Different Lengths Of Data Research Articles

Investigating the effect of observational data length on ARIMA modeling and forecasting accuracy: a case study of Kortian Stream watershed, Iran

Abstract Using autoregressive integrated moving average (ARIMA) for modeling and predicting time series is worldwide, but how many available recorded observations can be used for modeling to achieve better results is debatable. The length of data can significantly affect the results of ARIMA models. This article investigates the effect of different lengths on prediction accuracy. For this purpose, 732 monthly data of streamflow of the Kortian gauging station at the Kortian Stream watershed were used. To study the impact of the type of data in terms of monthly or seasonal observation data on the accuracy of modeling results, monthly data were converted into seasonal data and the results of monthly and seasonal modeling were compared. Therefore, multiplicative ARIMA models were performed for the monthly and seasonal modeling. Compared with the seasonal modeling, the monthly modeling presented more precise results than the sum of the square errors of monthly and seasonal modeling, which were 0.9408 and 2.5, respectively. For the monthly modeling, five different lengths of data were used. The C1 model used the last 60 data, C2 used the last 120 recorded observations, C3 used the last 240 data, C4 used the last 480 observations, and C5 used the last 708 data. To test the precision of models, 24 observations were put aside. Among the C1 to C5 models, the C4 model presented the best results in predicting 2 years ahead and C1 had the worst results.

A Training Data-Driven Canonical Correlation Analysis Algorithm for Designing Spatial Filters to Enhance Performance of SSVEP-Based BCIs.

Canonical correlation analysis (CCA) is an effective spatial filtering algorithm widely used in steady-state visual evoked potential (SSVEP)-based brain-computer interfaces (BCIs). In existing CCA methods, training data are used for constructing templates of stimulus targets and the spatial filters are created between the template signals and a single-trial testing signal. The fact that spatial filters rely on testing data, however, results in low classification performance of CCA compared to other state-of-the-art algorithms such as task-related component analysis (TRCA). In this study, we proposed a novel CCA method in which spatial filters are estimated using training data only. This is achieved by using observed EEG training data and their SSVEP components as the two inputs of CCA and the objective function is optimized by averaging multiple training trials. In this case, we proved in theory that the two spatial filters estimated by the CCA are equivalent, and that the CCA and TRCA are also equivalent under certain hypotheses. A benchmark SSVEP data set from 35 subjects was used to compare the performance of the two algorithms according to different lengths of data, numbers of channels and numbers of training trials. In addition, the CCA was also compared with power spectral density analysis (PSDA). The experimental results suggest that the CCA is equivalent to TRCA if the signal-to-noise ratio of training data is high enough; otherwise, the CCA outperforms TRCA in terms of classification accuracy. The CCA is much faster than PSDA in detecting time of targets. The robustness of the training data-driven CCA to noise gives it greater potential in practical applications.

Searching for g modes

Context. The recent claims of g-mode detection have restarted the search for these potentially extremely important modes. The claimed detection of g modes was obtained from the analysis of the power spectrum of the time series of round-trip travel time of p modes. Aims. The goal of this paper is to reproduce these results on which the claims are based for confirming or invalidating the detection of g modes with the method used to make the claims. Methods. We computed the time series of round-trip travel time using the procedure given in Fossat et al. (2017, A&A, 604, A40), and used different variations of the times series for comparison. We used the recently calibrated GOLF data (published in Paper I) with different sampling, different photomultipliers, different length of data for reproducing the analysis. We also correlated the power spectrum with an asymptotic model of g-mode frequencies in a similar manner to Fossat and Schmider (2018, A&A, 612, L1). We devised a scheme for optimising the correlation both for pure noise and for the GOLF data. Results. We confirm the analysis performed in Fossat et al. (2017) but draw different conclusions. Their claims of detection of g modes cannot be confirmed when changing parameters such as sampling interval, length of time series, or photomultipliers. Other instrument such as GONG and BiSON do not confirm their detection. We also confirm the analysis performed in Fossat and Schmider (2018), but again draw different conclusions. For GOLF, the correlation of the power spectrum with the asymptotic model of g-mode frequencies for l = 1 and l = 2 show a high correlation at lag=0 and at lag corresponding to the rotational splitting νl, but the same occurs for pure noise due to the large number of peaks present in the model. In addition, other very different parameters defining the asymptotic model also provide a high correlation at these lags. We conclude that the detection performed in Fossat and Schmider (2018) is an artefact of the methodology.

Calibration of Conceptual Rainfall-Runoff Models Using Global Optimization

Parameter optimization for the conceptual rainfall-runoff (CRR) model has always been the difficult problem in hydrology since watershed hydrological model is high-dimensional and nonlinear with multimodal and nonconvex response surface and its parameters are obviously related and complementary. In the research presented here, the shuffled complex evolution (SCE-UA) global optimization method was used to calibrate the Xinanjiang (XAJ) model. We defined the ideal data and applied the method to observed data. Our results show that, in the case of ideal data, the data length did not affect the parameter optimization for the hydrological model. If the objective function was selected appropriately, the proposed method found the true parameter values. In the case of observed data, we applied the technique to different lengths of data (1, 2, and 3 years) and compared the results with ideal data. We found that errors in the data and model structure lead to significant uncertainties in the parameter optimization.

Vibration Signal Analysis of High Voltage Circuit Breakers System Based on Hybrid Model of Power Spectrum Estimation

This paper discusses several methods of power spectrum estimation, respectively using the indirect method and Welch method to estimate power spectrum distribution through the acquisition of vibration signals of circuit breakers, and use the AR hybrid model to estimate different orders of power spectrum estimation. Under different length of data, the or- der selection method can be determined. Power spectrum estimation method is a power spectrum calculation method of vibration or random signal. It is an important link in the signal analysis, which can be used to detect the periodic component and the percentage of the sig- nal (1). And it is the great significance for the diagnosis of mechanical failure. Using a given set of sample data to esti- mate the power spectral density of a stationary random sig- nal is called power spectrum estimation. Power spectral den- sity is the discrete time Fourier transform of the random sig- nal autocorrelation sequence, it is used to characterize the statistical properties of random signals. The power spectrum of random signal reflects its frequency components and the relative strength of each component, it can reveal the signal rhythm from the frequency domain, and it is the important characteristic of random signals. Found in the study, statistical properties of CB vibration signal under different working conditions, the results show that when the circuit breaker is in normal working condition or state change is very small, the action of mechanical vibra- tion signal can be approximated at a stationary random pro- cess, which is consistent with the AR hybrid model assump- tion is usually described by. Therefore, the AR hybrid mod- el power spectrum estimation can achieve the desired effect of vibration signal.

The Simulation Research of Classic Spectrum Estimation Periodogram Method Based on Matlab

The spectrum estimation is a main content of modern signal processing, it is very important for random signal detection and analysis. This paper researched the classical spectrum estimation method, simulated the periodogram method, Barlett method, and Welch method of power spectrum estimation, then mainly discussed the spectral resolution about different length of data, also discussed the resolution of the spectral estimation and the performance of variance in the different way.

Effect of data length on rainfall–runoff modelling

A 64-year data set of daily rainfall and runoff, and average monthly potential evapotranspiration (PET) was split into subsets of 2, 5, 10, 20 and 30 years. Each subset was used to calibrate the AWBM daily rainfall–runoff model. Each subset calibration was then used to estimate runoff from the 64 years of rainfall and PET data. The ratios of calculated to actual total runoff were used to determine the ranges of error from the different lengths of data used for calibration. There was little difference in results from the 2- and 5-year subsets with 90% of estimates of long term runoff in the range of −21% to +31% of the recorded value. Overestimation of long term runoff reduced with length of calibration data of 10 or more years; however, the chances of underestimating were only slightly reduced even with 30 years of calibration data. Some limited repetition of the calculations with the Curve Number rainfall–runoff model indicated that the error characteristics were inherent in the data set and not an artifact of the model used. The ramifications for applications of rainfall–runoff modelling are briefly discussed.

Impacts of data length on optimal parameter and uncertainty estimation of a land surface model

The optimal parameters and uncertainty estimation of land surface models require that appropriate length of forcing and calibration data be selected for computing error functions. Most of the previous studies used less than two years of data to optimize land surface models. In this study, 18‐year hydrometeorological data at Valdai, Russia, were used to run the Chameleon Surface Model (CHASM). The optimal parameters were obtained by employing a global optimization technique called very fast simulated annealing. The uncertainties of model parameters were estimated by the Bayesian stochastic inversion technique. Forty‐four experiments were conducted by using different lengths of data from the 18‐year record, and a total of about 3 million parameter sets were produced. This study found that different calibration variables require different lengths of data to obtain optimal parameters and uncertainty estimates which are insensitive to the period selected. In the case of optimal parameters, monthly root‐zone soil moisture, runoff, and evapotranspiration require 8, 3, and 1 years of data, respectively. In the case of uncertainty estimates, monthly root‐zone soil moisture, runoff, and evapotranspiration require 8, 8, and 3 years of data, respectively. Spin‐up has little impact on the selection of optimal parameters and uncertainty estimates when evapotranspiration and runoff were calibrated. However, spin‐up affects the selection of optimal parameters when soil moisture was calibrated.

Using Age Structure to Detect Impacts on Threatened Populations: a Case Study with Steller Sea Lions

Abstract: A delayed response to change is often a characteristic of long‐lived species and presents a major challenge to monitoring their status. However, rapid shifts in age structure can occur even while population size remains relatively static. We used time‐varying matrix models to study age‐structure information as a tool for improving detection of survivorship and fecundity change and status. We applied the methods to Steller sea lions ( Eumetopias jubatus), a long‐lived endangered marine mammal found throughout the North Pacific Rim. Population and newborn counts were supplemented with information on the fraction of the population that was juvenile, obtained by measuring animals in aerial photographs taken during range‐wide censuses. By fitting the model to 1976–1998 data, we obtained maximum‐likelihood estimates and 95% confidence intervals for juvenile survivorship, adult survivorship, and adult fecundity in the mid‐1980s, late 1980s, and 1990s. We used a series of nested models to test whether the data were best fit by a model with one, two, or three temporal changes in demographic rates, and we fit the models to different lengths of data to test the number of years of data needed to detect a demographic change. The declines in the early 1980s were associated with severely low juvenile survivorship, whereas declines in the 1990s were associated with disproportionately low fecundity. We repeated these analyses, fitting only to the count data without the juvenile‐fraction information, to determine whether the age‐structure information changed the conclusions and/or changed the certainty and speed with which demographic‐rate changes could be detected. The juvenile‐fraction data substantially improved the degree to which estimates from the model were consistent with field data and significantly improved the speed and certainty with which changes in demographic rates were detected.

Automatic calibration of conceptual rainfall-runoff models: sensitivity to calibration data

The identification of hydrologic models requires that appropriate data be selected for model calibration. In the research presented here, the shuffled complex evolution (SCE-UA) global optimization method was used to calibrate the NWSRFS-SMA conceptual rainfall-runoff flood forecasting model of the US National Weather Service, using a 40-year record of historical data. Based on 344 calibration runs using different lengths of data from different sections of the historical record, we conclude that approximately 8 years of data are required to obtain calibrations that are relatively insensitive to the period selected. Further, the reduction in parameter uncertainty is maximal when the wettest data periods on record are used. A residual analysis is used to compare the performance of the daily root mean square (DRMS) and heteroscedastic maximum likelihood error (HMLE) objective functions. The results suggest that the factor currently limiting model performance is the unavailability of strategies that explicitly account for model error during calibration.

Complex ambiguity functions using nonstationary higher order cumulant estimates

The complex ambiguity function based on second-order statistics (CAF-SOS) has been used to simultaneously estimate the frequency-delay of arrival (FDOA) and time-delay of arrival (TDOA) between two signal measurements; its performance, however, is sensitive to the correlation between two additive noise sources. When the noise sources are assumed to be Gaussian, we develop a new complex ambiguity function based on higher order statistics (CAF-HOS) that reduces the unknown noise-correlation effect. The new CAF-HOS algorithm utilizes nonstationary higher order cross cumulant estimates and their Fourier transform. In fact, we suggest a nonstationary estimate of fourth-order cross-cumulants and obtain the analytical expressions for its mean value and variance. We compare the analytical expressions with results obtained by Monte Carlo runs. Also, we compare the performance of the new complex ambiguity function based on fourth-order statistics (CAF-FOS) against the CAF-SOS algorithm using different Gaussian noise sources, different signals of interest, different signal-to-noise ratios, and different lengths of data.

Estimation of frequency-delay of arrival (FDOA) using fourth-order statistics in unknown correlated Gaussian noise sources

A new family of nonparametric and parametric methods based on fourth-order statistics for the estimation of the frequency-delay of arrival (FDOA) between two sensor signal measurements, corrupted by correlated Gaussian noise sources in an unknown way, is presented. The new family of FDOA estimation methods utilizes the fourth-order cumulants or 1-D Fourier transforms of sliced fourth-order cumulants of the two signal measurements. It is demonstrated that the new family of FDOA estimation methods suppresses the effect due to correlated Gaussian measurement noises and outperforms existing second-order statistics-based FDOA estimation methods using either cross-ambiguity function or MUSIC algorithm. Various simulation results are presented for different types of signals, different lengths of data, and different signal-to-noise ratios.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>