Статті в журналах: "Nonlinear Autoregressive model"

1

Meitz, Mika, and Pentti Saikkonen. "PARAMETER ESTIMATION IN NONLINEAR AR–GARCH MODELS." Econometric Theory 27, no. 6 (May 31, 2011): 1236–78. http://dx.doi.org/10.1017/s0266466611000041.

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This paper develops an asymptotic estimation theory for nonlinear autoregressive models with conditionally heteroskedastic errors. We consider a general nonlinear autoregression of order p (AR(p)) with the conditional variance specified as a general nonlinear first-order generalized autoregressive conditional heteroskedasticity (GARCH(1,1)) model. We do not require the rescaled errors to be independent, but instead only to form a stationary and ergodic martingale difference sequence. Strong consistency and asymptotic normality of the global Gaussian quasi-maximum likelihood (QML) estimator are established under conditions comparable to those recently used in the corresponding linear case. To the best of our knowledge, this paper provides the first results on consistency and asymptotic normality of the QML estimator in nonlinear autoregressive models with GARCH errors.

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2

Kresnawati, Gayuh, Budi Warsito, and Abdul Hoyyi. "PERAMALAN INDEKS HARGA SAHAM GABUNGAN DENGAN METODE LOGISTIC SMOOTH TRANSITION AUTOREGRESSIVE (LSTAR)." Jurnal Gaussian 7, no. 1 (February 28, 2018): 84–95. http://dx.doi.org/10.14710/j.gauss.v7i1.26638.

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Smooth Transition Autoregressive (STAR) Model is one of time series model used in case of data that has nonlinear tendency. STAR is an expansion of Autoregressive (AR) Model and can be used if the nonlinear test is accepted. If the transition function G(st,γ,c) is logistic, the method used is Logistic Smooth Transition Autoregressive (LSTAR). Weekly IHSG data in period of 3 January 2010 until 24 December 2017 has nonlinier tend and logistic transition function so it can be modeled with LSTAR . The result of this research with significance level of 5% is the LSTAR(1,1) model. The forecast of IHSG data for the next 15 period has Mean Absolute Percentage Error (MAPE) 2,932612%. Keywords : autoregressive, LSTAR, nonlinier, time series

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3

Sheng Lu and Ki H. Chon. "Nonlinear autoregressive and nonlinear autoregressive moving average model parameter estimation by minimizing hypersurface distance." IEEE Transactions on Signal Processing 51, no. 12 (December 2003): 3020–26. http://dx.doi.org/10.1109/tsp.2003.818999.

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4

Bauldry, Shawn, and Kenneth A. Bollen. "Nonlinear Autoregressive Latent Trajectory Models." Sociological Methodology 48, no. 1 (August 2018): 269–302. http://dx.doi.org/10.1177/0081175018789441.

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Autoregressive latent trajectory (ALT) models combine features of latent growth curve models and autoregressive models into a single modeling framework. The development of ALT models has focused primarily on models with linear growth components, but some social processes follow nonlinear trajectories. Although it is straightforward to extend ALT models to allow for some forms of nonlinear trajectories, the identification status of such models, approaches to comparing them with alternative models, and the interpretation of parameters have not been systematically assessed. In this paper we focus on two forms of nonlinear autoregressive latent trajectory (NLALT) models. The first form allows for a quadratic growth trajectory, a popular form of nonlinear latent growth curve models. The second form derives from latent basis models, or freed loading models, that allow for arbitrary growth processes. We discuss details concerning parameterization, model identification, estimation, and testing for the two forms of NLALT models. We include a simulation study that illustrates potential biases that may arise from fitting alternative models to data derived from an autoregressive process and individual-specific nonlinear trajectories. In addition, we include an extended empirical example modeling growth trajectories of weight from birth through age 2.

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5

Srinivasan, Sundararajan, Tao Ma, Georgios Lazarou, and Joseph Picone. "A nonlinear autoregressive model for speaker verification." International Journal of Speech Technology 17, no. 1 (June 6, 2013): 17–25. http://dx.doi.org/10.1007/s10772-013-9201-9.

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6

Ikoma, Norikazu, and Kaoru Hirota. "Nonlinear autoregressive model based on fuzzy relation." Information Sciences 71, no. 1-2 (June 1993): 131–44. http://dx.doi.org/10.1016/0020-0255(93)90068-w.

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7

Wang, Meiqi, Enli Chen, Pengfei Liu, and Wenwu Guo. "Multivariable nonlinear predictive control of a clinker sintering system at different working states by combining artificial neural network and autoregressive exogenous." Advances in Mechanical Engineering 12, no. 1 (January 2020): 168781401989650. http://dx.doi.org/10.1177/1687814019896509.

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The clinker sintering system is widely controlled manually in the factory, and there is a large divergence between a linearized control model and the nonlinear rotary kiln system, so the controlled variables cannot be calculated accurately. To accommodate the multivariable and nonlinear features of cement clinker sintering systems, steady-state model and dynamic models are established using extreme learning machine and autoregressive exogenous models. The steady-state model is used to describe steady-state nonlinear relations, and the dynamic model is used to describe the dynamic characteristics of the sintering system. By obtaining the system gains based on the steady-state model, the parameters of the dynamic model are rectified online to conform to the system gain. Thus, a dynamic model named extreme learning machine-autoregressive exogenous is proposed, which can describe the nonlinear dynamic features of a sintering system. The results show that, compared with the autoregressive exogenous model, the extreme learning machine-autoregressive exogenous model has good control performance on the multivariable and nonlinear system and can reduce computing resource requirements during the online running. In addition, fluctuations of NOx and O2 concentrations decreases, again demonstrating good control performance of an actual clinker sintering system using the extreme learning machine-autoregressive exogenous model.

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8

Xiong, Weili, Wei Fan, and Rui Ding. "Least-Squares Parameter Estimation Algorithm for a Class of Input Nonlinear Systems." Journal of Applied Mathematics 2012 (2012): 1–14. http://dx.doi.org/10.1155/2012/684074.

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This paper studies least-squares parameter estimation algorithms for input nonlinear systems, including the input nonlinear controlled autoregressive (IN-CAR) model and the input nonlinear controlled autoregressive autoregressive moving average (IN-CARARMA) model. The basic idea is to obtain linear-in-parameters models by overparameterizing such nonlinear systems and to use the least-squares algorithm to estimate the unknown parameter vectors. It is proved that the parameter estimates consistently converge to their true values under the persistent excitation condition. A simulation example is provided.

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9

Sapra, Sunil. "A comparative study of parametric and semiparametric autoregressive models." International Journal of Accounting and Economics Studies 10, no. 1 (April 5, 2022): 15–19. http://dx.doi.org/10.14419/ijaes.v10i1.31978.

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Dynamic linear regression models are used widely in applied econometric research. Most applications employ linear autoregressive (AR) models, distributed lag (DL) models or autoregressive distributed lag (ARDL) models. These models, however, perform poorly for data sets with unknown, complex nonlinear patterns. This paper studies nonlinear and semiparametric extensions of the dynamic linear regression model and explores the autoregressive (AR) extensions of two semiparametric techniques to allow unknown forms of nonlinearities in the regression function. The autoregressive GAM (GAM-AR) and autoregressive multivariate adaptive regression splines (MARS-AR) studied in the paper automatically discover and incorporate nonlinearities in autoregressive (AR) models.Â Performance comparisons among these semiparametric AR models and the linear AR model are carried out via their application to Australian data on growth in GDP and unemployment using RMSE and GCV measures.Â Â

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10

Blanchard, Tyler, and Biswanath Samanta. "Wind speed forecasting using neural networks." Wind Engineering 44, no. 1 (May 29, 2019): 33–48. http://dx.doi.org/10.1177/0309524x19849846.

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The prediction of wind speed is critical in the assessment of feasibility of a potential wind turbine site. This work presents a study on prediction of wind speed using artificial neural networks. Two variations of artificial neural networks, namely, nonlinear autoregressive neural network and nonlinear autoregressive neural network with exogenous inputs, were used to predict wind speed utilizing 1 year of hourly weather data from four locations around the United States to train, validate, and test these networks. This study optimized both neural network configurations and it demonstrated that both models were suitable for wind speed prediction. Both models outperformed persistence model (with a factor of about 2 to 10 in root mean square error ratio). Both artificial neural network models were implemented for single-step and multi-step-ahead prediction of wind speed for all four locations and results were compared. Nonlinear autoregressive neural network with exogenous inputs model gave better prediction performance than nonlinear autoregressive model and the difference was statistically significant.

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11

Han, Xu, Huoyue Xiang, Yongle Li, and Yichao Wang. "Predictions of vertical train-bridge response using artificial neural network-based surrogate model." Advances in Structural Engineering 22, no. 12 (May 26, 2019): 2712–23. http://dx.doi.org/10.1177/1369433219849809.

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To improve the efficiency of reliability calculations for vehicle-bridge systems, we present a surrogate modeling method based on a nonlinear autoregressive with exogenous input artificial neural network model and an important sample, which can forecast responses of dynamic systems, such as vehicle-bridge systems, subjected to stochastic excitations. We also propose a process to analyze the method. A quarter-vehicle model is used to verify the proposed method’s precision, and the nonlinear autoregressive with exogenous input artificial neural network model is used to predict responses of vertical vehicle-bridge systems. The results show that, compared to other training samples, the nonlinear autoregressive with exogenous input artificial neural network model has better prediction accuracy when the sample with the maximum response is considered as an important sample and is used to train the nonlinear autoregressive with exogenous input artificial neural network model, and it requires only two-time numerical simulation (or Monte Carlo simulation) at most, which is used in the training of the nonlinear autoregressive with exogenous input artificial neural network model.

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12

Min, Chen, and An Hongzhi. "The existence of moments of nonlinear autoregressive model." Acta Mathematicae Applicatae Sinica 14, no. 3 (July 1998): 328–32. http://dx.doi.org/10.1007/bf02677414.

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13

Yokota, Yasunari, Masaomi Koizumi, and Noritaka Matsuoka. "Prediction coding of ECG by nonlinear autoregressive model." Systems and Computers in Japan 31, no. 7 (July 2000): 66–74. http://dx.doi.org/10.1002/(sici)1520-684x(200007)31:7<66::aid-scj8>3.0.co;2-q.

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14

Yang, Xiao-Hua, and Yu-Qi Li. "DNA Optimization Threshold Autoregressive Prediction Model and Its Application in Ice Condition Time Series." Mathematical Problems in Engineering 2012 (2012): 1–10. http://dx.doi.org/10.1155/2012/191902.

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There are many parameters which are very difficult to calibrate in the threshold autoregressive prediction model for nonlinear time series. The threshold value, autoregressive coefficients, and the delay time are key parameters in the threshold autoregressive prediction model. To improve prediction precision and reduce the uncertainties in the determination of the above parameters, a new DNA (deoxyribonucleic acid) optimization threshold autoregressive prediction model (DNAOTARPM) is proposed by combining threshold autoregressive method and DNA optimization method. The above optimal parameters are selected by minimizing objective function. Real ice condition time series at Bohai are taken to validate the new method. The prediction results indicate that the new method can choose the above optimal parameters in prediction process. Compared with improved genetic algorithm threshold autoregressive prediction model (IGATARPM) and standard genetic algorithm threshold autoregressive prediction model (SGATARPM), DNAOTARPM has higher precision and faster convergence speed for predicting nonlinear ice condition time series.

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15

Pereira, Janser Moura, Joel Augusto Muniz, and Carlos Alberto Silva. "Nonlinear models to predict nitrogen mineralization in an Oxisol." Scientia Agricola 62, no. 4 (August 2005): 395–400. http://dx.doi.org/10.1590/s0103-90162005000400014.

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This work was carried out to evaluate the statistical properties of eight nonlinear models used to predict nitrogen mineralization in soils of the Southern Minas Gerais State, Brazil. The parameter estimations for nonlinear models with and without structure of autoregressive errors was made by the least squares method. First, a structure of second order autoregressive errors, AR(2) was considered for all nonlinear models and then the significance of the autocorrelation parameters was verified. Among the models, the Juma presented an autocorrelation of second order, and the model of Broadbent presented one of first order. In summary, these models presented significant autocorrelation parameters. To estimate the parameters of nonlinear models, the SAS procedure MODEL was used (SAS). The comparison of the models was made by measuring the fitted parameters: adjusted R-square, mean square error and mean predicted error. The Juma model with AR(2) best fitted for nitrogen mineralization without liming, followed by Cabrera, Stanford & Smith without autoregressive errors, for both with and without soil acidity correction.

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16

Su, Liyun, and Chenlong Li. "Local Prediction of Chaotic Time Series Based on Polynomial Coefficient Autoregressive Model." Mathematical Problems in Engineering 2015 (2015): 1–14. http://dx.doi.org/10.1155/2015/901807.

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We apply the polynomial function to approximate the functional coefficients of the state-dependent autoregressive model for chaotic time series prediction. We present a novel local nonlinear model called local polynomial coefficient autoregressive prediction (LPP) model based on the phase space reconstruction. The LPP model can effectively fit nonlinear characteristics of chaotic time series with simple structure and have excellent one-step forecasting performance. We have also proposed a kernel LPP (KLPP) model which applies the kernel technique for the LPP model to obtain better multistep forecasting performance. The proposed models are flexible to analyze complex and multivariate nonlinear structures. Both simulated and real data examples are used for illustration.

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17

Hermansah, Hermansah, Dedi Rosadi, Abdurakhman Abdurakhman, and Herni Utami. "SELECTION OF INPUT VARIABLES OF NONLINEAR AUTOREGRESSIVE NEURAL NETWORK MODEL FOR TIME SERIES DATA FORECASTING." MEDIA STATISTIKA 13, no. 2 (December 28, 2020): 116–24. http://dx.doi.org/10.14710/medstat.13.2.116-124.

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NARNN is a type of ANN model consisting of a limited number of parameters and widely used for various applications. This study aims to determine the appropriate NARNN model, for the selection of input variables of nonlinear autoregressive neural network model for time series data forecasting, using the stepwise method. Furthermore, the study determines the optimal number of neurons in the hidden layer, using a trial and error method for some architecture. The NARNN model is combined in three parts, namely the learning method, the activation function, and the ensemble operator, to get the best single model. Its application in this study was conducted on real data, such as the interest rate of Bank Indonesia. The comparison results of MASE, RMSE, and MAPE values with ARIMA and Exponential Smoothing models shows that the NARNN is the best model used to effectively improve forecasting accuracy.

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18

Yu, Pen-Ning, Charles Y. Liu, Christianne N. Heck, Theodore W. Berger, and Dong Song. "A sparse multiscale nonlinear autoregressive model for seizure prediction." Journal of Neural Engineering 18, no. 2 (February 26, 2021): 026012. http://dx.doi.org/10.1088/1741-2552/abdd43.

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19

Kato, Hiroko, and Tohru Ozaki. "Adding data process feedback to the nonlinear autoregressive model." Signal Processing 82, no. 9 (September 2002): 1189–204. http://dx.doi.org/10.1016/s0165-1684(02)00139-1.

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20

Li, Junxing, Zhihua Wang, Yongbo Zhang, Chengrui Liu, and Huimin Fu. "A nonlinear Wiener process degradation model with autoregressive errors." Reliability Engineering & System Safety 173 (May 2018): 48–57. http://dx.doi.org/10.1016/j.ress.2017.11.003.

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21

Vesin, J. M. "A nonlinear autoregressive signal model with state-dependent gain." Signal Processing 26, no. 1 (January 1992): 37–48. http://dx.doi.org/10.1016/0165-1684(92)90054-z.

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22

Bai, Yu-ting, Xiao-yi Wang, Xue-bo Jin, Zhi-yao Zhao, and Bai-hai Zhang. "A Neuron-Based Kalman Filter with Nonlinear Autoregressive Model." Sensors 20, no. 1 (January 5, 2020): 299. http://dx.doi.org/10.3390/s20010299.

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The control effect of various intelligent terminals is affected by the data sensing precision. The filtering method has been the typical soft computing method used to promote the sensing level. Due to the difficult recognition of the practical system and the empirical parameter estimation in the traditional Kalman filter, a neuron-based Kalman filter was proposed in the paper. Firstly, the framework of the improved Kalman filter was designed, in which the neuro units were introduced. Secondly, the functions of the neuro units were excavated with the nonlinear autoregressive model. The neuro units optimized the filtering process to reduce the effect of the unpractical system model and hypothetical parameters. Thirdly, the adaptive filtering algorithm was proposed based on the new Kalman filter. Finally, the filter was verified with the simulation signals and practical measurements. The results proved that the filter was effective in noise elimination within the soft computing solution.

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23

Xaba, Diteboho, Ntebogang Dinah Moroke, Johnson Arkaah, and Charlemagne Pooe. "A Comparative Study Of Stock Price Forecasting Using Nonlinear Models." Risk Governance and Control: Financial Markets and Institutions 7, no. 2 (2017): 7–17. http://dx.doi.org/10.22495/rgcv7i2art1.

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This study compared the in-sample forecasting accuracy of three forecasting nonlinear models namely: the Smooth Transition Regression (STR) model, the Threshold Autoregressive (TAR) model and the Markov-switching Autoregressive (MS-AR) model. Nonlinearity tests were used to confirm the validity of the assumptions of the study. The study used model selection criteria, SBC to select the optimal lag order and for the selection of appropriate models. The Mean Square Error (MSE), Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) served as the error measures in evaluating the forecasting ability of the models. The MS-AR models proved to perform well with lower error measures as compared to LSTR and TAR models in most cases.

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24

Ma, Qingwen, Sihan Liu, Xinyu Fan, Chen Chai, Yangyang Wang, and Ke Yang. "A Time Series Prediction Model of Foundation Pit Deformation Based on Empirical Wavelet Transform and NARX Network." Mathematics 8, no. 9 (September 8, 2020): 1535. http://dx.doi.org/10.3390/math8091535.

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Large deep foundation pits are usually in a complex environment, so their surface deformation tends to show a stable rising trend with a small range of fluctuation, which brings certain difficulty to the prediction work. Therefore, in this study we proposed a nonlinear autoregressive exogenous (NARX) prediction method based on empirical wavelet transform (EWT) pretreatment is proposed for this feature. Firstly, EWT is used to conduct adaptive decomposition of the measured deformation data and extract the modal signal components with characteristic differences. Secondly, the main components affecting the deformation of the foundation pit are analyzed as a part of the external input. Then, we established a NARX prediction model for different components. Finally, all predicted values are superpositioned to obtain a total value, and the result is compared with the predicted results of the nonlinear autoregressive (NAR) model, empirical mode decomposition-nonlinear autoregressive (EMD-NAR) model, EWT-NAR model, NARX model, EMD-NARX model and EWT-NARX model. The results showed that, compared with the EWT-NAR and EWT-NARX models, the EWT-NARX model reduced the mean square error of KD25 by 91.35%, indicating that the feature of introducing external input makes NARX more suitable for combining with the EWT method. Meanwhile, compared with the EMD-NAR and EWT-NAR models, the introduction of the NARX model reduced the mean square error of KD25 by 78.58% and 95.71%, indicating that EWT had better modal decomposition capability than EMD.

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25

Goryainov, A. V., V. B. Goryainov, and W. M. Khing. "Robust Identification of an Exponential Autoregressive Model." Herald of the Bauman Moscow State Technical University. Series Natural Sciences, no. 4 (91) (August 2020): 42–57. http://dx.doi.org/10.18698/1812-3368-2020-4-42-57.

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One of the most common nonlinear time series (random processes with discrete time) models is the exponential autoregressive model. In particular, it describes such nonlinear effects as limit cycles, resonant jumps, and dependence of the oscillation frequency on amplitude. When identifying this model, the problem arises of estimating its parameters --- the coefficients of the corresponding autoregressive equation. The most common methods for estimating the parameters of an exponential model are the least squares method and the least absolute deviation method. Both of these methods have a number of disadvantages, to eliminate which the paper proposes an estimation method based on the robust Huber approach. The obtained estimates occupy an intermediate position between the least squares and least absolute deviation estimates. It is assumed that the stochastic sequence is described by the autoregressive equation of the first order, is stationary and ergodic, and the probability distribution of the innovations process of the model is unknown. Unbiased, consistency and asymptotic normality of the proposed estimate are established by computer simulation. Its asymptotic variance was found, which allows to obtain an explicit expression for the relative efficiency of the proposed estimate with respect to the least squares estimate and the least absolute deviation estimate and to calculate this efficiency for the most widespread probability distributions of the innovations sequence of the equation of the autoregressive model

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26

Syed Asad, Hussain, Yuen Richard Kwok Kit, and Lee Eric Wai Ming. "Energy Modeling with Nonlinear-Autoregressive Exogenous Neural Network." E3S Web of Conferences 111 (2019): 03059. http://dx.doi.org/10.1051/e3sconf/201911103059.

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The model-based predictive control (MPC) is considered to be an effective tool for optimal control of building heating, ventilation, and air-conditioning (HVAC) systems. MPC need to update the operating set points of the local control loops that have a significant influence on the energy performance of the system. Performance of MPC relies on the accuracy of the system performance model. There are two commonly used modeling approach – conventional or analytical approach that is the way of process modeling for some time, but it tends to increase the online computational load as it requires a full mathematical description of the real system. Furthermore, such techniques rely on different simplifying assumptions that limit the accuracy of the performance model. A second commonly used technique is the data-driven approach. The neural network (NN) is the most potent data-driven approach. NN can accurately model complex nonlinear systems without even knowing the structure of the system and it also addresses the problem of the online computational load since the computational load moves to the offline training step. In order to set up neural network model-based predictive control (NNMPC), it is important to build a reliable energy model of HVAC system that can be used to perform multi-step-ahead prediction of system energy performance. In this paper, the energy modeling of the chiller plant is conducted. Data for the training of chiller plant energy model is generated from HVAC testbed build in TRNSYS simulation environment. The nonlinear-autoregressive neural network with exogenous input (NARX) is used to model the energy performance of the chiller plant. The NARX is a powerful method for forecasting of time series data and dynamic control problems. NARX model is first trained in the open-loop form with the actual output instead of feedback, using back-propagation with the Levenberg-Marquardt method; this model can be used to perform only one-step-ahead prediction. Open-loop NARX model is transformed into a closed-loop form, by connecting the internal feedback, i.e. actual output is replaced by predicted output, to perform multi-step-ahead prediction (for predictive control). Comparative analysis of developed NARX-based chiller model is carried out with respect to process data from testbed, which demonstrated the good accuracy of the NARX-based chiller model.

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Sousa, Iábita Fabiana, Johan Eugen Kunzle Neto, Joel Augusto Muniz, Renato Mendes Guimarães, Taciana Villela Savian, and Fabiana Rezende Muniz. "Fitting nonlinear autoregressive models to describe coffee seed germination." Ciência Rural 44, no. 11 (November 2014): 2016–21. http://dx.doi.org/10.1590/0103-8478cr20131341.

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Cumulative germination of coffee has a longitudinal behavior mathematically characterized by a sigmoidal model. In the seed germination evaluation, the study of the germination curve may contribute to better understanding of this process. The aim of this study was to evaluate the goodness of fit of Logistic and Gompertz models, with independent and first-order autoregressive errors structure, AR (1), in the description of coffee (Coffea arabica L.) line Catuai vermelho IAC 99 germination, at five different potential germination. The data used were from an experiment conducted in 2011 at the Seed Analysis Laboratory of the Federal University of Lavras. The Logistic and Gompertz nonlinear models were appropriately adjusted to the percentage germination data. The Gompertz model with first-order autoregressive errors structure was the best to describe the germination process

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28

Chen, Yiding, and Xiaojin Zhu. "Optimal Attack against Autoregressive Models by Manipulating the Environment." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 04 (April 3, 2020): 3545–52. http://dx.doi.org/10.1609/aaai.v34i04.5760.

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We describe an optimal adversarial attack formulation against autoregressive time series forecast using Linear Quadratic Regulator (LQR). In this threat model, the environment evolves according to a dynamical system; an autoregressive model observes the current environment state and predicts its future values; an attacker has the ability to modify the environment state in order to manipulate future autoregressive forecasts. The attacker's goal is to force autoregressive forecasts into tracking a target trajectory while minimizing its attack expenditure. In the white-box setting where the attacker knows the environment and forecast models, we present the optimal attack using LQR for linear models, and Model Predictive Control (MPC) for nonlinear models. In the black-box setting, we combine system identification and MPC. Experiments demonstrate the effectiveness of our attacks.

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29

Solikhah, Arifatus, Heri Kuswanto, Nur Iriawan, and Kartika Fithriasari. "Fisher’s z Distribution-Based Mixture Autoregressive Model." Econometrics 9, no. 3 (June 29, 2021): 27. http://dx.doi.org/10.3390/econometrics9030027.

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We generalize the Gaussian Mixture Autoregressive (GMAR) model to the Fisher’s z Mixture Autoregressive (ZMAR) model for modeling nonlinear time series. The model consists of a mixture of K-component Fisher’s z autoregressive models with the mixing proportions changing over time. This model can capture time series with both heteroskedasticity and multimodal conditional distribution, using Fisher’s z distribution as an innovation in the MAR model. The ZMAR model is classified as nonlinearity in the level (or mode) model because the mode of the Fisher’s z distribution is stable in its location parameter, whether symmetric or asymmetric. Using the Markov Chain Monte Carlo (MCMC) algorithm, e.g., the No-U-Turn Sampler (NUTS), we conducted a simulation study to investigate the model performance compared to the GMAR model and Student t Mixture Autoregressive (TMAR) model. The models are applied to the daily IBM stock prices and the monthly Brent crude oil prices. The results show that the proposed model outperforms the existing ones, as indicated by the Pareto-Smoothed Important Sampling Leave-One-Out cross-validation (PSIS-LOO) minimum criterion.

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30

Zheng, Dawei. "Prediction of the Length of Day from Atmospheric Angular Momentum with LSTAR Model." Symposium - International Astronomical Union 156 (1993): 335. http://dx.doi.org/10.1017/s0074180900173449.

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Adopting the time series of atmospheric angular momentum (AAM) from the National Meteorological Center of USA, the study of the prediction of the length of day (LOD) has been made by the Leap-Step Threshold AutoRegressive (LSTAR) model. The LSTAR model presented by the author is a sort of models for nonlinear time series analysis such as where Dj is the j-th leap-step domain of the data series Zn, and (j) if the sample number N=L×M, then Zj+(L×K) εDj and K=0,1,…,M−1. En denotes the white noise of data in the j-th leap-step domain. TSM denotes a class of models in time series analysis and the nonlinear threshold autoregressive model is used here.

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31

CHONG, TERENCE TAI-LEUNG, TAU-HING LAM, and MELVIN J. HINICH. "ARE NONLINEAR TRADING RULES PROFITABLE IN THE CHINESE STOCK MARKET?" Annals of Financial Economics 05, no. 01 (June 2009): 0950002. http://dx.doi.org/10.1142/s201049520950002x.

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The rise of China in the world economy has attracted a great deal of international attention. This paper investigates the performance of nonlinear self-exciting threshold autoregressive (SETAR) model-based trading rules in the Chinese stock market. We compare the performance of the SETAR model with the autoregressive (AR) model and the moving average (MA) trading rules. Our results indicate that trading rules are profitable in the B-share market, and that the nonlinear SETAR rule outperforms the other two linear rules in general.

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32

Chi, Yeong Nain, and Orson Chi. "Application of Nonlinear Autoregressive Neural Network to Model and Forecast Time Series Global Price of Bananas." International Journal of Data Science 2, no. 1 (March 5, 2021): 19–37. http://dx.doi.org/10.18517/ijods.2.1.19-37.2021.

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The primary purpose of this study was to apply the nonlinear autoregressive neural network to model the long-term records of monthly global price of bananas from January 1990 to November 2020. The development of the optimal architecture for the nonlinear autoregressive neural network requires determination of time delays, the number of hidden neurons, and an efficient training algorithm. Through training of the nonlinear autoregressive neural network models, the prediction performance of the models was evaluated by its mean squared error value, the average squared difference between the observed and predicted values. In this study, the empirical results revealed that the NAR-BR model with 13 neurons in the hidden layer and 6 time delays provided the best performance at its smaller mean squared error value and yielded higher accuracy than the NAR-LM model with 12 neurons in the hidden layer and 4 time delays and NAR-SCG model with 12 neurons in the hidden layer and 6 time delays. Understanding past global price of bananas is important for the analyses of current and future global price of bananas changes. In order to sustain these observations, research programs utilizing the resulting data should be able to improve our understanding and narrow projections of future global price of bananas significantly.

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33

Fueda, Kaoru. "AN ADAPTIVE VARIABLE SELECTION FOR NONLINEAR AUTOREGRESSIVE TIME SERIES MODEL." Bulletin of informatics and cybernetics 37 (December 2005): 109–21. http://dx.doi.org/10.5109/12594.

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34

Hwang, Eunju, and Dong Wan Shin. "Stationary bootstrapping for non-parametric estimator of nonlinear autoregressive model." Journal of Time Series Analysis 32, no. 3 (November 15, 2010): 292–303. http://dx.doi.org/10.1111/j.1467-9892.2010.00699.x.

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35

Elhassanein, A. "On the Control of Forced Process Feedback Nonlinear Autoregressive Model." Journal of Computational and Theoretical Nanoscience 12, no. 8 (August 1, 2015): 1519–26. http://dx.doi.org/10.1166/jctn.2015.3923.

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36

Hajrajabi, Arezo. "Markov switching model of nonlinear autoregressive with skew-symmetric innovations." Journal of Statistical Computation and Simulation 89, no. 4 (January 6, 2019): 559–75. http://dx.doi.org/10.1080/00949655.2018.1563089.

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37

Eikenberry, Steffen E., and Vasilis Z. Marmarelis. "A nonlinear autoregressive Volterra model of the Hodgkin–Huxley equations." Journal of Computational Neuroscience 34, no. 1 (August 10, 2012): 163–83. http://dx.doi.org/10.1007/s10827-012-0412-x.

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38

CHELANI, A., and S. DEVOTTA. "Air quality forecasting using a hybrid autoregressive and nonlinear model." Atmospheric Environment 40, no. 10 (March 2006): 1774–80. http://dx.doi.org/10.1016/j.atmosenv.2005.11.019.

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39

Sakhabakhsh, Leila, Rahman Farnoosh, Afshin Fallah, and Mohammadhassan Behzadi. "A Semiparametric Approach for Modeling Partially Linear Autoregressive Model with Skew Normal Innovations." Advances in Mathematical Physics 2022 (February 25, 2022): 1–17. http://dx.doi.org/10.1155/2022/7863474.

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The nonlinear autoregressive models under normal innovations are commonly used for nonlinear time series analysis in various fields. However, using this class of models for modeling skewed data leads to unreliable results due to the disability of these models for modeling skewness. In this setting, replacing the normality assumption with a more flexible distribution that can accommodate skewness will provide effective results. In this article, we propose a partially linear autoregressive model by considering the skew normal distribution for independent and dependent innovations. A semiparametric approach for estimating the nonlinear part of the regression function is proposed based on the conditional least squares approach and the nonparametric kernel method. Then, the conditional maximum-likelihood approach is used to estimate the unknown parameters through the expectation-maximization (EM) algorithm. Some asymptotic properties for the semiparametric method are established. Finally, the performance of the proposed model is verified through simulation studies and analysis of a real dataset.

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40

Nadirah Mohd Johari, Sarah, Fairuz Husna Muhamad Farid, Nur Afifah Enara Binti Nasrudin, Nur Sarah Liyana Bistamam, and Nur Syamira Syamimi Muhammad Shuhaili. "Predicting Stock Market Index Using Hybrid Intelligence Model." International Journal of Engineering & Technology 7, no. 3.15 (August 13, 2018): 36. http://dx.doi.org/10.14419/ijet.v7i3.15.17403.

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Predicting financial market changes is an important issue in time series analysis, receiving an increasing attention due to financial crisis. Autoregressive integrated moving average (ARIMA) model has been one of the most widely used linear models in time series forecasting but ARIMA model cannot capture nonlinear patterns easily. Generalized autoregressive conditional heteroscedasticity (GARCH) model applied understanding of volatility depending to the estimation of previous forecast error and current volatility, improving ARIMA model. Support vector machine (SVM) and artificial neural network (ANN) have been successfully applied in solving nonlinear regression estimation problems. This study proposes hybrid methodology that exploits unique strength of GARCH + SVM model, and GARCH + ANN model in forecasting stock index. Real data sets of stock prices FTSE Bursa Malaysia KLCI were used to examine the forecasting accuracy of the proposed model. The results shows that the proposed hybrid model achieves best forecasting compared to other model.

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41

Kim, Hee-Young, Christian H. Weiß, and Tobias A. Möller. "Models for autoregressive processes of bounded counts: How different are they?" Computational Statistics 35, no. 4 (March 27, 2020): 1715–36. http://dx.doi.org/10.1007/s00180-020-00980-6.

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Abstract We focus on purely autoregressive (AR)-type models defined on the bounded range $$\{0,1,\ldots , n\}$$ { 0 , 1 , … , n } with a fixed upper limit $$n \in \mathbb {N}$$ n ∈ N . These include the binomial AR model, binomial AR conditional heteroscedasticity (ARCH) model, binomial-variation AR model with their linear conditional mean, nonlinear max-binomial AR model, and binomial logit-ARCH model. We consider the key problem of identifying which of these AR-type models is the true data-generating process. Despite the volume of the literature on model selection, little is known about this procedure in the context of nonnested and nonlinear time series models for counts. We consider the most popular approaches used for model identification, Akaike’s information criterion and the Bayesian information criterion, and compare them using extensive Monte Carlo simulations. Furthermore, we investigate the properties of the fitted models (both the correct and wrong models) obtained using maximum likelihood estimation. A real-data example demonstrates our findings.

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42

S. Khalaf, Zena, and ,. Azher A. Mohammad. "On stability Conditions of Burr X Autoregressive model." Tikrit Journal of Pure Science 24, no. 5 (September 13, 2019): 91. http://dx.doi.org/10.25130/j.v24i5.873.

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This article deals with proposed nonlinear autoregressive model based on Burr X cumulative distribution function known as Burr X AR (p), we demonstrate stability conditions of the proposed model in terms of its parameters by using dynamical approach known as local linearization method to find stability conditions of a nonzero fixed point of the proposed model, in addition the study demonstrate stability condition of a limit cycle if Burr X AR (1) model have a limit cycle of period greater than one. http://dx.doi.org/10.25130/tjps.24.2019.096

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43

Ghosh, Himadri, G. Sunilkumar, and Prajneshu. "Mixture Nonlinear Time-Series Analysis : Modelling and Forecasting." Calcutta Statistical Association Bulletin 57, no. 1-2 (March 2005): 95–108. http://dx.doi.org/10.1177/0008068320050108.

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Gaussian mixture transition distribution (GMTD) models and mixture autoregressive (MAR) models are generally employed to describe those data sets that depict sudden bursts, outliers and flat stretches at irregular time epochs. In this paper , these two approaches are compared by considering weekly wholesale onion price data during April, 1998 to November, 2001. After eliminating trend, seasonal fluctuations are studied by fitting BoxJenkins airline model to residual series. To this end, null hypothesis of presence of nonseasonal and seasonal stochastic trends is tested by using OsboruChuiSmithBirchenhall (OCSB) auxiliary regression. Subsequently, appropriate filters in airline model for seasonal fluctuations are selected. Presence of autoregressive co nditional heteroscedasticity (ARCH) is tested by Naive Lagrange multiplier (Nave LM) test. Estimation of parameters is carric~d out using ExpectationMaximization (EM) algorithm and the best model is selected on the basis of Bayesian information criterion (BIC). Outofsample forecasting is performed for onestep and twostep ahead prediction by uaive approach, proposed by Wong and Li (2000). It is concluded that, for data under consideration, a threecomponent MAR model performs the best.

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44

Li, Maobin, Shouwen Ji, and Gang Liu. "Forecasting of Chinese E-Commerce Sales: An Empirical Comparison of ARIMA, Nonlinear Autoregressive Neural Network, and a Combined ARIMA-NARNN Model." Mathematical Problems in Engineering 2018 (November 19, 2018): 1–12. http://dx.doi.org/10.1155/2018/6924960.

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With the rapid development of e-commerce (EC) and shopping online, accurate and efficient forecasting of e-commerce sales (ECS) is very important for making strategies for purchasing and inventory of EC enterprises. Affected by many factors, ECS volume range varies greatly and has both linear and nonlinear characteristics. Three forecast models of ECS, autoregressive integrated moving average (ARIMA), nonlinear autoregressive neural network (NARNN), and ARIMA-NARNN, are used to verify the forecasting efficiency of the methods. Several time series of ECS from China’s Jingdong Corporation are selected as experimental data. The result shows that the ARIMA-NARNN model is more effective than ARIMA and NARNN models in forecasting ECS. The analysis found that the ARIMA-NARNN model combines the linear fitting of ARIMA and the nonlinear mapping of NARNN, so it shows better prediction performance than the ARIMA and NARNN methods.

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45

Szolgayová, Elena Peksová, Michaela Danačová, Magda Komorniková, and Ján Szolgay. "Hybrid Forecasting of Daily River Discharges Considering Autoregressive Heteroscedasticity." Slovak Journal of Civil Engineering 25, no. 2 (June 27, 2017): 39–48. http://dx.doi.org/10.1515/sjce-2017-0011.

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AbstractIt is widely acknowledged that in the hydrological and meteorological communities, there is a continuing need to improve the quality of quantitative rainfall and river flow forecasts. A hybrid (combined deterministic-stochastic) modelling approach is proposed here that combines the advantages offered by modelling the system dynamics with a deterministic model and a deterministic forecasting error series with a data-driven model in parallel. Since the processes to be modelled are generally nonlinear and the model error series may exhibit nonstationarity and heteroscedasticity, GARCH-type nonlinear time series models are considered here. The fitting, forecasting and simulation performance of such models have to be explored on a case-by-case basis. The goal of this paper is to test and develop an appropriate methodology for model fitting and forecasting applicable for daily river discharge forecast error data from the GARCH family of time series models. We concentrated on verifying whether the use of a GARCH-type model is suitable for modelling and forecasting a hydrological model error time series on the Hron and Morava Rivers in Slovakia. For this purpose we verified the presence of heteroscedasticity in the simulation error series of the KLN multilinear flow routing model; then we fitted the GARCH-type models to the data and compared their fit with that of an ARMA - type model. We produced one-stepahead forecasts from the fitted models and again provided comparisons of the model’s performance.

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46

Samia, Ayari, Nouira Kaouther, and Trabelsi Abdelwahed. "A Hybrid ARIMA and Artificial Neural Networks Model to Forecast Air Quality in Urban Areas: Case of Tunisia." Advanced Materials Research 518-523 (May 2012): 2969–79. http://dx.doi.org/10.4028/www.scientific.net/amr.518-523.2969.

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Forecasting air quality time series represents a very difficult task since air quality contains autoregressive, linear and nonlinear patterns. Autoregressive Integrated Moving Average (ARIMA) models have been widely used in air quality time series forecasting. However, they fail to detect extreme events because of their presumed linear form of data. Artificial Neural Networks (ANN) models have proved to be promising nonlinear tools for air quality forecasting. A hybrid model combining ARIMA and ANN improved forecasting more than either of the models used independently. Experimental results with meteorological and Particulate Matter data indicated that the combined model can be used as an efficient forecasting and early warning system for providing air quality information towards the citizen, not only in Sfax Southern Suburbs but in other Tunisian regions that suffer from poor air quality conditions.

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47

Li, Lili, Shan Leng, Jun Yang, and Mei Yu. "Stock Market Autoregressive Dynamics: A Multinational Comparative Study with Quantile Regression." Mathematical Problems in Engineering 2016 (2016): 1–15. http://dx.doi.org/10.1155/2016/1285768.

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We study the nonlinear autoregressive dynamics of stock index returns in seven major advanced economies (G7) and China. The quantile autoregression model (QAR) enables us to investigate the autocorrelation across the whole spectrum of return distribution, which provides more insightful conditional information on multinational stock market dynamics than conventional time series models. The relation between index return and contemporaneous trading volume is also investigated. While prior studies have mixed results on stock market autocorrelations, we find that the dynamics is usually state dependent. The results for G7 stock markets exhibit conspicuous similarities, but they are in manifest contrast to the findings on Chinese stock markets.

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48

Razali, Widya Kartini Mohd. "Forecasting of Building Electrical Energy Consumption Using Nonlinear Autoregressive Exogenous Input (NARX) Neural Network Time Series (NNTS) Model." Journal of Advanced Research in Dynamical and Control Systems 12, no. 04-Special Issue (March 31, 2020): 1555–60. http://dx.doi.org/10.5373/jardcs/v12sp4/20201635.

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49

Suhartono, Suhartono, Dedy Dwi Prastyo, Heri Kuswanto, and Muhammad Hisyam Lee. "Comparison between VAR, GSTAR, FFNN-VAR and FFNN-GSTAR Models for Forecasting Oil Production." MATEMATIKA 34, no. 1 (May 28, 2018): 103–11. http://dx.doi.org/10.11113/matematika.v34.n1.1040.

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Monthly data about oil production at several drilling wells is an example of spatio-temporal data. The aim of this research is to propose nonlinear spatio-temporal model, i.e. Feedforward Neural Network - Vector Autoregressive (FFNN-VAR) and FFNN - Generalized Space-Time Autoregressive (FFNN-GSTAR), and compare their forecast accuracy to linear spatio-temporal model, i.e. VAR and GSTAR. These spatio-temporal models are proposed and applied for forecasting monthly oil production data at three drilling wells in East Java, Indonesia. There are 60 observations that be divided to two parts, i.e. the first 50 observations for training data and the last 10 observations for testing data. The results show that FFNN-GSTAR(11) and FFNN-VAR(1) as nonlinear spatio-temporal models tend to give more accurate forecast than VAR(1) and GSTAR(11) as linear spatio-temporal models. Moreover, further research about nonlinear spatio-temporal models based on neural networks and GSTAR is needed for developing new hybrid models that could improve the forecast accuracy.

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50

Laadissi, El Mehdi, Anas El Filali, and Malika Zazi. "A Nonlinear TSNN Based Model of a Lead Acid Battery." Bulletin of Electrical Engineering and Informatics 7, no. 2 (June 1, 2018): 169–75. http://dx.doi.org/10.11591/eei.v7i2.675.

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The paper studies a nonlinear model based on time series neural network system (TSNN) to improve the highly nonlinear dynamic model of an automotive lead acid cell battery. Artificial neural network (ANN) take into consideration the dynamic behavior of both input-output variables of the battery charge-discharge processes. The ANN works as a benchmark, its inputs include delays and charging/discharging current values. To train our neural network, we performed a pulse discharge on a lead acid battery to collect experimental data. Results are presented and compared with a nonlinear Hammerstein-Wiener model. The ANN and nonlinear autoregressive exogenous model (NARX) models achieved satisfying results.

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