Nonlinear Time Series Models Research Articles

GARCH and ANN-based DDoS detection and filtering in cloud computing environment

Nowadays, distributed denial-of-service (DDoS) attack is one of the major security threats in cloud computing environment as it compromises the availability of the services and risks everything including financial loss, reputation and losing faith of the customers. In this paper, we have proposed a novel solution, which can detect DDoS attack traffic in cloud environment using chaos theory. To predict the network traffic state, nonlinear time series model [i.e., generalised autoregressive conditional heteroskedasticity (GARCH) model] is used as it can capture the long-range dependence (LRD) and long-tail distribution which is an important property of network traffic. Prediction error is calculated using the prediction made by GARCH model and actual traffic pattern. Filtering is carried out using back propagation artificial neural network (ANN) on the traffic that exceeds the certain limit specified by some threshold. In our proposed approach, threshold is calculated dynamically, which makes our approach platform independent.

Asymmetric Adjustments of U.S. Interest Rates

Literature on dynamics of the term structure of interest rates supports that the adjustment of interest rate spread may be well described by nonlinear time series models. This paper examines the relationship between the 3-Month Treasury Bill Rate (DTB3) and 10-Year Treasury Rate (DSG10) from January 1962 to November 2015 by employing the Markov-switching VEC model, which allows for the asymmetric adjustment of interest rates to the long run equilibrium across regimes. We find that the high-volatility regime more frequently exists prior to the 1990s, and the low-volatility one occurs more often after 1990s. Secondly, with allowing for the distinct short-run adjustment parameters in the MS-VECM setup, we find that the evidence of asymmetric adjustments of interest rates to the long run equilibrium in difference regimes. More specifically, the long-term interest rate adjusts more quickly towards the long run equilibrium in the high-volatility regimes than in the low-volatility one. Moreover, by comparing the impulses response functions of linear and nonlinear models, we find that empirical results could be misleading if the regime shift is not taken into account.

Out-of-sample forecasting of the Canadian unemployment rates using univariate models

ABSTRACTThis article investigates the out-of-sample forecasting performance of some linear and nonlinear univariate time series models on the monthly seasonally adjusted Canadian unemployment rates during the 1980–2013 period. The findings reveal that nonlinear time series models better capture the asymmetry present in the unemployment rate series at short and long forecast horizons.

An Improved Particle Swarm Optimization Algorithm Of Radial Basis Neural Network

The core issues of RBF network design are to design the minimum structure neural networks that can meet the accuracy requirements, in order to ensure the generalization ability of the network. For the purpose of simplifying the structure of RBF network, proposes a learning method of RBF network based on improved particle swarm. The method automatically constructs frugal structure of RBF network model by the combining algorithm of regularized least squares method and Doptimal experimental design; chooses three learning parameters of the combining algorithm that can affect network generalization performance by the improved particle swarm optimization algorithm. By nonlinear time series modeling, verifies the effectiveness of the method in this paper.

Adaptive traffic parameter prediction: Effect of number of states and transferability of models

Traffic parameters can show shifts due to factors such as weather, accidents, and driving characteristics. This study develops a model for predicting traffic speeds under these abrupt changes within regime switching framework. The proposed approach utilizes Hidden Markov, Expectation Maximization, Recursive Least Squares Filtering, and ARIMA methods for an adaptive forecasting method. The method is compared with naive and mean updating linear and nonlinear time series models. The model is fitted and tested extensively using 1993 I-880 loop data from California and January 2014 INRIX data from Virginia. Analysis for number of states, impact of number of states on forecasting, prediction scope, and transferability of the model to different locations are investigated. A 5-state model is found to be providing best results. Developed model is tested for 1-step to 45-step forecasts. The accuracy of predictions are improved until 15-step over nonadaptive and mean adaptive models. Except 1-step predictions, the model is found to be transferable to different locations. Even if the developed model is not retrained on different datasets, it is able to provide better or close results with nonadaptive and adaptive models that are retrained on the corresponding dataset.

A New Multivariate Nonlinear Time Series Model for Portfolio Risk Measurement: The Threshold Copula‐Based TAR Approach

We propose a threshold copula‐based nonlinear time series model for evaluating quantitative risk measures for financial portfolios with a flexible structure to incorporate nonlinearities in both univariate (component) time series and their dependent structure. We incorporate different dependent structures of asset returns over different market regimes, which are manifested in their price levels. We estimate the model parameters by a two‐stage maximum likelihood method. Real financial data and appropriate statistical tests are used to illustrate the efficacy of the proposed model. Simulated results for sampling distribution of parameters estimates are given. Empirical results suggest that the proposed model leads to significant improvement of the accuracy of value‐at‐risk forecasts at the portfolio level.

Modelling of nonlinear filtering Poisson time series

In this article, algorithms of non-linear filtering of Poisson time series are tested using statistical modelling. The objective is to find a representation of a time series as a wavelet series with a small number of non-linear coefficients, which allows distinguishing statistically significant details. There are well-known efficient algorithms of non-linear wavelet filtering for the case when the values of a time series have a normal distribution. However, if the distribution is not normal, good results can be expected using the maximum likelihood estimations. The filtration is studied according to the criterion of maximum likelihood by the example of Poisson time series. For direct optimisation of the likelihood function, different stochastic (genetic algorithms, annealing method) and deterministic optimization algorithms are used. Testing of the algorithm using both simulated series and empirical data (series of rare words frequencies according to the Google Books Ngram data were used) showed that filtering based on the criterion of maximum likelihood has a great advantage over well-known algorithms for the case of Poisson series. Also, the most perspective methods of optimisation were selected for this problem.

Short-term wind speed forecasting: Application of linear and non-linear time series models

ABSTRACTThis study forecasts day-ahead wind speed at 15 minute intervals at the site of a wind turbine located in Maharashtra, India. Wind speed exhibits non-stationarity, seasonality and time-varying volatility clustering. Univariate linear and non-linear time series techniques namely MSARIMA, MSARIMA-GARCH and MSARIMA-EGARCH have been employed for forecasting wind speed using data span ranging from 3 days to 15 days. Study suggests that mean absolute percentage error (MAPE) values first decrease with the increase in data span, reaches its minima and then start increasing. All models provide superior forecasting performances with 5 days data span. It is further evident that ARIMA-GARCH model generates lowest MAPE with 5 days data span. All these models provide superior forecasts with respect to current industry practices. This study establishes that employing various linear and non-linear time series techniques for forecasting day-ahead wind speed can benefit the industry in terms of better operational management of wind turbines and better integration of wind energy into the power system, which have huge financial implications for wind power generators in India.

Analysis of cyclical fish landings through ESTAR nonlinear time-series approach

Exponential smooth transition autoregressive (ESTAR) is a family of parametric nonlinear time-series models capable of capturing the non-Gaussian characteristics of the time-series along with cyclical fluctuations. The present study is based on the time-series data on oilsardine landings from Kerala during the period 1961 to 2008. The parameters of the model were estimated by genetic algorithm (GA). From the analysis of data it was concluded that ESTAR model fitted through GA has performed better than ARIMA model.

Modelling directionality for paleoclimatic time series

The ice core time series from Vostok Station in Antarctica and the North Greenland Ice Core Project have seasonal variation corresponding to the Milankovitch cycles. After removing these cycles, and interpolating to equal time intervals, stationary time series models are fitted. The series show clear directionality and this feature is modelled by either non-Gaussian errors or non-linear time series models. Threshold autoregressive models are fitted by penalized least squares and compared with non-threshold autoregressive models. Since both ice core time series are reasonably modelled as first order autoregressive series with parameters close to one, directionality will arise from non-symmetric error distributions. However, two regime threshold autoregressive models, of order one and two for Greenland and Vostok, respectively, give an improved match to the observed directionality and a reduced sum of squared residuals. Realizations from the threshold autoregressive models are noticeably different from the non-threshold models. Since the non-threshold models are a restricted case of the threshold models, and the threshold models are a better fit to the observed time series, threshold models should provide more realistic realizations. References C. Chatfield. The Analysis of Time Series: An Introduction . CRC Press, 2004. https://www.crcpress.com/The-Analysis-of-Time-Series-An-Introduction-Sixth-Edition/Chatfield/p/book/9781584883173 A. J. Lawrance. Directionality and reversibility in time series. Int. Stat. Rev. 59(1):67–79, 1991. doi:10.2307/1403575 M. M. Mansor, M. E. Glonek, D. A. Green and A. V. Metcalfe. Threshold autoregressive models for directional time series. In I. Rojas and H. Pomares (Eds.), Time Series Analysis and Forecasting Selected Contributions from the ITISE Conference (ITISE 2015) . pp. 13–25, 2016. doi:10.1007/978-3-319-28725-6 M. M. Mansor, M. E. Glonek, D. A. Green and A. V. Metcalfe. Modelling directionality in stationary geophysical time series. International work-conference on Time Series (ITISE 2015) . http://www.researchgate.net/publication/281835075 M. M. Mansor, D. A. Green and A. V. Metcalfe. Modelling and simulation of directional financial time series. Proceedings of the 21st International Congress on Modelling and Simulation (MODSIM 2015) , pp. 1022–1028, 2015. http://www.mssanz.org.au/modsim2015/E4/mansor.pdf M. M. Mansor, D. A. Green and A. V. Metcalfe. Directionality and volatility in electroencephalogram time series. Proceedings of the 2nd International Conference on Mathematical Sciences and Statistics (ICMSS 2016), AIP Conf. Proc. 1739:020080, 2016. doi:10.1063/1.4952560 North Greenland Ice Core Project members. High-resolution record of Northern Hemisphere climate extending into the last interglacial period. Nature , 431:147–151, 2004. doi:10.1038/nature02805 J. R. Petit, J. Jouzel, D. Raynaud, N. I. Barkov, J.-M. Barnola, I. Basile, M. Bender, J. Chappellaz, M. Davis, G. Delaygue, M. Delmotte, V. M. Kotlyakov, M. Legrand, V. Y. Lipenkov, C. Lorius, L. Pepin, C. Ritz, E. Saltzman and M. Stievenard. Climate and atmospheric history of the past 420,000 years from the Vostok ice core, Antarctica. Nature , 399:429–436, 1999. doi:10.1038/20859 S. Soubeyrand, C. E. Morris and E. K. Bigg. Analysis of fragmented time directionality in time series to elucidate feedbacks in climate data. Environ. Modell. Softw. 61:78–86, 2014. doi:10.1016/j.envsoft.2014.07.003

Short-term freeway traffic parameter prediction: Application of grey system theory models

Intelligent transportation systems applications require accurate and robust prediction of traffic parameters such as speed, travel time, and flow. However, traffic exhibits sudden shifts due to various factors such as weather, accidents, driving characteristics, and demand surges, which adversely affect the performance of the prediction models. This paper studies possible applications and accuracy levels of three Grey System theory models for short-term traffic speed and travel time predictions: first order single variable Grey model (GM(1,1)), GM(1,1) with Fourier error corrections (EFGM), and the Grey Verhulst model with Fourier error corrections (EFGVM). Grey models are tested on datasets from California and Virginia. They are compared to nonlinear time series models. Grey models are found to be simple, adaptive, able to deal better with abrupt parameter changes, and not requiring many data points for prediction updates. Based on the sample data used, Grey models consistently demonstrate lower prediction errors over all the time series improving the accuracy on average about 50% in Root Mean Squared Errors and Mean Absolute Percent Errors.

An evolutionary hybrid Fuzzy Computationally Efficient EGARCH model for volatility prediction

Accurate modeling for forecasting of stock market volatility is a widely interesting research area both in academia as well as financial markets. This paper proposes an innovative Fuzzy Computationally Efficient EGARCH model to forecast the volatility of three stock market indexes. The proposed model represents a joint estimation of the membership function parameters of a TSK-type fuzzy inference system along with the leverage effect, asymmetric shock by leverage effect of EGARCH model in forecasting highly nonlinear and complicated financial time series model more accurately. Further unlike the conventional TSK type fuzzy neural network the proposed model uses a functional link neural network (FLANN) in the consequent part of the fuzzy rules to provide an improved mapping. Moreover, a differential evolution (DE) algorithm is suggested to solve the parameters estimation problem of Fuzzy Computationally Efficient EGARCH model. Being a parallel direct search algorithm, DE has the strength of finding global optimal solutions regardless of the initial values of its few control parameters. Furthermore, the DE based algorithm aims to achieve an optimal solution with a rapid convergence rate. The proposed model has been compared with some GARCH family models and hybrid fuzzy systems and GARCH models based on three performance metrics: MSFE, RMSFE, and MAFE. The results indicate that the proposed method offers significant improvements in volatility forecasting performance in comparison with all other specified models.

Local Gaussian Autocorrelation and Tests for Serial Independence

The traditional and most used measure for serial dependence in a time series is the autocorrelation function. This measure gives a complete characterization of dependence for a Gaussian time series, but it often fails for nonlinear time series models as, for instance, the generalized autoregressive conditional heteroskedasticity model (GARCH), where it is zero for all lags. The autocorrelation function is an example of aglobalmeasure of dependence. The purpose of this article is to apply to time series a well‐definedlocalmeasure of serial dependence called the local Gaussian autocorrelation. It generally works well also for nonlinear models, and it can distinguish between positive and negative dependence. We use this measure to construct a test of independence based on the bootstrap technique. This procedure requires the choice of a bandwidth parameter that is calculated using a cross validation algorithm. To ensure the validity of the test, asymptotic properties are derived for the test functional and for the bootstrap procedure, together with a study of its power for different models. We compare the proposed test with one based on the ordinary autocorrelation and with one based on the Brownian distance correlation. The new test performs well. Finally, there are also two empirical examples.

Forecasting with nonlinear time series model: A Monte-Carlo bootstrap approach

In this paper, we propose a new method of forecasting with nonlinear time series model using Monte-Carlo Bootstrap method. This new method gives better result in terms of forecast root mean squared error (RMSE) when compared with the traditional Bootstrap method and Monte-Carlo method of forecasting using a special nonlinear time series model, called logistic smooth transition autoregressive (LSTAR) model. We illustrate this new method using some simulation experiments. Keywords : Bootstrap, Forecasting, LSTAR, Monte-Carlo, Monte-Carlo Bootstrap

Investigating Changes in Brain Network Properties in HIV-Associated Neurocognitive Disease (HAND) using Mutual Connectivity Analysis (MCA).

About 50% of subjects infected with HIV present deficits in cognitive domains, which are known collectively as HIV associated neurocognitive disorder (HAND). The underlying synaptodendritic damage can be captured using resting state functional MRI, as has been demonstrated by a few earlier studies. Such damage may induce topological changes of brain connectivity networks. We test this hypothesis by capturing the functional interdependence of 90 brain network nodes using a Mutual Connectivity Analysis (MCA) framework with non-linear time series modeling based on Generalized Radial Basis function (GRBF) neural networks. The network nodes are selected based on the regions defined in the Automated Anatomic Labeling (AAL) atlas. Each node is represented by the average time series of the voxels of that region. The resulting networks are then characterized using graph-theoretic measures that quantify various network topology properties at a global as well as at a local level. We tested for differences in these properties in network graphs obtained for 10 subjects (6 male and 4 female, 5 HIV+ and 5 HIV-). Global network properties captured some differences between these subject cohorts, though significant differences were seen only with the clustering coefficient measure. Local network properties, such as local efficiency and the degree of connections, captured significant differences in regions of the frontal lobe, precentral and cingulate cortex amongst a few others. These results suggest that our method can be used to effectively capture differences occurring in brain network connectivity properties revealed by resting-state functional MRI in neurological disease states, such as HAND.

Nonlinear Time Series and Neural-Network Models of Exchange Rates between the US Dollar and Major Currencies

This paper features an analysis of major currency exchange rate movements in relation to the US dollar, as constituted in US dollar terms. Euro, British pound, Chinese yuan, and Japanese yen are modelled using a variety of non-linear models, including smooth transition regression models, logistic smooth transition regressions models, threshold autoregressive models, nonlinear autoregressive models, and additive nonlinear autoregressive models, plus Neural Network models. The models are evaluated on the basis of error metrics for twenty day out-of-sample forecasts using the mean average percentage errors (MAPE). The results suggest that there is no dominating class of time series models, and the different currency pairs relationships with the US dollar are captured best by neural net regression models, over the ten year sample of daily exchange rate returns data, from August 2005 to August 2015.

Jump-Preserving Varying-Coefficient Models for Nonlinear Time Series

An important and widely used class of semiparametric models is formed by the varying-coefficient models. Although the varying coefficients are traditionally assumed to be smooth functions, the varying-coefficient model is considered here with the coefficient functions containing a finite set of discontinuities. Contrary to the existing nonparametric and varying-coefficient estimation of piecewise smooth functions, the varying-coefficient models are considered here under dependence and are applicable in time series with heteroscedastic and serially correlated errors. Additionally, the conditional error variance is allowed to exhibit discontinuities at a finite set of points too. The (uniform) consistency and asymptotic normality of the proposed estimators are established and the finite-sample performance is tested via a simulation study.

Information criteria for nonlinear time series models

AbstractIn this paper the performance of different information criteria for simultaneous model class and lag order selection is evaluated using simulation studies. We focus on the ability of the criteria to distinguish linear and nonlinear models. In the simulation studies, we consider three different versions of the commonly known criteria AIC, SIC and AICc. In addition, we also assess the performance of WIC and evaluate the impact of the error term variance estimator. Our results confirm the findings of different authors that AIC and AICc favor nonlinear over linear models, whereas weighted versions of WIC and all versions of SIC are able to successfully distinguish linear and nonlinear models. However, the discrimination between different nonlinear model classes is more difficult. Nevertheless, the lag order selection is reliable. In general, information criteria involving the unbiased error term variance estimator overfit less and should be preferred to using the usual ML estimator of the error term variance.

Application of Chaos Theory in the Prediction of Motorised Traffic Flows on Urban Networks

In recent times, urban road networks are faced with severe congestion problems as a result of the accelerating demand for mobility. One of the ways to mitigate the congestion problems on urban traffic road network is by predicting the traffic flow pattern. Accurate prediction of the dynamics of a highly complex system such as traffic flow requires a robust methodology. An approach for predicting Motorised Traffic Flow on Urban Road Networks based on Chaos Theory is presented in this paper. Nonlinear time series modeling techniques were used for the analysis of the traffic flow prediction with emphasis on the technique of computation of the Largest Lyapunov Exponent to aid in the prediction of traffic flow. The study concludes that algorithms based on the computation of the Lyapunov time seem promising as regards facilitating the control of congestion because of the technique’s effectiveness in predicting the dynamics of complex systems especially traffic flow.

On business cycle fluctuations in USA macroeconomic time series

This study employs eighteen USA macroeconomic time series variables to investigate possible existence of asymmetries in business cycle fluctuations in the series. Detection of asymmetric fluctuations in economic activity is important for policymakers since effective monetary policy relies on asymmetric business cycle fluctuations in all the series. The asymmetric deviations from the long-term growth trend in each of the series are modeled using regime switching models and artificial neural networks. The results based on nonlinear switching time series models reveal strong evidence of business cycle asymmetries in most of the series. The results based on in-sample approximations from artificial neural networks show statistically significant evidence of asymmetries in all the series. Similar results are obtained when jackknife out-of-sample approximations from artificial neural networks are used. Thus, the study results show statistically significant evidence of asymmetries in all the series which indicates that business cycle fluctuations in the series are asymmetric, thus alike. Therefore, the impact of monetary policy shocks on the output and the other macroeconomic variables can be anticipated using nonlinear models only. The results on asymmetric business cycle fluctuations in real GDP are in line with recent studies but in sharp contrast with Balke and Fomby (1994).