difficult to identify their respective contributions from temporal population patterns. In the case of disease, immunity is an important intrinsic factor. However, for many diseases, such as cholera, for which immunity is temporary, the duration and decay pattern of immunity is not well known. We present a nonlinear time series model with two related objectives: the reconstruction of immunity patterns from data on cases and population sizes and the identification of the respective roles of extrinsic and intrinsic factors in the dynamics. Extrinsic factors here include both seasonality and long-term changes or interannual variability in forcing. Results with simulated data show that this semiparametric method successfully recovers the decay of immunity and identifies the origin of interannual variability. An application to historical cholera data indicates that temporary immunity can be long-lasting and decays in approximately 9 yr. Extrinsic forcing of transmissibility is identified to have a strong seasonal component along with a long-term decrease. Furthermore, noise appears to sustain the multiple frequencies in the long-term dynamics. Similar semiparametric models should apply to population data other than for disease.

Optimization of Dynamic Neural Network Performance for Short-Term Traffic Prediction

An approach is presented for optimizing short-term traffic-prediction performance by using multiple topologies of dynamic neural networks and various network-related and traffic-related settings. The conducted study emphasized the potential benefit of optimizing the prediction performance by deploying multimodel approaches under parameters and traffic-condition settings. Emphasis was placed on the application of temporal-processing topologies in short-term speed predictions in the range of 5-min to 20-min horizons. Three network topologies were used: Jordan–Elman networks, partially recurrent networks, and time-lagged feedforward networks. The input patterns were constructed from data collected at the target location and at upstream and downstream locations. However, various combinations were also considered. To encourage the networks to associate with historical information on recurrent conditions, a time factor was attached to the input patterns to introduce time-recognition capabilities, in addition to information encoded in the recent past data. The optimal prediction settings (type of topology and input settings) were determined so that performance was maximized under different traffic conditions at the target and adjacent locations. The optimized performance of the dynamic neural networks was compared to that of a statistical nonlinear time series approach, which was outperformed in most cases. The study showed that no single topology consistently outperformed the others for all prediction horizons considered. However, the results showed that the significance of introducing the time factor was more pronounced under longer prediction horizons. A comparative evaluation of performance of optimal and nonoptimal settings showed substantial improvement in most cases. The applied procedure can also be used to identify the prediction reliability of information-dissemination systems.

A non-linear time series approach to modelling asymmetry in stock market indexes

In this paper we analyse the performances of a novel approach to modelling non-linear conditionally heteroscedastic time series characterised by asymmetries in both the conditional mean and variance. This is based on the combination of a TAR model for the conditional mean with a Constrained Changing Parameters Volatility (CPV-C) model for the conditional variance. Empirical results are given for the daily returns of the S&P 500, NASDAQ composite and FTSE 100 stock market indexes.

Travel-Time Prediction for Freeway Corridors

The application of a nonlinear time series model to the prediction of traffic parameters on a freeway network is investigated. The nonlinear time series approach is a statistical technique that has strong potential for on-line implementation. A new approach for predicting corridor travel times is developed and tested with travel-time data. The travel-time data are derived from observed speed data, which are collected from an 18-km (11.2-mi) freeway section in Orlando, Florida. The westbound Interstate-4 morning peak period (6:00 to 10:00 a.m.) for 20 incident-free days is tested with the goal of predicting recurrent congestion. The problem is addressed from the perspectives of single-variable and multiple-variable prediction of corridor travel times. In single-variable prediction, speed time-series data are used to forecast travel times along the freeway corridor. A calibrated single-variable prediction model is developed through the application of decay factors to smooth out the input data and the establishment of a threshold on the minimum speed prediction permitted. Multivariable prediction schemes are developed using speed, occupancy, and volume data provided by inductive loop detectors on the study section. The prediction performance of the calibrated single-variable model is shown to be superior to the multivariable prediction schemes. This new approach produces reasonable errors for short-term (5-min) travel-time predictions. The developed model can be implemented on-line with minimal effort.

Empirical determinants of measles metapopulation dynamics in England and Wales.

A key issue in metapopulation dynamics is the relative impact of internal patch dynamics and coupling between patches. This problem can be addressed by analysing large spatiotemporal data sets, recording the local and global dynamics of metapopulations. In this paper, we analyse the dynamics of measles meta-populations in a large spatiotemporal case notification data set, collected during the pre-vaccination era in England and Wales. Specifically, we use generalized linear statistical models to quantify the relative importance of local influences (birth rate and population size) and regional coupling on local epidemic dynamics. Apart from the proportional effect of local population size on case totals, the models indicate patterns of local and regional dynamic influences which depend on the current state of epidemics. Birth rate and geographic coupling are not associated with the size of major epidemics. By contrast, minor epidemics--and especially the incidence of local extinction of infection--are influenced both by birth rate and geographical coupling. Birth rate at a lag of four years provides the best fit, reflecting the delayed recruitment of susceptibles to school cohorts. A hierarchical index of spatial coupling to large centres provides the best spatial model. The model also indicates that minor epidemics and extinction patterns are more strongly influenced by this regional effect than the local impact of birth rate.

Physical nearest-neighbour models and non-linear time-series. II Further discussion of approximate solutions and exact equations

The approximate two- and three-dimensional solutions for spatial correlations, using the non-linear time-series approach for nearest-neighbour systems developed in my previous paper, are further discussed.Orthogonal expansions for the correlation functions are also developed which determine with this approach, though so far only in principle, the exact solutions.

Physical nearest-neighbour models and non-linear time-series. II Further discussion of approximate solutions and exact equations

The approximate two- and three-dimensional solutions for spatial correlations, using the non-linear time-series approach for nearest-neighbour systems developed in my previous paper, are further discussed. Orthogonal expansions for the correlation functions are also developed which determine with this approach, though so far only in principle, the exact solutions.