ARMA model

Suppose we are interested in forecasting a time series and, in addition to the time series data, we have data from many time series related to the one we want to forecast. Since building a dynamic multivariate model for the set of time series can be a complex task, it is important to measure in advance the increase in precision to be attained by using multivariate forecasts with respect to univariate ones. This article presents a simple procedure designed to obtain a consistent estimate of this measure. Its performance is illustrated with Monte Carlo simulations and examples.

We compare forecasts of the realized volatility of the pound, mark and yen exchange rates against the dollar, calculated from intraday rates, over horizons ranging from one day to three months. Our forecasts are obtained from a short memory ARMA model, a long memory ARFIMA model, a GARCH model and option implied volatilities. We find intraday rates provide the most accurate forecasts for the one-day and one-week forecast horizons while implied volatilities are at least as accurate as the historical forecasts for the one-month and three-month horizons. The superior accuracy of the historical forecasts, relative to implied volatilities, comes from the use of high frequency returns, and not from a long memory specification. We find significant incremental information in historical forecasts, beyond the implied volatility information, for forecast horizons up to one week.

Studies of the nonlinear magnetospheric dynamics have led to several directions useful in understanding space physics processes, in particular those related to magnetospheric currents, and making space weather forecasts possible. Four such directions are identified: (a) empirical time series prediction with nonlinear autoregressive moving-average (ARMA) models, for which an example is given in terms of a geosynchronous electron flux index model. (b) Measurement of physical properties of the currents from the coefficients of the ARMA models, such as characteristic time scales and coupling strengths. Using a Dst index model we measure the ring current decay time as a function of storm phase and activity, and identify new oscillation time scales correlating with the substorm injection activity. (c) Spatiotemporal nonlinear modeling predicts the amplitude and location of the disturbance as a function of space, as well as its time evolution. An example is given in terms of predicting the longitudinal and temporal profile of midlatitude geomagnetic disturbances. (d) Nonlinear dynamical models can be coupled to other physical or empirical approaches to build comprehensive space weather models. SWIFT, an ionospheric space weather model, is discussed as an example. Other applications of nonlinear dynamics are briefly discussed.

Most of the advanced nonlinear control algorithms require a model of the system to be controlled. Unfortunately, most of the processes in the chemical industry are nonlinear, and fundamental models describing them are lacking. Thus there is a need for the identification and control of nonlinear systems through available inputoutput data. In this article, we brief& introduce the input-output model used (polynomial ARMA models), and analyze its stability and invertibility. This paves the way to the development of a nonlinear-model-predictive controller. Implementation issues such as modeling of disturbance, state and parameter estimation are discussed. The theory presented is illustrated through examples.

The standing debate over whether hydrological systems are deterministic or stochastic has been taken to a new level by controversial applications of chaos mathematics. This paper reviews the procedure, constraints, and past usage of a popular chaos time series analysis method, correlation integral analysis, in hydrology and adds a new analysis of daily stream¯ow from a pristine watershed. Signi®cant problems with the use of correlation integral analysis (CIA) were found to include a continued reliance on the original algorithm even though it was corrected subsequently and failure to consider the physics underlying mathematical results. The new analysis of daily stream¯ow reported here found no attractor with D T 5. Phase randomization of the Fourier Transform of stream¯ow was used to provide a better stochastic surrogate than an Autoregressive Moving Average (ARMA) model or gaussian noise for distinguishing between chaotic and stochastic dynamics. Ó : S 0 3 0 9 -1 7 0 8 ( 9 9 ) 0 0 0 0 8 -1

A firm in the early stages of financial distress exhibits characteristics different from those of healthy firms. As the economic condition of a firm worsens, its financial characteristics shift toward those of failed firms. Practitioners in the financial sector have long been interested in the early detection of a firm's slide toward insolvency. Several models have been developed with this purpose in mind, but these older models are static in nature. Therefore, a need exists for the development of business failure prediction models that assess the financial condition of firms sequentially over time. This article addresses this need by presenting a sequential business failure prediction model.

This paper presents an algorithm to perform online tremor characterization from motion sensors measurements, while filtering the voluntary motion performed by the patient. In order to estimate simultaneously both nonstationary signals in a stochastic filtering framework, pathological tremor was represented by a time-varying harmonic model and voluntary motion was modeled as an auto-regressive moving-average (ARMA) model. Since it is a nonlinear problem, an extended Kalman filter (EKF) was used. The developed solution was evaluated with simulated signals and experimental data from patients with different pathologies. Also, the results were comprehensively compared with alternative techniques proposed in the literature, evidencing the better performance of the proposed method. The algorithm presented in this paper may be an important tool in the design of active tremor compensation systems.

This paper investigates the prediction of a Lorenz chaotic attractor having relatively high values of Lypunov's exponents. The characteristic of this time series is its rich chaotic behavior. For such dynamic reconstruction problem, regularized radial basis function (RBF) neural network (NN) models have been widely employed in the literature. However, author recommends using a two-layer multi-layer perceptron (MLP) NN-based recurrent model. When none of the available linear models have been able to learn the dynamics of this attractor, it is shown that the proposed NN-based auto regressive (AR) and auto regressive moving average (ARMA) models with regularization have not only learned the true trajectory of this attractor, but also performed much better in multi-step-ahead predictions. However, equivalent linear models seem to fail miserably in learning the dynamics of the time series, despite the low values of Akaike's final prediction error (FPE) estimate. Author proposes to employ the recurrent NN-based ARMA model with regularization which clearly outperforms all other models and thus, it is possible to obtain good results for prediction and reconstruction of the dynamics of the chaotic time series with NN-based models.

This paper addresses parametric system identification of linear and nonlinear dynamic systems by analysis of the input and output signals. Specifically, we investigate the relationship between estimation of the system using a feedforward neural network model and estimation of the system by use of linear and nonlinear autoregressive moving-average (ARMA) models. By utilizing a neural network model incorporating a polynomial activation function, we show the equivalence of the artificial neural network to the linear and nonlinear ARMA models. We compare the parameterization of the estimated system using the neural network and ARMA approaches by utilizing data generated by means of computer simulations. Specifically, we show that the parameters of a simulated ARMA system can be obtained from the neural network analysis of the simulated data or by conventional least squares ARMA analysis. The feasibility of applying neural networks with polynomial activation functions to the analysis of experimental data is explored by application to measurements of heart rate (HR) and instantaneous lung volume (ILV) fluctuations.

In this article we have used the ARMA (autoregressive moving average process) and persistence models to predict the hourly average wind speed up to 10 h in advance. In order to adjust the time series to the ARMA models, it has been necessary to carry out their transformation and standardization, given the non-Gaussian nature of the hourly wind speed distribution and the non-stationary nature of its daily evolution. In order to avoid seasonality problems we have adjusted a different model to each calendar month. The study expands to five locations with different topographic characteristics and to nine years. It has been proven that the transformation and standardization of the original series allow the use of ARMA models and these behave significantly better in the forecast than the persistence model, especially in the longer-term forecasts. When the acceptable RMSE (root mean square error) in the forecast is limited to 1.5 m/s, the models are only valid in the short term.

This study aims to develop a stochastic framework of model to forecast future sales for pharmaceutical industry. In this regard, the study focuses on Merck Pharmaceutical monthly sales data. This study examines the Sale forecasting models. The study includes monthly data published in the annual reports of the company from Jan. 2008 to Dec. 2012.The time series diagram shows unequal means over the time period that suggests the data is stationary. Having transformed the data, ARMA (1, 1) model is applied which shows that there will be increase
in sales by $6.784m given that in the last month sales were $1bn. On the contrary, last month’s residual has an
adverse effect on current month sales up to the extent of $432.942m. In this study AR (1) and MA (1) both the processes are significant at 1%.

The purpose of this paper is to apply the Box±Jenkins methodology to ARIMA models and determine the reasons why in empirical tests it is found that the post-sample forecasting the accuracy of such models is generally worse than much simpler time series methods. The paper concludes that the major problem is the way of making the series stationary in its mean (i.e. the method of dierencing) that has been proposed by Box and Jenkins. If alternative approaches are utilized to remove and extrapolate the trend in the data, ARMA models outperform the models selected through Box±Jenkins methodology. In addition, it is shown that using ARMA models to seasonally adjusted data slightly improves post-sample accuracies while simplifying the use of ARMA models. It is also con®rmed that transformations slightly improve post-sample forecasting accuracy, particularly for long forecasting horizons. Finally, it is demonstrated that AR(1), AR(2) and ARMA(1,1) models can produce more accurate post-sample forecasts than those found through the application of Box± Jenkins methodology. # 1997 by John Wiley & Sons, Ltd.

Absfmct-Magnitude. squared coherence (MSC) and time delay are two important quantities needed for passive detection and localization of a radiating source. using several sensors. This paper presents a novel approach to esiimating the MSC and time delay from the outputs of two sensors. It first.models the MSC as the product of the transfer functions of two autoregressive moving-average (ARMA) filters. The ARMA coefficients are then determined by a least squares, matrix pseudoinverse solution to the estimation equation. Time delay estimation follows as a byproduct, since both phase and MSC estimates are now available. Simulation results obtained from this modeling approach are compared against those estimated from the traditional periodograms. In the majority of cases studied, the ARMA approach appears to be superior, giving smaller bias and variances in both MSC and time delay estimations.

The challenge of predicting future values of a time series covers a variety of disciplines. The fundamental problem of selecting the order and identifying the time varying parameters of an autoregressive moving average model (ARMA) concerns many important fields of interest such as linear prediction, system identification and spectral analysis. Recent research activities in forecasting with artificial neural networks (ANNs) suggest that ANNs can be a promising alternative to the traditional ARMA structure. These linear models and ANNs are often compared with mixed conclusions in terms of the superiority in forecasting performance. This study was designed: (a) to investigate a hybrid methodology that combines ANN and ARMA models; (b) to resolve one of the most important problems in time series using ARMA structure and Box-Jenkins methodology: the identification of the model. In this paper, we present a new procedure to predict time series using paradigms such as: fuzzy systems, neural networks and evolutionary algorithms. Our goal is to obtain an expert system based on paradigms of artificial intelligence, so that the linear model can be identified automatically, without the need of human expert participation. The obtained linear model will be combined with ANN, making up an hybrid system that could outperform the forecasting result. r

This paper considers adaptive estimation in nonstationary autoregressive moving average models with the noise sequence satisfying a generalised autoregressive conditional heteroscedastic process. The locally asymptotic quadratic form of the log-likelihood ratio for the model is obtained. It is shown that the limit experiment is neither LAN nor LAMN, but is instead LABF. Adaptivity is discussed and it is found that the parameters in the model are generally not adaptively estimable if the density of the rescaled error is asymmetric. For the model with symmetric density of the rescaled error, a new efficiency criterion is established for a class of defined M ν -estimators. It is shown that such efficient estimators can be constructed when the density is known. Using the kernel estimator for the score function, adaptive estimators are constructed when the density of the rescaled error is symmetric, and it is shown that the adaptive procedure for the parameters in the conditional mean part uses the full sample without splitting. These estimators are demonstrated to be asymptotically efficient in the class of M ν -estimators. The paper includes the results that the stationary ARMA-GARCH model is LAN, and that the parameters in the model with symmetric density of the rescaled error are adaptively estimable after a reparameterisation of the GARCH process.

The integration of wind farms in power networks has become an important problem. This is because the electricity produced cannot be preserved because of the high cost of storage and electricity production must follow market demand. Short-long-range wind forecasting over different lengths/periods of time is becoming an important process for the management of wind farms. Time series modelling of wind speeds is based upon the valid assumption that all the causative factors are implicitly accounted for in the sequence of occurrence of the process itself. Hence time series modelling is equivalent to physical modelling. Auto Regressive Moving Average (ARMA) models, which perform a linear mapping between inputs and outputs, and Artificial Neural Networks (ANNs) and Adaptive Neuro-Fuzzy Inference Systems (ANFIS), which perform a non-linear mapping, provide a robust approach to wind power prediction. In this work, these models are developed in order to forecast power production of a wind farm with three wind turbines, using real load data and comparing different time prediction periods. This comparative analysis takes in the first time, various forecasting methods, time horizons and a deep performance analysis focused upon the normalised mean error and the statistical distribution hereof in order to evaluate error distribution within a narrower curve and therefore forecasting methods whereby it is more improbable to make errors in prediction.

Traditionally, the autoregressive moving average (ARMA) model has been one of the most widely used linear models in time series prediction. Recent research activities in forecasting with artificial neural networks (ANNs) suggest that ANNs can be a promising alternative to the traditional ARMA structure. These linear models and ANNs are often compared with mixed conclusions in terms of the superiority in forecasting performance. In this paper we propose a hybridization of intelligent techniques such as ANNs, fuzzy systems and evolutionary algorithms, so that the final hybrid ARIMA-ANN model could outperform the prediction accuracy of those models when used separately. More specifically, we propose the use of fuzzy rules to elicit the order of the ARMA or ARIMA model, without the intervention of a human expert, and the use of a hybrid ARIMA-ANN model that combines the advantages of the easy-to-use and relatively easy-to-tune ARIMA models, and the computational power of ANNs. Fig. 15. Lorenz time series: (a) histogram, (b) phase diagram, (c) original and predicted Lorenz time series using the proposed methodology (which are indistinguishable) and (d) prediction error.

This note obtains the theoretical autocorrelation function of an ARMA model with multiplicative seasonality. It is shown that this function can be interpretated as the result of the interaction between the seasonal and regular autocorrelation patterns of the ARMA model. The use of this result makes easier the identification of the structure of the model, is helpful in choosing between a multiplicative or additive seasonal component and leads to a better understanding of the properties of the estimated autocorrelation function of scalar ARMA processes.

This paper considers adaptive estimation in nonstationary autoregressive moving average models with the noise sequence satisfying a generalized autoregressive conditional heteroscedastic process. The locally asymptotic quadratic form of the log-likelihood ratio for the model is obtained. It is shown that the limit experiment is neither LAN nor LAMN, but is instead LABF. For the model with symmetric density of the rescaled error, a new efficiency criterion is established for a class of defined M ν -estimators. It is shown that such efficient estimators can be constructed when the density is known. Using the kernel estimator for the score function, adaptive estimators are constructed when the density of the rescaled error is symmetric, and it is shown that the adaptive procedure for the parameters in the conditional mean part uses the full sample without splitting. These estimators are demonstrated to be asymptotically efficient in the class of M ν -estimators. The paper includes the results that the stationary ARMA-GARCH model is LAN, and that the parameters in the model with symmetric density of the rescaled error are adaptively estimable after a reparameterization of the GARCH process. This paper also establishes the locally asymptotic quadratic form of the loglikelihood ratio for nonlinear time series models with ARCH-type errors.

We analyze the nature of persistence in macroeconomic fluctuations. The current view is that shocks to macroeconomic variables (in particular real GNP) have effects that endure over an indefinite horizon. This conclusion is drawn from the presence of a unit root in the univariate time series representation. Following Perron (1989), we challenge this assessment arguing that most macroeconomic variables are better construed as stationary fluctuations around a breaking trend function. The trend function is linear in time except for a sudden change in its intercept in 1929 (The Great Crash) and a change in slope after 1973 (following the oil price shock). Using a measure of persistence suggested by Cochrane (1988) we find that shocks have small permanent effects, if any, To analyze the effects of shocks at finite horizon, we select a member of the ARMA(p, q) class applied to the appropriately detrended series. For the majority of the variables analyzed the implied weights of the moving-average representation have the once familiar humped shape.

Conventional vibration signal processing techniques are most suitable for stationary processes. However, most mechanical faults in machinery reveal themselves through transient events in vibration signals. Timeseries modelling, including autoregressive moving average (ARMA) modelling and autoregressive (AR) modelling, is an efficient approach for transient signal analysis. Based on the adaptive prediction technique, this paper applies the principle of the adaptive line enhancer (ALE) to the modelling of transient vibration signals. The time-series models, adaptive algorithms and the rational time-frequency transfer function are investigated in the paper. Simulation and experimental studies with different time-frequency-amplitude distributions and transient vibration responses are described. The results show that the adaptive modelling method can trace the time-frequency signal and extract dynamic features such as time-frequency distributions and time-amplitude distributions from sample signals. Given the simple programming and potentially easy implementation in on-line applications, this method should have application in machine monitoring and fault diagnosis. r

In recent years, the bootstrap method has been extended to time series analysis where the observations are serially correlated. Contributions have focused on the autoregressive model producing alternative resampling procedures. In contrast, apart from some empirical applications, very little attention has been paid to the possibility of extending the use of the bootstrap method to pure moving average (MA) or mixed ARMA models. In this paper, we present a new bootstrap procedure which can be applied to assess the distributional properties of the moving average parameters estimates obtained by a least square approach. We discuss the methodology and the limits of its usage. Finally, the performance of the bootstrap approach is compared with that of the competing alternative given by the Monte Carlo simulation.

Luna august a anului 2015 marchează un deceniu de țintire directă a inflației (engl. inflation targeting – IT) în România, motiv pentru care dorim să dedicăm acest buletin problematicii acestui regim de politică monetară. Provocarea principală a acestuia o reprezintă dezvoltarea unui model de prognoză în baza căruia pot fi fundamentate deciziile privind acțiunile Băncii Naționale a României (BNR).

Stock price forecasting has attracted tremendous attention of researchers over the past several decades. Many techniques thus have been proposed so far to deal with the problem. This paper presents an application of a computational intelligence technique - a fuzzy inference system, namely Standard Additive Model (SAM), for predicting stock price time series data. The modelling and learning power of the SAM have been benefited to build the model that is capable of prediction functionalities. Experimental results have demonstrated that the proposed approach outperforms the traditional Auto Regressive Moving Average (ARMA) model in terms of the forecasting performance.

This paper presents a technique to derive the unit impulse response functions (UIRF) used for determination of unit hydrograph by employing the Z-transform technique to the response function derived from the Auto Regressive Moving Average (ARMA) process of order (p, q). The proposed approach was applied to reproduce direct surface runoff for single storm event data registered over four watersheds of area ranging from 0.42 to 295 km 2 . It is observed that the UIRF based on ARMA (1, 2) and ARMA (2, 2) provides a better representation of the watershed response. Further, to test the superiority of the developed impulse response function form ARMA process, the direct runoff hydrographs were computed using the simple ARMA process and optimized Nash's two parameter model and compared with the results obtained from UIRF's of ARMA model. The performance of the models based on the graphical presentation as well as from the test statistics viz. RMSE and MAPE indicates that UIRF-ARMA (p, q) performs better than optimized Nash Model and mostly similar to simple ARMA (p,q) model. Further more, the ARMA process of order p≤2 and q≤2 is generally sufficient and less cumbersome than the Argand diagram based approach for UIRF derivation.

This paper aims at developing a robust and omnibus procedure for checking the independence of two time series. proposed a robustified version of classic portmanteau statistic which is based on a fixed number of lagged residual cross-correlations. In order to obtain a consistent test for independence against an alternative of serial crosscorrelation of an arbitrary form between the two series, Hong's (1996a) introduced a class of statistics that take into account all possible lags. The test statistic is a weighted sum of residual cross-correlations and the weighting is determined by a kernel function. With the truncated uniform kernel, we retrieve a normalized version of Haugh's statistic. However, several kernels lead to a greater power. Here, we introduce a robustified version of Hong's statistic. We suppose that for each series, the true ARMA model is estimated by a n 1/2 -consistent robust method and the robust cross-correlation is so obtained. Under the null hypothesis of independence, we show that the robust statistic asymptotically follows a N (0, 1) distribution. Using a result of Li and Hui, we also propose a robust procedure for checking independence at individual lags and a descriptive causality analysis in the Granger's sense is discussed. The level and power of the robust version of Hong's statistic are studied by simulation in finite samples. Finally, the proposed robust procedures are applied to a set of financial data.

We investigate the predictability of both volatility and volume for a large sample of Japanese stocks. The particular emphasis of this paper is on assessing the performance of long memory time series models in comparison to their short-memory counterparts. Since long memory models should have a particular advantage over long forecasting horizons, we consider predictions of up to 100 days ahead. In most respects, the long memory models (ARFIMA, FIGARCH and the recently introduced multifractal model) dominate over GARCH and ARMA models. However, while FIGARCH and ARFIMA also have quite a number of cases with dramatic failures of their forecasts, the multifractal model does not suffer from this shortcoming and its performance practically always improves upon the naïve forecast provided by historical volatility. As a somewhat surprising result, we also find that, for FIGARCH and ARFIMA models, pooled estimates (i.e. averages of parameter estimates from a sample of time series) give much better results than individually estimated models.

In recent years the ecological conditions in areas of important wetlands have markedly changed. One of the areas is also Kláštorské Lúky the national natural reservation wetland, which is situated in the Strážovské mountains in the northwest of the Slovak Republic. This study deals with the modeling and forecasting of discharge and rainfall time series in the area of the

The statistical properties of the Autoregressive distance between ARIM A processes are investigated. In particular, the asymptotic distribution of the squared AR distance and an approximation which is computationally efficient are derived. Moreover, the problem of time series clustering and classification is discussed and the performance of the AR distance is illustrated by means of some empirical applications.

Subset models are often useful in the analysis of stationary time series. Although subset autoregressive models have received a lot of attention, the same attention has not been given to subset autoregressive moving-average (ARMA) models, as their identi®cation can be computationally cumbersome. In this paper we propose to overcome this disadvantage by employing a genetic algorithm. After encoding each ARMA model as a binary string, the iterative algorithm attempts to mimic the natural evolution of the population of such strings by allowing strings to reproduce, creating new models that compete for survival in the next population. The success of the proposed procedure is illustrated by showing its ef®ciency in identifying the true model for simulated data. An application to real data is also considered.

Using intraday returns on four futures contracts over a 5-year period, we calculate and analyze model-free measures of futures return volatility. We focus on the temporal characteristics and distributional properties of daily returns, return volatilities, (log of) standard deviations, standardized returns and pairwise correlations. The behavior of a number of tests for Gaussianity under long memory is explored via a simulation study. The simulation results indicate that tests of the ''goodness-of-fit'' variety are appropriate to use while the commonly employed Jarque -Bera test is severely oversized and its use is not recommended. We find that the standard deviations and the pairwise correlations exhibit long memory while the standardized returns are serially uncorrelated. We also find that the (unconditional) distributions of daily returns' volatility are leptokurtic and highly skewed to the right while the distributions of the standardized returns, the standard deviations and the pairwise correlations are statistically indistinguishable from the Gaussian distribution. Our results are consistent with that of Andersen et al. [Journal of the American Statistical Association 96 (2001a) 42; Journal of Financial Economics 61 (2001c) 43] on the time-series properties of realized volatility. The dynamic characteristics of the volatility series are modelled using fractionally integrated ARMA models. D

The field of higher order statistics is emerging rapidly for analyzing non-Gaussian processes. There are several motivations behind the use of higher order statistics. The emphasis of this paper is based on the property that higher order cumulants are blind to any kind of Gaussian process. Hence, when the processed signal is non-Gaussian stationary and the additive noise is stationary Gaussian, the noise will vanish in the cumulant domain. This paper presents an extension to recent results by Liang et al. This extension is a straightforward generalization of Liang's approach to third-order cumulants (TOCs). The new cumulant-based algorithm provides a higher level of accuracy in the presence of noise than the original second-order algorithm. In addition, the original results of Liang have been extended to the case of colored Gaussian noise. Examples are given to demonstrate the performance of this algorithm even when the observed signal is heavily corrupted by Gaussian noise.

The problem of determining simultaneously the model order and coefficient of an Autoregressive Moving Average (ARMA) model is examined in this paper. An Evolutionary Algorithm (EA) comprising two-level Differential Evolution (DE) optimization scheme is proposed. The first level searches for the appropriate model order while the second level computes the optimal/sub-optimal corresponding parameters. The performance of the algorithm is evaluated using both simulated ARMA models and practical rotary motion system. The results of both examples show the effectiveness of the proposed algorithm over a well known conventional technique.

lower bound (CRLB) Fisher information matrix (FIM) Nonsymmetric half-plane (NSHP) Two-dimensional (2-D) Autoregressive (AR) model Moving average (MA) model Autoregressive moving average (ARMA) model Parameter estimation Homogeneous random fields The Cramer-Rao lower bound (CRLB) that gives the minimal achievable variance/standard deviation for any unbiased estimator offers a useful tool for an assessment of the consistency of parameter estimation techniques. In this paper, a closed-form expression for the computation of the exact CRLB on unbiased estimates of the parameters of a twodimensional (2-D) autoregressive moving average (ARMA) model with a nonsymmetric half-plane (NSHP) region of support is developed. The proposed formulation is mainly based on a matrix representation of 2-D real-valued discrete and homogeneous random field characterized by the NSHP ARMA model. Assuming that the random field is Gaussian, the covariance matrix of the NSHP ARMA random field is first expressed in terms of the model parameters. Then, using this matrix structure, a closed-form expression of the exact Fisher information matrix required for the CRLB computation of the NSHP ARMA model parameters is developed. Finally, the main formulas derived for the NSHP ARMA model are rearranged for its autoregressive and moving average counterparts, separately. Numerical simulations are included to demonstrate the behavior of the derived CRLB formulas.

In system identification and parametric spectral estimation by two-dimensional (2-D) autoregressive (AR) and 2-D autoregressive moving average (ARMA) models, the order selection problem is often required. In this correspondence, we show that the information of 2-D AR model order is implicitly contained in a correlation matrix. An algorithm for 2-D quarter-plane AR model order determination is proposed. Numerical simulations are presented to show the efficiency of the proposed singular value decomposition (SVD) based algorithm.

In this paper, a time series algorithm is presented for damage identification and localization. The vibration signals obtained from sensors are modeled as autoregressive moving average (ARMA) time series. A new damage-sensitive feature, DSF, is defined as a function of the first three auto regressive (AR) components. It is found that the mean values of the DSF for the damaged and undamaged signals are different. Thus, a hypothesis test involving the t-test is used to obtain a damage decision. Two damage localization indices LI 1 and LI 2 , are introduced based on the AR coefficients. At the sensor locations where damage is introduced, the values of LI 1 and LI 2 appear to increase from their values obtained at the undamaged baseline state. The damage detection and localization algorithms are valid for stationary signals obtained from linear systems. To test the efficacy of the damage detection and localization methodologies, the algorithm has been tested on the analytical and experimental results of the ASCE benchmark structure. In contrast to prior pattern classification and statistical signal processing algorithms that have been able to identify primarily severe damage and have not been able to localize the damage effectively, the proposed algorithm is able to identify and localize minor to severe damage as defined for the benchmark structure. r

This article applied GARCH model instead AR or ARMA model to compare with the standard BP and SVM in forecasting of the four international including two Asian stock markets indices.These models were evaluated on five performance metrics or criteria. Our experimental results showed the superiority of SVM and GARCH models, compared to the standard BP in forecasting of the four international stock markets indices.

A method is proposed to forecast Turkey's total electric load one day in advance by neural networks. A hybrid learning scheme that combines off-line learning with real-time forecasting is developed to use the available data for adapting the weights and to further adjust these connections according to changing conditions. Data are clustered due to the differences in their characteristics. Special days are extracted from the normal training sets and handled separately. In this way, a solution is provided for all load types, including working days, weekends and special holidays. A traditional ARMA model is constructed for the same data as a benchmark. Proposed method gives lower percent errors all the time, especially for holidays. The average error for year 2002 is obtained as 1.60%.

Artificial neural network (ANN) Sediment prediction Multiple linear regressions (MLR) Multiple non-linear regression (MNLR) Autoregressive integrated moving average (ARIMA) Mississippi Missouri Rio Grande a b s t r a c t Information on suspended sediment load is crucial to water management and environmental protection. Suspended sediment loads for three major rivers (Mississippi, Missouri and Rio Grande) in USA are estimated using artificial neural network (ANN) modeling approach. A multilayer perceptron (MLP) ANN with an error back propagation algorithm, using historical daily and weekly hydroclimatological data (precipitation P (t) , current discharge Q (t) , antecedent discharge Q (t−1) , and antecedent sediment load SL (t−1) ), is used to predict the suspended sediment load SL (t) at the selected monitoring stations. Performance of ANN was evaluated using different combinations of input data sets, length of record for training, and temporal resolution (daily and weekly data). Results from ANN model were compared with results from multiple linear regressions (MLR), multiple non-linear regression (MNLR) and Autoregressive integrated moving average (ARIMA) using correlation coefficient (R), mean absolute percent error (MAPE) and model efficiency (E). Comparison of training period length was also made (4, 3 and 2 years of training and 1, 2 and 3 years of testing, respectively). The model efficiency (E) and R 2 values were slightly higher for the 4 years of training and 1 year of testing (4 * 1) for Mississippi River, indifferent for Missouri and slightly lower for Rio Grande River. Daily simulations using Input 1 (P (t) , Q (t) , Q (t−1) , SL (t−1) ) and three years of training and two years of testing (3 * 2) performed better (R 2 and E of 0.85 and 0.72, respectively) than the simulation with two years of training and three years of testing (2 * 3) (R 2 and E of 0.64 and 0.46, respectively). ANN predicted daily values using Input 1 and 3 * 2 architecture for Missouri (R 2 = 0.97) and Mississippi (R 2 = 0.96) were better than those of Rio Grande (R 2 = 0.65). Daily predictions were better compared to weekly predictions for all three rivers due to higher correlation within daily than weekly data. ANN predictions for most simulations were superior compared to predictions using MLR, MNLR and ARIMA. The modeling approach presented in this paper can be potentially used to reduce the frequency of costly operations for sediment measurement where hydrological data is readily available. (A.M. Melesse).

Most high-frequency asset returns exhibit seasonal volatility patterns. This article proposes a new class of models featuring periodicity in conditional heteroscedasticity explicitly designed to capture the repetitive seasonal time variation in the second-order moments. ...