Search results for: time series models

Authors: Shigeaki Sakurai, Ken Ueno, Ryohei Orihara

Abstract:

This paper proposes a method that discovers time series event patterns from textual data with time information. The patterns are composed of sequences of events and each event is extracted from the textual data, where an event is characteristic content included in the textual data such as a company name, an action, and an impression of a customer. The method introduces 7 types of time constraints based on the analysis of the textual data. The method also evaluates these constraints when the frequency of a time series event pattern is calculated. We can flexibly define the time constraints for interesting combinations of events and can discover valid time series event patterns which satisfy these conditions. The paper applies the method to daily business reports collected by a sales force automation system and verifies its effectiveness through numerical experiments.

Keywords: Text mining, sequential mining, time constraints, daily business reports.

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Authors: Muhammad Imran, Iqra Basit, Mobushir Riaz Khan, Sajid Rasheed Ahmad

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The present study investigates the space-time impact of climate change on the rice crop calendar in tropical Gujranwala, Pakistan. The climate change impact was quantified through the climatic variables, whereas the existing calendar of the rice crop was compared with the phonological stages of the crop, depicted through the time series of the Normalized Difference Vegetation Index (NDVI) derived from Landsat data for the decade 2005-2015. Local maxima were applied on the time series of NDVI to compute the rice phonological stages. Panel models with fixed and cross-section fixed effects were used to establish the relation between the climatic parameters and the time-series of NDVI across villages and across rice growing periods. Results show that the climatic parameters have significant impact on the rice crop calendar. Moreover, the fixed effect model is a significant improvement over cross-sectional fixed effect models (R-squared equal to 0.673 vs. 0.0338). We conclude that high inter-annual variability of climatic variables cause high variability of NDVI, and thus, a shift in the rice crop calendar. Moreover, inter-annual (temporal) variability of the rice crop calendar is high compared to the inter-village (spatial) variability. We suggest the local rice farmers to adapt this change in the rice crop calendar.

Keywords: Landsat NDVI, panel models, temperature, rainfall.

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Authors: S. V. Yendiyarov

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Pattern discovery from time series is of fundamental importance. Particularly, when information about the structure of a pattern is not complete, an algorithm to discover specific patterns or shapes automatically from the time series data is necessary. The dynamic time warping is a technique that allows local flexibility in aligning time series. Because of this, it is widely used in many fields such as science, medicine, industry, finance and others. However, a major problem of the dynamic time warping is that it is not able to work with structural changes of a pattern. This problem arises when the structure is influenced by noise, which is a common thing in practice for almost every application. This paper addresses this problem by means of developing a novel technique called adaptive dynamic time warping.

Keywords: Pattern recognition, optimal control, quadratic programming, dynamic programming, dynamic time warping, sintering control.

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Authors: Tahseen A. Jilani, S. M. Aqil Burney, C. Ardil

Abstract:

In this paper, we have presented a new multivariate fuzzy time series forecasting method. This method assumes mfactors with one main factor of interest. History of past three years is used for making new forecasts. This new method is applied in forecasting total number of car accidents in Belgium using four secondary factors. We also make comparison of our proposed method with existing methods of fuzzy time series forecasting. Experimentally, it is shown that our proposed method perform better than existing fuzzy time series forecasting methods. Practically, actuaries are interested in analysis of the patterns of causalities in road accidents. Thus using fuzzy time series, actuaries can define fuzzy premium and fuzzy underwriting of car insurance and life insurance for car insurance. National Institute of Statistics, Belgium provides region of risk classification for each road. Thus using this risk classification, we can predict premium rate and underwriting of insurance policy holders.

Keywords: Average forecasting error rate (AFER), Fuzziness offuzzy sets Fuzzy, If-Then rules, Multivariate fuzzy time series.

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Authors: Shumin Hou, Yourong Li, Sanxing Zhao

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Much time series data is generally from continuous dynamic system. Firstly, this paper studies the detection of the nonlinearity of time series from continuous dynamics systems by applying the Phase-randomized surrogate algorithm. Then, the Delay Vector Variance (DVV) method is introduced into nonlinearity test. The results show that under the different sampling conditions, the opposite detection of nonlinearity is obtained via using traditional test statistics methods, which include the third-order autocovariance and the asymmetry due to time reversal. Whereas the DVV method can perform well on determining nonlinear of Lorenz signal. It indicates that the proposed method can describe the continuous dynamics signal effectively.

Keywords: Nonlinearity, Time series, continuous dynamics system, DVV method

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Authors: B. Q. Huang, Tarik Rashid, M-T. Kechadi

Abstract:

this paper presents a multi-context recurrent network for time series analysis. While simple recurrent network (SRN) are very popular among recurrent neural networks, they still have some shortcomings in terms of learning speed and accuracy that need to be addressed. To solve these problems, we proposed a multi-context recurrent network (MCRN) with three different learning algorithms. The performance of this network is evaluated on some real-world application such as handwriting recognition and energy load forecasting. We study the performance of this network and we compared it to a very well established SRN. The experimental results showed that MCRN is very efficient and very well suited to time series analysis and its applications.

Keywords: Gradient descent method, recurrent neural network, learning algorithms, time series, BP

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Authors: Darren Zou

Abstract:

Forecasting the stock market is a very challenging task. Various economic indicators such as GDP, exchange rates, interest rates, and unemployment have a substantial impact on the stock market. Time series models are the traditional methods used to predict stock market changes. In this paper, a machine learning method, Bayesian Additive Regression Tree (BART) is used in predicting stock market indexes based on multiple economic indicators. BART can be used to model heterogeneous treatment effects, and thereby works well when models are misspecified. It also has the capability to handle non-linear main effects and multi-way interactions without much input from financial analysts. In this research, BART is proposed to provide a reliable prediction on day-to-day stock market activities. By comparing the analysis results from BART and with time series method, BART can perform well and has better prediction capability than the traditional methods.

Keywords: Bayesian, Forecast, Stock, BART.

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Authors: Rampal Singh, S. Balasundaram

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In this paper, we study the application of Extreme Learning Machine (ELM) algorithm for single layered feedforward neural networks to non-linear chaotic time series problems. In this algorithm the input weights and the hidden layer bias are randomly chosen. The ELM formulation leads to solving a system of linear equations in terms of the unknown weights connecting the hidden layer to the output layer. The solution of this general system of linear equations will be obtained using Moore-Penrose generalized pseudo inverse. For the study of the application of the method we consider the time series generated by the Mackey Glass delay differential equation with different time delays, Santa Fe A and UCR heart beat rate ECG time series. For the choice of sigmoid, sin and hardlim activation functions the optimal values for the memory order and the number of hidden neurons which give the best prediction performance in terms of root mean square error are determined. It is observed that the results obtained are in close agreement with the exact solution of the problems considered which clearly shows that ELM is a very promising alternative method for time series prediction.

Keywords: Chaotic time series, Extreme learning machine, Generalization performance.

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Authors: Rao Fu, Jie Chen, Shutian Zeng, Yiping Zhuang, Agus Sudjianto

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Generative Adversarial Net (GAN) has proved to be a powerful machine learning tool in image data analysis and generation. In this paper, we propose to use Conditional Generative Adversarial Net (CGAN) to learn and simulate time series data. The conditions include both categorical and continuous variables with different auxiliary information. Our simulation studies show that CGAN has the capability to learn different types of normal and heavy-tailed distributions, as well as dependent structures of different time series. It also has the capability to generate conditional predictive distributions consistent with training data distributions. We also provide an in-depth discussion on the rationale behind GAN and the neural networks as hierarchical splines to establish a clear connection with existing statistical methods of distribution generation. In practice, CGAN has a wide range of applications in market risk and counterparty risk analysis: it can be applied to learn historical data and generate scenarios for the calculation of Value-at-Risk (VaR) and Expected Shortfall (ES), and it can also predict the movement of the market risk factors. We present a real data analysis including a backtesting to demonstrate that CGAN can outperform Historical Simulation (HS), a popular method in market risk analysis to calculate VaR. CGAN can also be applied in economic time series modeling and forecasting. In this regard, we have included an example of hypothetical shock analysis for economic models and the generation of potential CCAR scenarios by CGAN at the end of the paper.

Keywords: Conditional Generative Adversarial Net, market and credit risk management, neural network, time series.

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Authors: Ilaria Lucrezia Amerise

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Electricity markets throughout the world have undergone substantial changes. Accurate, reliable, clear and comprehensible modeling and forecasting of different variables (loads and prices in the first instance) have achieved increasing importance. In this paper, we describe the actual state of the art focusing on reg-SARMA methods, which have proven to be flexible enough to accommodate the electricity price/load behavior satisfactory. More specifically, we will discuss: 1) The dichotomy between point and interval forecasts; 2) The difficult choice between stochastic (e.g. climatic variation) and non-deterministic predictors (e.g. calendar variables); 3) The confrontation between modelling a single aggregate time series or creating separated and potentially different models of sub-series. The noteworthy point that we would like to make it emerge is that prices and loads require different approaches that appear irreconcilable even though must be made reconcilable for the interests and activities of energy companies.

Keywords: Forecasting problem, interval forecasts, time series, electricity prices, reg-plus-SARMA methods.

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Authors: M. A. Torkamani, S. Mahmoodzadeh, S. Pourroostaei, C. Lucas

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Daily production of information and importance of the sequence of produced data in forecasting future performance of market causes analysis of data behavior to become a problem of analyzing time series. But time series that are very complicated, usually are random and as a result their changes considered being unpredictable. While these series might be products of a deterministic dynamical and nonlinear process (chaotic) and as a result be predictable. Point of Chaotic theory view, complicated systems have only chaotically face and as a result they seem to be unregulated and random, but it is possible that they abide by a specified math formula. In this article, with regard to test of strange attractor and biggest Lyapunov exponent probability of chaos on several foreign exchange rates vs. IRR (Iranian Rial) has been investigated. Results show that data in this market have complex chaotic behavior with big degree of freedom.

Keywords: Chaos, Exchange Rate, Nonlinear Models.

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Authors: Farhad Asadi, Mohammad Javad Mollakazemi, Aref Ghafouri

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Recent research in neural networks science and neuroscience for modeling complex time series data and statistical learning has focused mostly on learning from high input space and signals. Local linear models are a strong choice for modeling local nonlinearity in data series. Locally weighted projection regression is a flexible and powerful algorithm for nonlinear approximation in high dimensional signal spaces. In this paper, different learning scenario of one and two dimensional data series with different distributions are investigated for simulation and further noise is inputted to data distribution for making different disordered distribution in time series data and for evaluation of algorithm in locality prediction of nonlinearity. Then, the performance of this algorithm is simulated and also when the distribution of data is high or when the number of data is less the sensitivity of this approach to data distribution and influence of important parameter of local validity in this algorithm with different data distribution is explained.

Keywords: Local nonlinear estimation, LWPR algorithm, Online training method.

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Authors: Guoyuan Qi , Yskandar Hamam, Barend Jacobus van Wyk, Shengzhi Du

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The majority of existing predictors for time series are model-dependent and therefore require some prior knowledge for the identification of complex systems, usually involving system identification, extensive training, or online adaptation in the case of time-varying systems. Additionally, since a time series is usually generated by complex processes such as the stock market or other chaotic systems, identification, modeling or the online updating of parameters can be problematic. In this paper a model-free predictor (MFP) for a time series produced by an unknown nonlinear system or process is derived using tracking theory. An identical derivation of the MFP using the property of the Newton form of the interpolating polynomial is also presented. The MFP is able to accurately predict future values of a time series, is stable, has few tuning parameters and is desirable for engineering applications due to its simplicity, fast prediction speed and extremely low computational load. The performance of the proposed MFP is demonstrated using the prediction of the Dow Jones Industrial Average stock index.

Keywords: Forecast, model-free predictor, prediction, time series

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Authors: Tushnik Sarkar, Mofazzal H. Khondekar, Subrata Banerjee

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This paper investigates the nature of the fluctuation of the daily average Solar wind speed time series collected over a period of 2492 days, from 1^st January, 1997 to 28^th October, 2003. The degree of self-similarity and scalability of the Solar Wind Speed signal has been explored to characterise the signal fluctuation. Multi-fractal Detrended Fluctuation Analysis (MFDFA) method has been implemented on the signal which is under investigation to perform this task. Furthermore, the singularity spectra of the signals have been also obtained to gauge the extent of the multifractality of the time series signal.

Keywords: Detrended fluctuation analysis, generalized Hurst exponent, holder exponents, multifractal exponent, multifractal spectrum, singularity spectrum, time series analysis.

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Authors: Chee Peng Lim, Wei Yee Goh

Abstract:

In this paper, the application of multiple Elman neural networks to time series data regression problems is studied. An ensemble of Elman networks is formed by boosting to enhance the performance of the individual networks. A modified version of the AdaBoost algorithm is employed to integrate the predictions from multiple networks. Two benchmark time series data sets, i.e., the Sunspot and Box-Jenkins gas furnace problems, are used to assess the effectiveness of the proposed system. The simulation results reveal that an ensemble of boosted Elman networks can achieve a higher degree of generalization as well as performance than that of the individual networks. The results are compared with those from other learning systems, and implications of the performance are discussed.

Keywords: AdaBoost, Elman network, neural network ensemble, time series regression.

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Authors: Mogari I. Rapoo, Diteboho Xaba

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This paper examines the forecasting performance of Autoregressive Integrated Moving Average (ARIMA) and Artificial Neural Networks (ANN) models with the published exchange rate obtained from South African Reserve Bank (SARB). ARIMA is one of the popular linear models in time series forecasting for the past decades. ARIMA and ANN models are often compared and literature revealed mixed results in terms of forecasting performance. The study used the MSE and MAE to measure the forecasting performance of the models. The empirical results obtained reveal the superiority of ARIMA model over ANN model. The findings further resolve and clarify the contradiction reported in literature over the superiority of ARIMA and ANN models.

Keywords: ARIMA, artificial neural networks models, error metrics, exchange rates.

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Authors: Rana Khalid Naeem, Asif Mansoor

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Periodicities in the environmetric time series can be idyllically assessed by utilizing periodic models. In this communication fugitive emission of gases from open sewer channel Lyari which follows periodic behaviour are approximated by employing periodic autoregressive model of order p. The orders of periodic model for each season are selected through the examination of periodic partial autocorrelation or information criteria. The parameters for the selected order of season are estimated individually for each emitted air toxin. Subsequently, adequacies of fitted models are established by examining the properties of the residual for each season. These models are beneficial for schemer and administrative bodies for the improvement of implemented policies to surmount future environmental problems.

Keywords: Exchange of Gases, Goodness of Fit, Open Sewer Channel, PAR(p) Models, Periodicities, Season Wise Models.

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Authors: Sudip Kumar Kundu, Charu Singh

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As a great physiographic divide, the Himalayas affecting a large system of water and air circulation which helps to determine the climatic condition in the Indian subcontinent to the south and mid-Asian highlands to the north. It creates obstacles by defending chill continental air from north side into India in winter and also defends rain-bearing southwesterly monsoon to give up maximum precipitation in that area in monsoon season. Nowadays extreme weather conditions such as heavy precipitation, cloudburst, flash flood, landslide and extreme avalanches are the regular happening incidents in the region of North Western Himalayan (NWH). The present study has been planned to investigate the suitable model(s) to find out the rainfall pattern over that region. For this investigation, selected models from Coordinated Regional Climate Downscaling Experiment (CORDEX) and Coupled Model Intercomparison Project Phase 5 (CMIP5) has been utilized in a consistent framework for the period of 1976 to 2000 (historical). The ability of these driving models from CORDEX domain and CMIP5 has been examined according to their capability of the spatial distribution as well as time series plot of rainfall over NWH in the rainy season and compared with the ground-based Indian Meteorological Department (IMD) gridded rainfall data set. It is noted from the analysis that the models like MIROC5 and MPI-ESM-LR from the both CORDEX and CMIP5 provide the best spatial distribution of rainfall over NWH region. But the driving models from CORDEX underestimates the daily rainfall amount as compared to CMIP5 driving models as it is unable to capture daily rainfall data properly when it has been plotted for time series (TS) individually for the state of Uttarakhand (UK) and Himachal Pradesh (HP). So finally it can be said that the driving models from CMIP5 are better than CORDEX domain models to investigate the rainfall pattern over NWH region.

Keywords: Global warming, rainfall, CMIP5, CORDEX, North Western Himalayan region.

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Authors: Nabilah Filzah Mohd Radzuan, Zalinda Othman, Azuraliza Abu Bakar, Abdul Razak Hamdan

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Uncertain data is believed to be an important issue in building up a prediction model. The main objective in the time series uncertainty analysis is to formulate uncertain data in order to gain knowledge and fit low dimensional model prior to a prediction task. This paper discusses the performance of a number of techniques in dealing with uncertain data specifically those which solve uncertain data condition by minimizing the loss of compression properties.

Keywords: Compression properties, uncertainty, uncertain time series, mining technique, weather prediction.

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Authors: Muzaffar Bashir, Jürgen Kempf

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The purpose of this paper is to present a Dynamic Time Warping technique which reduces significantly the data processing time and memory size of multi-dimensional time series sampled by the biometric smart pen device BiSP. The acquisition device is a novel ballpoint pen equipped with a diversity of sensors for monitoring the kinematics and dynamics of handwriting movement. The DTW algorithm has been applied for time series analysis of five different sensor channels providing pressure, acceleration and tilt data of the pen generated during handwriting on a paper pad. But the standard DTW has processing time and memory space problems which limit its practical use for online handwriting recognition. To face with this problem the DTW has been applied to the sum of the five sensor signals after an adequate down-sampling of the data. Preliminary results have shown that processing time and memory size could significantly be reduced without deterioration of performance in single character and word recognition. Further excellent accuracy in recognition was achieved which is mainly due to the reduced dynamic time warping RDTW technique and a novel pen device BiSP.

Keywords: Biometric character recognition, biometric person authentication, biometric smart pen BiSP, dynamic time warping DTW, online-handwriting recognition, multidimensional time series.

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Authors: Myint Myint Yi, Khin Sandar Linn, Marlar Kyaw

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This paper proposed a novel model for short term load forecast (STLF) in the electricity market. The prior electricity demand data are treated as time series. The model is composed of several neural networks whose data are processed using a wavelet technique. The model is created in the form of a simulation program written with MATLAB. The load data are treated as time series data. They are decomposed into several wavelet coefficient series using the wavelet transform technique known as Non-decimated Wavelet Transform (NWT). The reason for using this technique is the belief in the possibility of extracting hidden patterns from the time series data. The wavelet coefficient series are used to train the neural networks (NNs) and used as the inputs to the NNs for electricity load prediction. The Scale Conjugate Gradient (SCG) algorithm is used as the learning algorithm for the NNs. To get the final forecast data, the outputs from the NNs are recombined using the same wavelet technique. The model was evaluated with the electricity load data of Electronic Engineering Department in Mandalay Technological University in Myanmar. The simulation results showed that the model was capable of producing a reasonable forecasting accuracy in STLF.

Keywords: Neural network, Load forecast, Time series, wavelettransform.

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Authors: Salvatore Marra, Francesco C. Morabito

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In this paper we present an efficient approach for the prediction of two sunspot-related time series, namely the Yearly Sunspot Number and the IR5 Index, that are commonly used for monitoring solar activity. The method is based on exploiting partially recurrent Elman networks and it can be divided into three main steps: the first one consists in a “de-rectification" of the time series under study in order to obtain a new time series whose appearance, similar to a sum of sinusoids, can be modelled by our neural networks much better than the original dataset. After that, we normalize the derectified data so that they have zero mean and unity standard deviation and, finally, train an Elman network with only one input, a recurrent hidden layer and one output using a back-propagation algorithm with variable learning rate and momentum. The achieved results have shown the efficiency of this approach that, although very simple, can perform better than most of the existing solar activity forecasting methods.

Keywords: Elman neural networks, sunspot, solar activity, time series prediction.

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Authors: Mohamad Mahdavi, Mojtaba Mahdavi

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This paper tries to represent a new method for computing the reliability of a system which is arranged in series or parallel model. In this method we estimate life distribution function of whole structure using the asymptotic Extreme Value (EV) distribution of Type I, or Gumbel theory. We use EV distribution in minimal mode, for estimate the life distribution function of series structure and maximal mode for parallel system. All parameters also are estimated by Moments method. Reliability function and failure (hazard) rate and p-th percentile point of each function are determined. Other important indexes such as Mean Time to Failure (MTTF), Mean Time to repair (MTTR), for non-repairable and renewal systems in both of series and parallel structure will be computed.

Keywords: Reliability, extreme value, parallel, series, lifedistribution

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Authors: Li Yu, Chenlu Jiao, Hongrun Xin, Yan Wang, Kaiyang Wang

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In order to study the impact of various factors on the housing price, we propose to build different prediction models based on deep learning to determine the existing data of the real estate in order to more accurately predict the housing price or its changing trend in the future. Considering that the factors which affect the housing price vary widely, the proposed prediction models include two categories. The first one is based on multiple characteristic factors of the real estate. We built Convolution Neural Network (CNN) prediction model and Long Short-Term Memory (LSTM) neural network prediction model based on deep learning, and logical regression model was implemented to make a comparison between these three models. Another prediction model is time series model. Based on deep learning, we proposed an LSTM-1 model purely regard to time series, then implementing and comparing the LSTM model and the Auto-Regressive and Moving Average (ARMA) model. In this paper, comprehensive study of the second-hand housing price in Beijing has been conducted from three aspects: crawling and analyzing, housing price predicting, and the result comparing. Ultimately the best model program was produced, which is of great significance to evaluation and prediction of the housing price in the real estate industry.

Keywords: Deep learning, convolutional neural network, LSTM, housing prediction.

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Authors: Charline David, Alexandre Blondin Massé, Arnaud Zinflou

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We present a multiple equation time series approach for the short-term load forecasting applied to the electrical power load consumption for the whole Quebec province, in Canada. More precisely, we take into account three meteorological variables — temperature, cloudiness and wind speed —, and we use meteorological measurements taken at different locations on the territory. Our final model shows an average MAPE score of 1.79% over an 8-years dataset.

Keywords: Short-term load forecasting, special days, time series, multiple equations, parallelization, clustering.

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Authors: Hesham A. Elkaranshawy, Amr M. Abdelrazek, Hosam M. Ezzat

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The system of ordinary nonlinear differential equations describing sliding velocity during impact with friction for a three-dimensional rigid-multibody system is developed. No analytical solutions have been obtained before for this highly nonlinear system. Hence, a power series solution is proposed. Since the validity of this solution is limited to its convergence zone, a suitable time step is chosen and at the end of it a new series solution is constructed. For a case study, the trajectory of the sliding velocity using the proposed method is built using 6 time steps, which coincides with a Runge- Kutta solution using 38 time steps.

Keywords: Impact with friction, nonlinear ordinary differential equations, power series solutions, rough collision.

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Authors: A. I. Dounis, P. Tiropanis, D. Tseles, G. Nikolaou, G. P. Syrcos

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The prediction of meteorological parameters at a meteorological station is an interesting and open problem. A firstorder linear dynamic model GM(1,1) is the main component of the grey system theory. The grey model requires only a few previous data points in order to make a real-time forecast. In this paper, we consider the daily average ambient temperature as a time series and the grey model GM(1,1) applied to local prediction (short-term prediction) of the temperature. In the same case study we use a fuzzy predictive model for global prediction. We conclude the paper with a comparison between local and global prediction schemes.

Keywords: Fuzzy predictive model, grey model, local andglobal prediction, meteorological forecasting, time series.

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Authors: Snezhana G. Gocheva-Ilieva, Maya P. Stoimenova

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Ambient air pollution with fine particulate matter (PM10) is a systematic permanent problem in many countries around the world. The accumulation of a large number of measurements of both the PM10 concentrations and the accompanying atmospheric factors allow for their statistical modeling to detect dependencies and forecast future pollution. This study applies the classification and regression trees (CART) method for building and analyzing PM10 models. In the empirical study, average daily air data for the city of Pleven, Bulgaria for a period of 5 years are used. Predictors in the models are seven meteorological variables, time variables, as well as lagged PM10 variables and some lagged meteorological variables, delayed by 1 or 2 days with respect to the initial time series, respectively. The degree of influence of the predictors in the models is determined. The selected best CART models are used to forecast future PM10 concentrations for two days ahead after the last date in the modeling procedure and show very accurate results.

Keywords: Cross-validation, decision tree, lagged variables, short-term forecasting.

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Authors: Wullapa Wongsinlatam

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Back propagation algorithm (BP) is a widely used technique in artificial neural network and has been used as a tool for solving the time series problems, such as decreasing training time, maximizing the ability to fall into local minima, and optimizing sensitivity of the initial weights and bias. This paper proposes an improvement of a BP technique which is called IM-COH algorithm (IM-COH). By combining IM-COH algorithm with cuckoo search algorithm (CS), the result is cuckoo search improved control output hidden layer algorithm (CS-IM-COH). This new algorithm has a better ability in optimizing sensitivity of the initial weights and bias than the original BP algorithm. In this research, the algorithm of CS-IM-COH is compared with the original BP, the IM-COH, and the original BP with CS (CS-BP). Furthermore, the selected benchmarks, four time series samples, are shown in this research for illustration. The research shows that the CS-IM-COH algorithm give the best forecasting results compared with the selected samples.

Keywords: Artificial neural networks, back propagation algorithm, time series, local minima problem, metaheuristic optimization.

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Authors: Ε. Giovanis

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In this paper we present, propose and examine additional membership functions for the Smoothing Transition Autoregressive (STAR) models. More specifically, we present the tangent hyperbolic, Gaussian and Generalized bell functions. Because Smoothing Transition Autoregressive (STAR) models follow fuzzy logic approach, more fuzzy membership functions should be tested. Furthermore, fuzzy rules can be incorporated or other training or computational methods can be applied as the error backpropagation or genetic algorithm instead to nonlinear squares. We examine two macroeconomic variables of US economy, the inflation rate and the 6-monthly treasury bills interest rates.

Keywords: Forecast , Fuzzy membership functions, Smoothingtransition, Time-series

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