Дисертації з теми "Nonlinear Autoregressive model"

Popularity of nonlinear threshold models and unit root tests has increased after the recent empirical studies concerning the effects of business cycles on macroeconomic data. These studies have shown that an economic variable may react differently in response to downturns and recoveries in a business cycle. Inspiring from empirical results, this thesis investigates dynamics of Turkish key macroeconomic data, namely capacity utilization rate, growth of import and export volume indices, growth of gross domestic product, interest rate for cash loans in Turkish Liras and growth of industrial production index. Estimation results imply that capacity utilization rate and growth of industrial production index show M-TAR type nonlinear stationary behavior according to the unit root test proposed by Enders and Granger (1998).

This dissertation consists of 3 essays In the first essay, A Simple Variable Selection Technique for Nonlinear Models, written in cooperation with Timo Teräsvirta and Rolf Tschernig, I propose a variable selection method based on a polynomial expansion of the unknown regression function and an appropriate model selection criterion. The hypothesis of linearity is tested by a Lagrange multiplier test based on this polynomial expansion. If rejected, a kth order general polynomial is used as a base for estimating all submodels by ordinary least squares. The combination of regressors leading to the lowest value of the model selection criterion is selected.  The second essay, Modelling and Forecasting Economic Time Series with Single Hidden-layer Feedforward Autoregressive Artificial Neural Networks, proposes an unified framework for artificial neural network modelling. Linearity is tested and the selection of regressors performed by the methodology developed in essay I. The number of hidden units is detected by a procedure based on a sequence of Lagrange multiplier (LM) tests. Serial correlation of errors and parameter constancy are checked by LM tests as well. A Monte-Carlo study, the two classical series of the lynx and the sunspots, and an application on the monthly S&P 500 index return series are used to demonstrate the performance of the overall procedure. In the third essay, Forecasting with Artificial Neural Network Models (in cooperation with Marcelo Medeiros), the methodology developed in essay II, the most popular methods for artificial neural network estimation, and the linear autoregressive model are compared by forecasting performance on 30 time series from different subject areas. Early stopping, pruning, information criterion pruning, cross-validation pruning, weight decay, and Bayesian regularization are considered. The findings are that 1) the linear models very often outperform the neural network ones and 2) the modelling approach to neural networks developed in this thesis stands up well with in comparison when compared to the other neural network modelling methods considered here.

Diss. Stockholm : Handelshögskolan, 2002. Spikblad saknas

Anaerobic digestion, which is the process by which bacteria breakdown organic matter to produce biogas (renewable energy source) and digestate (biofertiliser) in the absence of oxygen, proves to be the ideal concept not only for sustainable energy provision but also for effective organic waste management. However, the production amount of biogas to keep up with the global demand is limited by the underperformance in the system implementing the AD process. This underperformance is due to the difficulty in obtaining and maintaining the optimal operating parameters/states for anaerobic bacteria to thrive with regards to attaining a specific critical population number, which results in maximising the biogas production. This problem continues to exist as a result of insufficient knowledge of the interactions between the operating parameters and bacterial community. In addition, the lack of sufficient knowledge of the composition of bacterial groups that varies with changes in the operating parameters such as temperature, substrate and retention time. Without sufficient knowledge of the overall impact of the physico-environmental operating parameters on anaerobic bacterial growth and composition, significant improvement of biogas production may be difficult to attain. In order to mitigate this problem, this study has presented a nonlinear multi-parameter system modelling of mesophilic AD. It utilised raw data sets generated from laboratory experimentation of the influence of four operating parameters, temperature, pH, mixing speed and pressure on biogas and methane production, signifying that this is a multiple input single output (MISO) system. Due to the nonlinear characteristics of the data, the nonlinear black-box modelling technique is applied. The modelling is performed in MATLAB through System Identification approach. Two nonlinear model structures, autoregressive with exogenous input (NARX) and Hammerstein-Wiener (NLHW) with different nonlinearity estimators and model orders are chosen by trial and error and utilised to estimate the models. The performance of the models is determined by comparing the simulated outputs of the estimated models and the output in the validation data. The approach is used to validate the estimated models by checking how well the simulated output of the models fits the measured output. The best models for biogas and methane production are chosen by comparing the outputs of the best NARX and NLHW models (each for biogas and methane production), and the validation data, as well as utilising the Akaike information criterion to measure the quality of each model relative to each of the other models. The NLHW models mhw2 and mhws2 are chosen for biogas and methane production, respectively. The identified NLHW models mhw2 and mhws2 represent the behaviour of the production of biogas and methane, respectively, from mesophilic AD. Among all the candidate models studied, the nonlinear models provide a superior reproduction of the experimental data over the whole analysed period. Furthermore, the models constructed in this study cannot be used for scale-up purpose because they are not able to satisfy the rules and criteria for applying dimensional analysis to scale-up.

Dans les séries temporelles neurophysiologiques, on observe de fortes oscillations neuronales, et les outils d'analyse sont donc naturellement centrés sur le filtrage à bande étroite.Puisque cette approche est trop réductrice, nous proposons de nouvelles méthodes pour représenter ces signaux.Nous centrons tout d'abord notre étude sur le couplage phase-amplitude (PAC), dans lequel une bande haute fréquence est modulée en amplitude par la phase d'une oscillation neuronale plus lente.Nous proposons de capturer ce couplage dans un modèle probabiliste appelé modèle autoregressif piloté (DAR). Cette modélisation permet une sélection de modèle efficace grâce à la mesure de vraisemblance, ce qui constitue un apport majeur à l'estimation du PAC.%Nous présentons différentes paramétrisations des modèles DAR et leurs algorithmes d'inférence rapides, et discutons de leur stabilité.Puis nous montrons comment utiliser les modèles DAR pour l'analyse du PAC, et démontrons l'avantage de l'approche par modélisation avec trois jeux de donnée.Puis nous explorons plusieurs extensions à ces modèles, pour estimer le signal pilote à partir des données, le PAC sur des signaux multivariés, ou encore des champs réceptifs spectro-temporels.Enfin, nous proposons aussi d'adapter les modèles de codage parcimonieux convolutionnels pour les séries temporelles neurophysiologiques, en les étendant à des distributions à queues lourdes et à des décompositions multivariées. Nous développons des algorithmes d'inférence efficaces pour chaque formulations, et montrons que l'on obtient de riches représentations de façon non-supervisée
In neurophysiological time series, strong neural oscillations are observed in the mammalian brain, and the natural processing tools are thus centered on narrow-band linear filtering.As this approach is too reductive, we propose new methods to represent these signals.We first focus on the study of phase-amplitude coupling (PAC), which consists in an amplitude modulation of a high frequency band, time-locked with a specific phase of a slow neural oscillation.We propose to use driven autoregressive models (DAR), to capture PAC in a probabilistic model. Giving a proper model to the signal enables model selection by using the likelihood of the model, which constitutes a major improvement in PAC estimation.%We first present different parametrization of DAR models, with fast inference algorithms and stability discussions.Then, we present how to use DAR models for PAC analysis, demonstrating the advantage of the model-based approach on three empirical datasets.Then, we explore different extensions to DAR models, estimating the driving signal from the data, PAC in multivariate signals, or spectro-temporal receptive fields.Finally, we also propose to adapt convolutional sparse coding (CSC) models for neurophysiological time-series, extending them to heavy-tail noise distribution and multivariate decompositions. We develop efficient inference algorithms for each formulation, and show that we obtain rich unsupervised signal representations

In this paper, we study the industrial production index of Sweden from Jan, 2000 to latest Feb, 2010. We find out there is a structural break at time point Dec, 2007, when the global financial crisis burst out first in U.S then spread to Europe. To model the industrial production index, one of the business cycle indicators which may behave nonlinear feature suggests utilizing a smooth transition autoregressive (STAR) model. Following the procedures given by Teräsvirta (1994), we carry out the linearity test against the STAR model, determine the delay parameter and choose between the LSTAR model and the ESTAR model. The results from the estimated model suggest the STAR model is better performing than the linear autoregressive model.

The analysis of time series has long been the subject of interest in different fields. For decades time series were analysed with linear models, which have many advantages. Nevertheless, an issue which has been raised is whether there exist other models that can explain and forecast real data better than linear ones. In this thesis, new nonlinear time series models are suggested, which consist of a nonlinear conditional mean model, such as an ExpAR or an Extended ExpAR, and a nonlinear conditional variance model, such as an ARCH or a GARCH. Since new models are introduced, simulated series of the new models are presented, as it is important in order to see what characteristics real data which could be explained by them should have. In addition, the models are applied to various stationary and nonstationary economic and financial time series and are compared to the classic AR-ARCH and AR-GARCH models, in terms of fitting and forecasting. It is shown that, although it is difficult to beat the AR-ARCH and AR-GARCH models, the ExpAR and Extended ExpAR models and their special cases, combined with conditional heteroscedastic errors, can be useful tools in fitting, describing and forecasting nonlinear behaviour in financial and economic time series, and can provide some improvement in terms of both fitting and forecasting compared to the AR-ARCH and AR-GARCH models.

時間序列之變點鬥檻模型是一種非線性的模型。此論文探討有關該模型之參數估計，同時對其參數估計作出統計分析。我們運用了遺傳式計算機運算來估計這些參數及對其作出研究。我們利用了MDL來對比不同的變點門檻模型，同時我們也利用了MDL來選取對應的變點門檻模型。
This article considers the problem of modeling non-linear time series by using piece-wise TAR model. The numbers of change points, the numbers of thresholds and the corresponding order of AR in each piecewise TAR segments are assumed unknown. The goal is to nd out the “best“ combination of the number of change points, the value of threshold in each time segment, and the underlying AR order for each threshold regime. A genetic algorithm is implemented to solve this optimization problem and the minimum description length principle is applied to compare various segmented TAR. We also show the consistency of the minimal MDL model selection procedure under general regularity conditions on the likelihood function.
Detailed summary in vernacular field only.
Tang, Chong Man.
Thesis (M.Phil.)--Chinese University of Hong Kong, 2012.
Includes bibliographical references (leaves 45-47).
Abstracts also in Chinese.
Chapter 1 --- Introduction --- p.1
Chapter 1.1 --- Introduction --- p.1
Chapter 2 --- Minimum Description Length for Pure TAR --- p.4
Chapter 2.1 --- Model selection using Minimum Description Length for Pure TAR --- p.4
Chapter 2.1.1 --- Derivation of Minimum Description Length for Pure TAR --- p.5
Chapter 2.2 --- Optimization Using Genetic Algorithms (GA) --- p.7
Chapter 2.2.1 --- General Description --- p.7
Chapter 2.2.2 --- Implementation Details --- p.9
Chapter 3 --- Minimum Description Length for TAR models with structural change --- p.13
Chapter 3.1 --- Model selection using Minimum Description Length for TAR models with structural change --- p.13
Chapter 3.1.1 --- Derivation of Minimum Description Length for TAR models with structural change --- p.14
Chapter 3.2 --- Optimization Using Genetic Algorithms --- p.17
Chapter 4 --- Main Result --- p.20
Chapter 4.1 --- Main results --- p.20
Chapter 4.1.1 --- Model Selection using minimum description length --- p.21
Chapter 5 --- Simulation Result --- p.24
Chapter 5.1 --- Simulation results --- p.24
Chapter 5.1.1 --- Example of TAR Model Without Structural Break --- p.24
Chapter 5.1.2 --- Example of TAR Model With Structural Break I --- p.26
Chapter 5.1.3 --- Example of TAR Model With Structural Break II --- p.29
Chapter 6 --- An empirical example --- p.33
Chapter 6.1 --- An empirical example --- p.33
Chapter 7 --- Consistency of the CLSE --- p.36
Chapter 7.1 --- Consistency of the TAR parameters --- p.36
Chapter 7.1.1 --- Consistency of the estimation of number of threshold --- p.36
Chapter 7.1.2 --- Consistency of the change point parameters --- p.43
Bibliography --- p.45

碩士
國立臺灣大學
工程科學及海洋工程學研究所
97
Since the real mechanical systems have nonlinear factors, the only differences are the extent of nonlinearity, so the vibration phenomenon actually are nonlinear. Since the real system has damping, so the oscillation frequency of non-linear system change with amplitude. Thus it’s difficult to estimate the oscillation frequency of a non-linear systems. However, the natural frequency of any system is natural and is not influenced by other factors. This article purposes a set of identification process to estimate the linear modal parameters of nonlinear systems. At first in this thesis, it is to simulate the output response on both a single and three degrees of freedom of the non-linear systems with damping by using numerical simulation. We can compute the output response of a nonlinear vibration system using system identification techniques by the mathematical model of Nonlinear AutoRegressive with eXogenous inputs model combined with Volterra series to estimate the linear modal parameters of nonlinear systems. Besides, in the analytic process, it also utilizes power spectral density diagram, time frequency analysis diagram and modal stabilization diagram to assist the reach. Finally, NARX method is applied to the two experimental examples, cantilever beam and framed structure of motorcycle. cantilever beam used to test the free response of the system identification information. Framed structure of motorcycle were excitation by hammer and shaker to discuss the identification ability of NARX method under some noise disturbance. By comparing the numerical and the experimental data, for system identificationtechnique involved can work well to estimate the linear modal parameters of nonlinear systems

碩士
國立成功大學
航空太空工程學系
104
In the recent years, renewable energy with zero pollution has been emphasized by many countries. Wind energy is wildly used due to its clean and renewable properties. Forecasting the output power of the wind turbine generators is a highly focus topic now. It’s important to the power company and the wind power company of predicting the wind energy precisely, which they applied to reduce cost and raise the quality. However, due to the randomness and the instability characteristics, it’s a great challenge to predict wind power accurately. Moreover, monitoring wind turbine health is also important. As long as an error is detected, it can be fixed right away. There are a lots of research that built plenty of mathematical models to predict wind power. An input-output property forecasting mathematical model is established to complete the forecasting and wind turbine health monitoring by using actual data recorded from the real wind turbines. By seeking out the time delay from the coherences between wind speed and output power, the accuracy can be improved by combining with autoregressive approach. By using the MANOVA of the multivariate analysis and applications to analysis the parameters of the model. The status of the wind turbine can be detected by finding the correlations between parameters to reach the goal of monitoring the health of the wind turbine.

碩士
國立臺灣大學
工程科學及海洋工程學研究所
99
During the past decade, although the linear structural system identification had been well developed, the nonlinear response was often taken as noise or neglected throughout the linear system identification procedure. Therefore, in this thesis, using the NARX (Nonlinear AutoRegressive with eXogenous input) model, a nonlinear characteristic parameters identification formula was derived. And combining with state-space system identification theorem, the linear and nonlinear characteristic parameters were estimated successfully. Furthermore, the differences between linear and nonlinear characteristics were discussed. Using Volterra series, the GFRF (generalized frequency response function) was derived; and basing on the GFRF, the nonlinear characteristics of nonlinear structural systems were examined. In the end, the nonlinear system identification procedure was applied on computer simulations, including free and forced vibrations in single-degree-of-freedom and three-degree-of-freedom structural systems. The procedure was then further applied on two real structural system identification cases, one is the impact test of a vertical cantilever steel beam structure, and the other one is the earthquake shaking test of a Bench-Mark-Model, which was conducted by National Center for Research on Earthquake Engineering of R.O.C. All the results of identifications are represented completely.

碩士
國立臺北科技大學
冷凍空調工程系所
105
Three methods are applied in this study to predict chiller performance.They are linear regression, backpropagation neural network and nonlinear autoregressive with exogenous input model. The power consumption models of chiller from two cases are established by using these three methods. After that, the simulated results and prediction are compared and the performance of models is improved by using these three methods under the same base. To compare two different cases, we need data accumulation, delete the irrational data, assort data to two cluster and select the data that remains in the same domain, set the parameters for the three method of building model, train the tree kind of model, compared the results of simulation and prediction.After we doing the steps from above, the results show two cases indicate that NARX is better than other two methods from simulation to prediction.It shows exectly that NARX has better dealing ability to the data that related from time and discontinuouty just like the data from chiller. For the adaptation to data, NARX also has good performance.You can see it well in case analysis. Although NARX is doing well in both simulation and prediction for the data related to time and discontinuouty, it has a disadvantage.“Finding a proper delay vector for Time Delay Line need lots of time”, we don’t have an effective Standard Operation Procedure for finding it. So the disadvantage cause a lots of time for building this model. If we can find a better way to finding it than we can improve this method.

碩士
淡江大學
財務金融學系碩士在職專班
97
Abstract： Because of factors such as transaction costs, the prices of ADRs and their underlying shares converge within a non-linear framework. This paper selected the STAR（smooth transition autoregressive）model, proposed by Teräsvirta（1994）to model the convergence. We used the STAR model and a sample of 6 dually listed shares（listed in Taiwan and on the NYSE and NASDAQ）to investigate the convergence between the prices of ADRs and the prices of the Taiwanese-traded shares. These 6 dually listed shares are TSM, UMC, ASX, SPIL, AUO and CHT. We found that the convergence of the ADRs and their underlying shares was non- linear except for ASX. Because the market is imperfect, it exhibits non-linear convergence, where the actual price deviates from price parity. In this study we offer investors in ADRs and their underlying shares information and knowledge about the market price convergence of ADRs and their underlying shares.

碩士
淡江大學
財務金融學系碩士班
102
The 2007 U.S. happened subprime mortgage crisis, coupled with the asset securitization and structured finance products. The financial institutions invest in subprime mortgage–related derivative financial instruments and suffered a shock, loss liquidity. A number of financial institutions went bankrupt, triggering the global financial crisis. To this end, BCBS released “International Framework for Liquidity Risk Measurement, Standards and Monitoring”. BSBC proposed liquidity coverage ratio and net stable funding ratio. This paper used panel smooth transition autoregressive model to determine whether the liquidity risk to banking performance exist panel smooth transition effect. When liquidity reserves ratio is less than 23.5375%, it is positively relevant between loan-to-deposit ratio and banking performance, while it is negatively relevant between non-performing loans ratio and banking performance, it is negatively relevant between banking size and banking performance. When liquidity reserves ratio is greater than 23.5375%, it is negatively relevant between non-performing loans ratio and banking performance, it is negatively relevant between banking size and banking performance. When liquid assets ratio is less than 0.119%, it is negatively relevant between banking size and banking performance ,but it is positively relevant between BIS ratio and banking performance. When liquid assets ratio is greater than 0.119%, it is negatively relevant between banking size, BIS ratio and banking performance.

MSc (Statistics)
Department of Statistics
Over the years researchers have been modeling inflation rate in Ghana using linear models such as Autoregressive Integrated Moving Average (ARIMA), Autoregressive Moving Average (ARMA) and Moving Average (MA). Empirical research however, has shown that financial data, such as inflation rate, does not follow linear patterns. This study seeks to model and forecast inflation in Ghana using nonlinear models and to establish the existence of nonlinear patterns in the monthly rates of inflation between the period January 1981 to August 2016 as obtained from Ghana Statistical Service. Nonlinearity tests were conducted using Keenan and Tsay tests, and based on the results, we rejected the null hypothesis of linearity of monthly rates of inflation. The Augmented Dickey-Fuller (ADF) was performed to test for the presence of stationarity. The test rejected the null Hypothesis of unit root at 5% significant level, and hence we can conclude that the rate of inflation was stationary over the period under consideration. The data were transformed by taking the logarithms to follow nornal distribution, which is a desirable characteristic feature in most time series. Monthly rates of inflation were modeled using threshold models and their fitness and forecasting performance were compared with Autoregressive (AR ) models. Two Threshold models: Self-Exciting Threshold Autoregressive (SETAR) and Logistic Smooth Threshold Autoregressive (LSTAR) models, and two linear models: AR(1) and AR(2), were employed and fitted to the data. The Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC) were used to assess each of the fitted models such that the model with the minimum value of AIC and BIC, was judged the best model. Additionally, the fitted models were compared according to their forecasting performance using a criterion called mean absolute percentage error (MAPE). The model with the minimum MAPE emerged as the best forecast model and then the model was used to forecast monthly inflation rates for the year 2017. The rationale for choosing this type of model is contingent on the behaviour of the time-series data. Also with the history of inflation modeling and forecasting, nonlinear models have proven to perform better than linear models. The study found that the SETAR and LSTAR models fit the data best. The simple AR models however, out-performed the nonlinear models in terms of forecasting. Lastly, looking at the upward trend of the out-sample forecasts, it can be predicted that Ghana would experience double digit inflation in 2017. This would have several impacts on many aspects of the economy and could erode the economic gains i made in the year 2016. Our study has important policy implications for the Central Bank of Ghana which can use the data to put in place coherent monetary and fiscal policies that would put the anticipated increase in inflation under control.