G.E.P. Box and G.M. Jenkins, Time Series Analysis. Forecasting and Control. San Francisco: Holden-Day, 1976.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....than # 2 = 10 4 . All experiments were run in the MATLAB environment. The purpose of these experiments was to compare the generalization ability of the proposed neuro fuzzy system with learning tolerant to imprecision and classical zero tolerance learning. Data originating from Box and Jenkins [3] work concerning the identification of a gas oven. Air and methane were delivered into the gas oven (gas flow in ft min an input signal x (n) to obtain a mixture of gases containing CO 2 (percentage content output signal y (n) The data consisted of 296 pairs of input output samples in 9 ....

G.E.P. Box and G.M. Jenkins, Time Series Analysis. Forecasting and Control. San Francisco: Holden-Day, 1976.

....The time step used in the method is 0.1 and initial condition were x(0) 1.2, #=17, x(t) 0 for t 0. First 500 data sets were used for training and remaining data for testing. c) Gas Furnace Time Series Data This time series was used to predict the CO 2 (carbon dioxide) concentration y(t 1) [7]. Data is represented as [u(t) y(t) y(t 1) The time series consists of 292 pairs of observation and 50 of data was used for training and remaining for testing. TABLE 1. PARAMETERS USED FOR EANNs Parameter Setting Population size 40 Maximum no of generations 40 Number of hidden ....

Box G E P and Jenkins G M, Time Series Analysis, Forecasting and Control, San Francisco: Holden Day, 1970.

....in Figs. 3 and 4, respectively. It can be seen that the model constructed by the LROLS algorithm captured the underlying dynamics of the system better than the OLS algorithm did. Example 2. This example was a two input two output data set collected from a turboalternator (Appendix A11.3 in [16]) The data set contained 100 samples. The system inputs, the in phase current deviation u 1 (k) and the out of phase current deviation u 2 (k) are plotted in Fig. 5; while the system outputs, the voltage deviation y 1 (k) and the frequency deviation y 2 (k) are shown in Fig. 6. The two output ....

G.M. Jenkins and D.G. Watts, Spectral Analysis and Its Applications. San Francisco: Holden-Day, 1986.

....patterns are propagated again, and in this epoch, back propagation is used to modify the antecedent parameters, while the conclusion parameters remain fixed. This procedure is then iterated. 6. Experimental Setup Using Soft Computing Models and MARS Gas Furnace Time Series Data This time series [12] was used to predict the CO 2 (carbon dioxide) concentration y(t 1) In a gas furnace system, air and methane are combined to form a mixture of gases containing CO 2 . Air fed into the gas furnace is kept constant, while the methane feed rate u(t) can be varied in any desired manner. After that, ....

Box G E P and Jenkins G M, Time Series Analysis, Forecasting and Control, San Francisco: Holden Day, 1970.

....the width of the window for computing the average of the periodogram for the frequency of the spectral analysis. The bandwidth was selected by using the narrowest bandwidth for which the spectral functions ceased being smooth, a standard procedure termed window closing that is recommended by Jenkins and Watts (1968). 17 See Jenkins and Watts (1968, p. 437) 9 where # represents the coherence between series X and series Y at frequency #, and m denotes the window width; m = N B W #, with N equaling the number of observations, and B W is the bandwidth used, B W = 0.0171. According to Brockwell and ....

....the average of the periodogram for the frequency of the spectral analysis. The bandwidth was selected by using the narrowest bandwidth for which the spectral functions ceased being smooth, a standard procedure termed window closing that is recommended by Jenkins and Watts (1968) 17 See Jenkins and Watts (1968, p. 437) 9 where # represents the coherence between series X and series Y at frequency #, and m denotes the window width; m = N B W #, with N equaling the number of observations, and B W is the bandwidth used, B W = 0.0171. According to Brockwell and Davis (1991) the coherence is ....

Jenkins, G.M., and Watts, D.G., Spectral Analysis and Its Applications. San Francisco: Holden-Day, 1968.

....Australia Email: Ajith.Abraham infotech.monash.edu.au Abstract In this paper, we review the speed of convergence and generalization performance of different Artificial Neural Network (ANN) learning algorithms for function approximation. We used the well known gas furnace time series data [2] for evaluating ANN performance using backpropagation algorithm (BP) BP with varying learning rate BP (VLR) Scaled Conjugate Gradient Algorithm (SCGA) and Levenberg Marquardt (LM) algorithm. For different learning algorithms, we altered the number of hidden neurons and node activation functions ....

Box G E P and Jenkins G M, Time Series Analysis, Forecasting and Control, San Francisco: Holden Day, 1970.

....dependence, traffic modeling, self similarity. 1. INTRODUCTION Time series modeling holds a great promise as a tool for studying network traffic. However, traditional models can only capture short range dependence; for examples, Poisson process, Markov processes, AR, MA, ARMA and ARIMA processes [1]. The studies of high quality traffic measurements have revealed that traffic in high speed networks exhibits selfsimilarity, i.e. long range dependence [2] that can t be captured by previous models. Hence, self similar models, such as FGN (fractional Gaussian noise) model [3] and FDN (fractional ....

....process. Section 4 shows how to build a FARIMA(p,d,q) model to describe a traffic trace. Section 5 studies the feasibility of FARIMA(p,d,q) models. Section 6 is the concluding remarks. 2. THE MODEL FARIMA processes are the natural generalizations of standard ARIMA (p,d,q) processes defined in [1] when the degree of differencing d is allowed to take nonintegeral values [4] A FARIMA(p,d,q) process X t : t= 1, 0, 1, is defined to be , t d a B X B Q = D F (2 1) where a t is a white noise and d ( 0.5, 0.5) 1 ) 2 2 1 p p B B B B f f f = F # , 1 ) ....

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. G. Box and G. Jenkins, Time series: Forecasting and control, revised ed., San Francisco: Holden-day,1976.

....0 OE u ( 0 8 9 = 22) It is important to remember that fuzzy models can have additional validation by comparing the linguistic rules with the knowledge of an expert. 9. Examples In this section we apply the techniques to the data of the example given by Box and Jenkins [21]. The process is a gas furnace with single input u(t) gas flow) and single output y(t) CO 2 concentration) The data set contains 296 data points, we use the last 290 points. For the first step (selection of the regressors) the Lipschitz Quotients method was applied, which yielded the surface ....

G.E.P. Box and G.M. Jenkins,Time Series Analysis, Forecasting and Control. San Francisco: Holden Day 1970.

....if is greater than the threshold value VT and H 0 is decided otherwise. Compensate Effect of x(n) X Compute Periodogram Shift f c P (f) I (f f ) df x a c 0.5 0.5 L V T H 0 H 1 x(n) L P (f) Finite Length a I (f f ) x c I (f) x P (f) a Fig. 1: System Block Diagram of the SMD Following [5], we can rewrite (4) as = N Gamma1 X m= Gamma(N Gamma1) r x (m) r a (m) exp( Gamma2 f c m) 5) so that the integration operation in computing is avoided. For implementation, we will use (5) instead of (4) The ACS of x(n) is given by r x (m) 1 N N Gammajmj Gamma1 X n=0 x(n)x(n ....

....the false alarm rates (PFA ) with respect to the threshold. For SMD, calculating its PFA is as difficult as finding the exact distribution of the BTSE. Very often, in the field of classical spectral analysis, the chi squared approximation is employed to evaluate the distribution of the BTSE [5]. Borrowing the result of [5] directly, we can obtain an approximate solution for PFA of the SMD: P ( V T jH 0 ) 1 Gamma fl Gamma cVT =oe v 2 ; c Delta ; 9) c = N= 0 N Gamma1 X m= Gamma(N Gamma1) r 2 a (m) 1 A : 10) where fl(x; y) R x 0 u y Gamma1 e Gammau ....

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G.M. Jenkins and D.G. Watts, Spectral Analysis and its Applications, San Francisco: Holden-day, 1968.

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Box, G. and Jenkins,G. #1970# Time Series Analysis. San Francisco: Holden Day.

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G.E.P. Box and G.M. Jenkins,Time Series Analysis, Forecasting and Control. (San Francisco: Holden Day 1970).

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