Final Prediction Error Criterion Research Articles

Modeling Socioeconomic Determinants of Building Fires through Backward Elimination by Robust Final Prediction Error Criterion

Fires in buildings are significant public safety hazards and can result in fatalities and substantial financial losses. Studies have shown that the socioeconomic makeup of a region can impact the occurrence of building fires. However, existing models based on the classical stepwise regression procedure have limitations. This paper proposes a more accurate predictive model of building fire rates using a set of socioeconomic variables. To improve the model’s forecasting ability, a backward elimination by robust final predictor error (RFPE) criterion is introduced. The proposed approach is applied to census and fire incident data from the South East Queensland region of Australia. A cross-validation procedure is used to assess the model’s accuracy, and comparative analyses are conducted using other elimination criteria such as p-value, Akaike’s information criterion (AIC), Bayesian information criterion (BIC), and predicted residual error sum of squares (PRESS). The results demonstrate that the RFPE criterion is a more accurate predictive model based on several goodness-of-fit measures. Overall, the RFPE equation was found to be a suitable criterion for the backward elimination procedure in the socioeconomic modeling of building fires.

Resonance Detection Method and Realization of Bearing Fault Signal Based on Kalman Filter and Spectrum Analysis

The rolling bearing is an important part of mechanical equipment, and its performance significantly affects the quality and life of the mechanical equipment. This article uses the integrated fiber Bragg grating resonant structure sensor excited by periodic micro-shocks caused by micro faults to realize the extraction of information relating to potential faults. Because the fault signal is weak and can easily be interfered with by ambient noise, in order to extract the effective signal, this article determines the autoregressive model of bearing vibration by the final prediction error criterion and the recursive least squares estimation algorithm. The augmented state space model is established based on the autoregressive model. A Kalman filter is used to reduce the noise interference, and then the reduction noisy signal is analyzed by power spectrum and improved autocorrelation envelope spectrum to realize the detection of bearing faults. Through data analysis and method comparison, the proposed improved autocorrelation envelope spectrum analysis can directly extract the bearing fault frequency, which is superior to other methods such as cepstral analysis.

ModelSampler: An R Tool for Variable Selection and Model Exploration in Linear Regression

We have developed a tool for model space exploration and variable selec tion in linear regression models based on a simple spike and slab model (Dey, 2012). The model chosen is the best model with minimum final prediction error (FPE) values among all other models. This is implemented via the R package modelSampler. However, model selection based on FPE criteria is dubious and question able as FPE criteria can be sensitive to perturbations in the data. This R package can be used for empirical assessment of the stability of FPE criteria. A stable model selection is accomplished by using a bootstrap wrapper that calls the primary function of the package several times on the bootstrapped data. The heart of the method is the notion of model averaging for sta ble variable selection and to study the behavior of variables over the entire model space, a concept invaluable in high dimensional situations.

Simple and Instantaneous Causality in A Multivariate Auto-Regressive Models: An Application On Some Monetary Variables of the Egyptian Economy

Granger`s (1969) concept and definitions of causality, feedback, and instantaneous causality and Akaike final prediction error criterion and extended by Chan et al (1982) to fit a multivariate autoregressive model are used. The objective of the paper is to distinguish between simple, feedback and instantaneous causality. The notion of feedback between endogenous and exogenous variables in the bivariate AR model and its extension to the tri-variate AR models is presented. As an application to these Causality notions, the paper aimed to reach the optimal lag structure in forecasting some monetary variables in the Egyptian economy from 2005 to 2018. Variables selected were “current deposits of local currency”, “loan totals” and “quasi-money”. The three variables were correlated, and each variable was used as an endogenous function of itself lagged and the other two variables as exogeneous. The study also aimed to test if prediction is improved if current values and previous values are used in the prediction equation. .. The analysis showed that a one-way simple causal model exists from “loans total” to “current deposits of local currency”, and from “quasi-money” to “loans total”. Instantaneous causality and feedback occur between the three variables.

Uncertain Autoregressive Model via LASSO Procedure

Uncertain time series analysis is a method to predict future values based on imprecisely observed values. As a basic model of uncertain time series, an uncertain autoregressive model has been presented. However, the existing paper ignores the temporal dependence information embedded in time-series data. In dealing with this issue, this paper adds a least absolute shrinkage and selection operator penalty to the traditional uncertain autoregressive model and selects the optimum order of the model according to Akaike’s final prediction error criterion. Finally, two numerical examples are given to illustrate the effectiveness of the model and compare the results predicted by the uncertain autoregressive model with the principle of least squares.

Lattice-Filter-Based Multivariate Autoregressive Spectral Estimation With Joint Model Order and Estimation Bandwidth Adaptation

The problem of parametric autoregressive model-based estimation of a time-varying spectral density function of a multivariate nonstationary process is considered. It is shown that estimation results can be considerably improved if identification of the autoregressive model is carried out using the two-sided doubly exponentially weighted lattice algorithm, which combines results yielded by two one-sided lattice algorithms running forward in time and backward in time, respectively. It is also shown that the model order and the most appropriate estimation bandwidth can be efficiently selected using the suitably modified Akaike's final prediction error criterion.

On Noncausal Identification of Nonstationary Multivariate Autoregressive Processes

The problem of identification of nonstationary multivariate autoregressive processes using noncausal local estimation schemes is considered and a new approach to joint selection of the model order and the estimation bandwidth is proposed. The new selection rule, based on evaluation of pseudoprediction errors, is compared with the previously proposed one, based on the modified Akaike's final prediction error criterion.

Compositional time series analysis for Air Pollution Index data

The increasing importance of understanding the structure of Air Pollution Index (API) makes it necessary to come out with a compositional of API based on its pollutants. This will be more comprehensible for the public and easier to cooperate with authorities in reducing the causes of air pollution. Since five pollutants contribute in determining the API values, API can be shown as a compositional data. This study is conducted based on the data of API and its pollutants collected from Klang city in Malaysia for the period of January 2005 to December 2014. The proportion of each pollutant in API is considered as a component with five components in a compositional API. The existence of zero components in some pollutants, that have no effect on API, is a serious problem that prevents the application of log-ratio transformation. Thus, the approach of amalgamation has been used to combine the components with zero in order to reduce the number of zeros. Also, a multiplicative replacement has been utilized to eliminate the zero components and replace them with a small value that maintains the ratios of nonzero components. Transforming the compositional data to log-ratio coordinates has been done using the additive log ratio transformation, and the transformed series is then modeled by using a VAR model. Four criteria are used to determine the number of lags p of VAR(p) and these are: the Akaike Information, the Schwartz, the Hannan–Quinn and the Final Prediction Error criteria. Based on the results, A VAR (1) model with no constants or trend is considered as the best fitted model and it is used to forecast 12 months ahead. In addition, API values are mainly determined by PM10 that has a proportion close to one most of the time during study period. Therefore, authorities and researchers need to study the sources of PM10 and provide the public with useful information and alternatives in term of reducing the air pollution.

NARX-based BPSO modelling for time-varying steam temperature of steam distillation pilot plant

This paper focuses on a nonlinear modelling for a time-varying process of steam temperature by employing a polynomial Nonlinear Auto-Regressive with Exogenous Input (NARX) structure based on Binary Particle Swarm Optimization (BPSO) algorithm. The system identification time-varying steam temperature data was collected from Steam Distillation Pilot Plant. Three models’ criterion were implemented; Akaike Information Criterion, Model Descriptor Length (MDL) and Final Prediction Error (FPE) for optimization process of NARX-based BPSO modelling. The results demonstrated that the FPE criterion model was presented a slightly better model with lowest CRV from the testing set, small fitness value and a minimum number of parameter in the output model. The accuracy was evaluated by the high R-squared, small MSE value and passed all the correlation and histogram tests.

New results on estimation bandwidth adaptation

The problem of identification of a nonstationary autoregressive signal using non-causal estimation schemes is considered. Noncausal estimators can be used in applications that are not time-critical, i.e., do not require real-time processing. A new adaptive estimation bandwidth selection rule based on evaluation of pseudoprediction errors is proposed, allowing one to adjust tracking characteristics of noncausal estimators to unknown and/or time-varying degree of signal nonstationary. The new rule is compared with the previously proposed one, based on the generalized Akaike’s final prediction error criterion.

Model Order Selection in Errors-in-Variables System Identification

This work studies the problem of model order selection in errors-in-variables (EIV) system identification. Two criteria, the final correlated prediction error (FCPE) criterion and the final correlated output error (FCOE) criterion are developed for estimating the order of EIV systems. The criteria are extensions of the final prediction error (FPE) criterion and the final output error (FOE) criterion. To eliminate the influence of the input noise in FPE criterion and FOE criterion, the idea of the new criteria is to correlate the prediction error and the output error with the output signal respectively. Simulations are used to illustrate the performance of the criteria.

On adaptive covariance and spectrum estimation of locally stationary multivariate processes

When estimating the correlation/spectral structure of a locally stationary process, one has to make two important decisions. First, one should choose the so-called estimation bandwidth, inversely proportional to the effective width of the local analysis window, in the way that complies with the degree of signal nonstationarity. Too small bandwidth may result in an excessive estimation bias, while too large bandwidth may cause excessive estimation variance. Second, but equally important, one should choose the appropriate order of the spectral representation of the signal so as to correctly model its resonant structure–when the order is too small, the estimated spectrum may not reveal some important signal components (resonances), and when it is too high, it may indicate the presence of some nonexistent components. When the analyzed signal is not stationary, with a possibly time-varying degree of nonstationarity, both the bandwidth and order parameters should be adjusted in an adaptive fashion. The paper presents and compares three approaches allowing for unified treatment of the problem of adaptive bandwidth and order selection for the purpose of identification of nonstationary vector autoregressive processes: the cross-validation approach, the full cross-validation approach, and the approach that incorporates the multivariate version of the generalized Akaike’s final prediction error criterion. It is shown that the latter solution yields the best results and, at the same time, is very attractive from the computational viewpoint.

Factor Modelling for High‐Dimensional Time Series: Inference and Model Selection

Analysis of high‐dimensional time series data is of increasing interest among different fields. This article studies high‐dimensional time series from a dimension reduction perspective using factor modelling. Statistical inference is conducted using eigen‐analysis of a certain non‐negative definite matrix related to autocovariance matrices of the time series, which is applicable to fixed or increasing dimension. When the dimension goes to infinity, the rate of convergence and limiting distributions of estimated factors are established. Using the limiting distributions of estimated factors, a high‐dimensional final prediction error criterion is proposed to select the number of factors. Asymptotic properties of the criterion are illustrated by simulation studies and real applications.

Calibration of optical tweezers based on an autoregressive model.

The power spectrum density (PSD) has long been explored for calibrating optical tweezers stiffness. Fast Fourier Transform (FFT) based spectral estimator is typically used. This approach requires a relatively longer data acquisition time to achieve adequate spectral resolution. In this paper, an autoregressive (AR) model is proposed to obtain the Spectrum Density using a limited number of samples. According to our method, the arithmetic model has been established with burg arithmetic, and the final prediction error criterion has been used to select the most appropriate order of the AR model, the power spectrum density has been estimated based the AR model. Then, the optical tweezers stiffness has been determined with the simple calculation from the power spectrum. Since only a small number of samples are used, the data acquisition time is significantly reduced and real-time stiffness calibration becomes feasible. To test this calibration method, we study the variation of the trap stiffness as a function of the parameters of the data length and the trapping depth. Both of the simulation and experiment results have showed that the presented method returns precise results and outperforms the conventional FFT method when using a limited number of samples.

Nanoparticle size measurement from dynamic light scattering data based on an autoregressive model

The letter puts forward a new method of nanoparticle size measurement using small amounts of data on a dynamic light scattering signal, and establishes an arithmetic model based on Burg arithmetic. According to our method, an autoregressive (AR) model of the nanoparticle dynamic light scattering signal was set up, and the parameters of the AR model were solved, the final prediction error criterion was used to select the most appropriate order of the AR model, the power spectrum density was estimated and the particle size distribution information could be deduced from the inverse of the power spectrum. Standard polystyrene particles of 50, 90 and 100 nm were measured using this method, and the experimental results indicated that the particle size inversion results of this method were more accurate than the autocorrelation method using small amounts of data.

System Identification with an Extended Threshold M-Estimator for Pseudo-Linear Models Structure

This paper deals with the problem of the estimation/validation of pseudo-linear models structure when outliers are present in the residuals. These corrupted data lead to unbounded modeling errors, involve long tail of the probability density function, and damage the model order estimation. Thus, from a ω-corrupted distribution model of these data, a parameterized robust estimation criterion (PREC) with an extended scaling factor in the Huber's norm and a robust final prediction error criterion (RFPE) based on M-estimates are proposed. Simulation results are given and the estimated orders of the robust models are derived from the new model validation criterion.

Stock Returns And Monetary Aggregates

This paper examines the relationship between stock returns and money growth using the regression framework of Sims and Akaikes final prediction error criterion. Stock returns are found to lead unexpected money growth. Investors seem to base their decisions on anticipated short run monetary policy. Empirical results suggest that the market is efficient, although returns for large firms seem to adjust to new information faster than their smaller counterparts.

Application of inverse data-driven parametric models in the reconstruction of passenger vehicle wheel vertical movement under ride conditions

This paper considers a method for reconstructing the vertical displacement of wheels resulting from the road profile, using an inverse parametric data-driven model. Wheel movement is required in variable damping semi-active suspension systems, which use an onboard control system that improves ride quality and vehicle handling in typical maneuvers. This paper presents a feasibility study of such an approach which was performed in laboratory conditions. Experimental validation tests were conducted on a setup consisting of a servo-hydraulic test rig equipped with displacement, force and acceleration transducers and a data-acquisition system. The fidelity and adequacy of various parametric single-input single-output model structures were evaluated in the time and frequency domain based on correlation coefficient, Akaike information criterion, and final prediction error criteria. The experimental test results showed that inverse models provide high-level accuracy of inversion in the time domain, ranging from more than 70% for the ARX model structure to over 90% for the OE model structure.

Using Some Information Criterion Determining the Best Multiplicative Seasonal Model

The main objective of this study is to select the best multiplicative seasonal model of the time series data using some information criteria; they are AIC, BIC, AICC, and SMAIC. Then prediction is made for the different models and calculates the final prediction error criterion to ensure the accuracy of our best selected model. In our study we select the model ARIMA(0,1,1)(0,1,1)12 as the best model for the wind speed series and the model ARIMA(0,1,1)(0,1,1)12 as the best model for the cloud series .

Development of Soft Sensors for Crude Distillation Unit Control

AbstractSoft sensors for distillation end point (D95) on-line estimation in crude distillation unit (CDU) are developed. Experimental data are acquired from the refinery distributed control system (DCS) and include on-line available continuously measured variables and laboratory assays. Soft sensors are developed using different linear and nonlinear identification methods. Additional laboratory data for model identification are generated by Multivariate Adaptive Regression Splines (MARSplines). The models are evaluated based on Route Mean Square (RMS), Absolute Error (AE), FIT and Final Prediction Error (FPE) criteria. The best results are achieved with Box Jenkins (BJ), Output Error (OE) and Hammerstein–Wiener (HW) model. Based on developed soft sensors it is possible to estimate fuel properties in continuous manner and apply inferential control. By real plant application of developed soft sensors considerable savings could be expected, as well as compliance with strict law regulations for product quality specifications.