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Electron fluxes (20 eV–2 MeV, RBSP‐A satellite) show reasonable simple correlation with a variety of parameters (solar wind, IMF, substorms, ultralow frequency (ULF) waves, geomagnetic indices) over L‐shells 2–6. Removing correlation‐inflating common cycles and trends (using autoregressive and moving average terms in an ARMAX analysis) results in a 10 times reduction in apparent association between drivers and electron flux, although many are still statistically significant (p < 0.05). Corrected influences are highest in the 20 eV–1 keV and 1–2 MeV electrons, more modest in the midrange (2–40 keV). Solar wind velocity and pressure (but not number density), IMF magnitude (with lower influence of Bz), SME (a substorm measure), a ULF wave index, and geomagnetic indices Kp and SymH all show statistically significant associations with electron flux in the corrected individual ARMAX analyses. We postulate that only pressure, ULF waves, and substorms are direct drivers of electron flux and compare their influences in a combined analysis. SME is the strongest influence of these three, mainly in the eV and MeV electrons. ULF is most influential on the MeV electrons. Pressure shows a smaller positive influence and some indication of either magnetopause shadowing or simply compression on the eV electrons. While strictly predictive models may improve forecasting ability by including indirect driver and proxy parameters, and while these models may be made more parsimonious by choosing not to explicitly model time series behavior, our present analyses include time series variables in order to draw valid conclusions about the physical influences of exogenous parameters. Plain Language Summary: High levels of satellite‐damaging electrons (both high and low energy) in the radiation belts appear to be driven by substorms and ultralow frequency waves. There is a positive association between these variables and electron levels even when the cycling behavior of satellite‐derived data is corrected. Solar wind pressure, thought to reduce electron levels either temporarily (by compressing the magnetosphere below the level of the nominal L‐shell) or permanently (via magnetopause shadowing), shows only a small influence on lower energy electrons. Other solar wind and magnetosphere parameters do show correlations with electron levels even if autocorrelation and cycling behavior is accounted for, but these are not postulated to be direct drivers. Key Points: Substorms are the predominant driver of eV and MeV electron flux, with less influence on keV fluxUltralow frequency waves also influence MeV electronsElectrons correlate with input variables even in ARMAX models that correct for autocorrelation and cycling [ABSTRACT FROM AUTHOR]

Parametric autoregressive moving average models with exogenous terms (ARMAX) have been widely used in the literature. Usually, these models consider a conditional mean or median dynamics, which limits the analysis. In this paper, we introduce a class of quantile ARMAX models based on log-symmetric distributions. This class is indexed by quantile and dispersion parameters. It not only accommodates the possibility to model bimodal and/or light/heavy-tailed distributed data but also accommodates heteroscedasticity. We estimate the model parameters by using the conditional maximum likelihood method. Furthermore, we carry out an extensive Monte Carlo simulation study to evaluate the performance of the proposed models and the estimation method in retrieving the true parameter values. Finally, the proposed class of models and the estimation method are applied to a dataset on the competition "M5 Forecasting - Accuracy" that corresponds to the daily sales history of several Walmart products. The results indicate that the proposed log-symmetric quantile ARMAX models have good performance in terms of model fitting and forecasting. [ABSTRACT FROM AUTHOR]

Although lagged correlations have suggested influences of solar wind velocity (V) and number density (N), Bz, ultralow frequency (ULF) wave power, and substorms (as measured by the auroral electrojet (AE) index) on MeV electron flux at geosynchronous orbit over an impressive number of hours and days, a satellite's diurnal cycle can inflate correlations, associations between drivers may produce spurious effects, and correlations between all previous time steps may create an appearance of additive influence over many hours. Autoregressive‐moving average transfer function (ARMAX) multiple regressions incorporating previous hours simultaneously can eliminate cycles and assess the impact of parameters, at each hour, while others are controlled. ARMAX influences are an order of magnitude lower than correlations uncorrected for time behavior. Most influence occurs within a few hours, not the many hours suggested by correlation. A log transformation accounts for nonlinearities. Over all hours, solar wind velocity (V) and number density (N) show an initial negative impact, with longer term positive influences over the 9 (V) or 27 (N) hr. Bz is initially a positive influence, with a longer term (6 hr) negative effect. ULF waves impact flux in the first (positive) and second (negative) hour before the flux measurement, with further negative influences in the 12–24 hr before. AE (representing electron injection by substorms) shows only a short term (1 hr) positive influence. However, when only recovery and after‐recovery storm periods are considered (using stepwise regression), there are positive influences of ULF waves, AE, and V, with negative influences of N and Bz. Plain Language Summary: The influence of solar wind, waves, and substorms on high energy electrons at geosynchronous orbit can appear to occur over a number of hours and days. However, these long duration correlations may be due to diurnal cycles in satellite data, associations between the driving parameters, or correlations of each variable with itself over previous time steps. These extraneous correlations can be corrected for using autoregressive‐moving average multiple regression models including previous hours simultaneously. Once these are controlled, the correlations between possible driving parameters and high energy electrons are both lower and influential only over a few hours. Key Points: Autoregressive‐moving average transfer function models show drivers of relativistic electron flux are influential only within a few hours or a day of flux changesContrary to simple correlation findings, influences are lower in magnitude and act more immediatelyStepwise multiple regression shows less cumulative effects of drivers in after‐storm periods than simple correlation would suggest [ABSTRACT FROM AUTHOR]

We investigate the drivers of 40–150 keV hourly electron flux at geostationary orbit (GOES 13) using autoregressive moving average transfer functions (ARMAX) multiple regression models which remove the confounding effect of diurnal cyclicity and allow assessment of each parameter independently. By taking logs of the variables, we create nonlinear models. While many factors show high correlation with flux in single variable analysis (substorms, ULF waves, solar wind velocity (V), pressure (P), number density (N) and electric field (Ey), IMF Bz, Kp, and SymH), ARMAX models show substorms are the dominant influence at 40–75 keV and over 20–12 MLT, with little difference seen between disturbed and quiet periods. The Ey influence is positive post‐midnight, negative post‐noon. Pressure shows a negative influence, strongest at 150 keV. ULF waves are a more modest influence than suggested by single variable correlation. Kp and SymH show little effect when other variables are included. Using path analysis, we calculate the summed direct and indirect influences through the driving of intermediate parameters. Pressure shows a summed direct and indirect influence nearly half that of the direct substorm effect. N, V, and Bz, as indirect drivers, are equally influential. While simple correlation or neural networks can be used for flux prediction, neither can effectively identify drivers. Instead, consideration of physical influences, removing cycles that artificially inflate correlations, and controlling the effects of other parameters gives a clearer picture of which are most influential in this system. Plain Language Summary: Satellites may experience damaging surface charging due to high energy electrons present in the radiation belts. In this study, we explore the various factors that may influence these electron populations. We use an autoregressive moving average transfer function (ARMAX) statistical model that removes the confounding effect of diurnal cyclicity and allows assessment of each variable independently of others. Substorms, which inject electrons into the magnetosphere, are found to be the strongest influence, with most of their effect seen near local midnight. The electric field and pressure of the solar wind also show moderate effects. Not all variables that show high single variable correlations retain this influence in multivariate analyses. Kp and SymH, two indices of geomagnetic activity are highly correlated with electron levels in the magnetosphere, but show little influence in models controlling for the effects of solar wind parameters. Identifying direct, physical drivers, removing cycles that artificially inflate correlations, and controlling the effects of other parameters using multiple regression (specifically, ARMAX) gives a clearer picture of which parameters are most influential in this system. Key Points: Substorms, as measured by AE, are the strongest direct influence on 40–150 keV electron fluxOf the possible indirect drivers N, V, Bz show fairly equal influence on fluxAn autoregressive moving average transfer functions model removes diurnal cyclicity and allows a more accurate assessment of the correlations [ABSTRACT FROM AUTHOR]

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In this study, the vibration ratios obtained from the sensor and smartphone placed in the steel model structure in the vibration table and the vibration ratios generated using the MATLAB mathematical prediction model were compared. The steel model structure used in the experimental study; made of single-span, four-ply steel. Column-beam connections in the steel model structure are rigid and the base connections on all four sides of the model building are mounted to the vibration table. The vibration values obtained from the experimental study were obtained from the sensor and the smartphone placed at the base of the vibration table and at the top of the steel model structure. The vibration table was forced with the vibration values of El-Centro, Loma-Prieta, Kobe and Sakarya earthquakes and the vibrations caused by the strain caused by the structure were recorded with the help of sensor and smart phone. Sensor and smartphone vibration values at the base of the shaking table are defined as input, sensor and smartphone vibration values at the top of the steel model structure are defined as output to the system. As a result of the studies, the compatibility ratios between the input-output data obtained experimentally, the autoregressive ARX in the Matlab program and the autoregressive moving averages were compared between the prediction-prediction found in the ARMAX model and the input-output produced. In addition, the difference between sensor and smartphone acceleration data was investigated and which of the methods used gave better results. [ABSTRACT FROM AUTHOR]

To find the best method of predicting when daily relativistic electron flux (>2 MeV) will rise at geosynchronous orbit, we compare model predictive success rates (true positive rate or TPR) for multiple regression, ARMAX, logistic regression, a feed‐forward multilayer perceptron (MLP), and a recurrent neural network (RNN) model. We use only those days on which flux could rise, removing days when flux is already high from the data set. We explore three input variable sets: (1) ground‐based data (Kp, Dst, and sunspot number), (2) a full set of easily available solar wind and interplanetary magnetic field parameters (|B|, Bz, V, N, P, Ey, Kp, Dst, and sunspot number, and (3) this full set with the addition of previous day's flux. Despite high validation correlations in the multiple regression and ARMAX predictions, these regression models had low predictive ability (TPR < 45%) and are not recommended for use. The three classifier model types (logistic regression, MLP, and RNN) performed better (TPR: 50.8–74.6%). These rates were increased further if the cost of missing an event was set at 4 times that of predicting an event that did not happen (TPR: 73.1–89.6%). The area under the receiver operating characteristic curves did not, for the most part, differ between the classifier models (logistic, MLP, and RNN), indicating that any of the three could be used to discriminate between events and nonevents, but validation suggests a full RNN model performs best. The addition of previous day's flux as a predictor provided only a slight advantage. Key Points: Multiple regression and ARMAX models performed much worse than classifier models at predicting relativistic electron fluxOf the three classifier models (logistic regression, MLP, and RNN) RNN performed bestPersistence (previous day's flux) is not a necessary predictor [ABSTRACT FROM AUTHOR]

We model lower band chorus observations from the DEMETER satellite using daily and hourly autoregressive‐moving average transfer function (ARMAX) equations. ARMAX models can account for serial autocorrelation between observations that are measured close together in time and can be used to predict a response variable based on its past behavior without the need for recent data. Unstable distributions of radiation belt source electrons (tens of keV) and the substorm activity (SMEd from the SuperMAG array) that is thought to inject these electrons were both statistically significant explanatory variables in a daily ARMAX model describing chorus. Predictions from this model correlated well with observations in a hold‐out test data set (validation correlation of 0.675). Source electron flux was most influential when observations came from the same day or the day before the chorus measurement, with effects decaying rapidly over time. Substorms were more influential when they occurred on previous days, presumably due to their injecting source electrons from the plasma sheet. A daily ARMAX model with interplanetary magnetic field (IMF)|B|, IMF Bz, and solar wind pressure as inputs instead of those given above was somewhat less predictive of chorus (r=0.611). An hourly ARMAX model with only solar wind and IMF inputs was even less successful, with a validation correlation of 0.502. Key Points: Empirically based autoregressive‐moving average transfer function models predict daily‐averaged lower band chorus power wellValidation correlation between chorus observations and predictions using source electron flux and substorm activity as inputs was 0.675Source electron flux showed an immediate influence on chorus, while substorms were influential over many days [ABSTRACT FROM AUTHOR]

The identification of a single global model for a stochastic dynamical system operating under various conditions is considered. Each operating condition is assumed to have a pseudo-static effect on the dynamics and be characterized by a single measurable scheduling variable. Identification is accomplished within a recently introduced Functionally Pooled (FP) framework, which offers a number of advantages over Linear Parameter Varying (LPV) identification techniques. The focus of the work is on the extension of the framework to include the important FP-ARMAX model case. Compared to their simpler FP–ARX counterparts, FP–ARMAX models are much more general and offer improved flexibility in describing various types of stochastic noise, but at the same time lead to a more complicated, non-quadratic, estimation problem. Prediction Error (PE), Maximum Likelihood (ML), and multi-stage estimation methods are postulated, and the PE estimator optimality, in terms of consistency and asymptotic efficiency, is analytically established. The postulated estimators are numerically assessed via Monte Carlo experiments, while the effectiveness of the approach and its superiority over its FP–ARX counterpart are demonstrated via an application case study pertaining to simulated railway vehicle suspension dynamics under various mass loading conditions. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we derive the maximum likelihood problem for missing data from a Gaussian model. We present in total eight different equivalent formulations of the resulting optimization problem, four out of which are nonlinear least squares formulations. Among these formulations are also formulations based on the expectation–maximization algorithm. Expressions for the derivatives needed in order to solve the optimization problems are presented. We also present numerical comparisons for two of the formulations for an ARMAX model. [Copyright &y& Elsevier]

Abstract: We present a quadratic programming framework to address the problem of finding optimal maintenance policies for multifacility transportation systems. The proposed model provides a computationally-appealing framework to support decision making, while accounting for functional interdependencies that link the facilities that comprise these systems. In particular, the formulation explicitly captures the bidirectional relationship between demand and deterioration. That is, the state of a facility, i.e., its condition or capacity, impacts the demand/traffic; while simultaneously, demand determines a facility’s deterioration rate. The elements that comprise transportation systems are linked because the state of a facility can impact demand at other facilities. We provide a series of numerical examples to illustrate the advantages of the proposed framework. Specifically, we analyze simple network topologies and traffic patterns where it is optimal to coordinate (synchronize or alternate) interventions for clusters of facilities in transportation systems. [Copyright &y& Elsevier]

This paper develops non-parametric techniques for dynamic models whose data have unknown probability distributions. Point estimators are obtained from the maximization of a semiparametric likelihood function built on the kernel density of the disturbances. This approach can also provide Kullback–Leibler cross-validation estimates of the bandwidth of the kernel densities. Confidence regions are derived from the dual-empirical likelihood method based on non-parametric estimates of the scores. Limit theorems for martingale difference sequences support the statistical theory; moreover, simulation experiments and a real case study show the validity of the methods. [ABSTRACT FROM AUTHOR]

Abstract: This paper uses linear and nonlinear statistical models, including artificial neural network (ANN) methods, to investigate the influence of the four economic factors, which are the national income (NI), population (POP), gross of domestic production (GDP), and consumer price index (CPI) on the electricity consumption in Taiwan and then to develop an economic forecasting model. Both methods agree that POP and NI influence electricity consumption the most, whereas GDP the least. The results of comparing the out-of-sample forecasting capabilities of the two methods indicate the following. (1) If given a large amount of historical data, the forecasts of ARMAX are better than the other linear models. (2) The linear model is weaker on foretelling peaks and bottoms regardless the amount of historical data. (3) The forecasting performance of ANN is higher than the other linear models based on two sets of historical data considered in the paper. This is probably due to the fact that the ANN model is capable of catching sophisticated nonlinear integrating effects through a learning process. To sum up, the ANN method is more appropriate than the linear method for developing a forecasting model of electricity consumption. Moreover, researchers can employ either ANN or linear model to extract the important economic factors of the electricity consumption in Taiwan. [Copyright &y& Elsevier]

Testing model performance on a data set other than the data set used for estimation is common practice in econometrics, technological stochastic modelling and environmetrics. In this paper, using an ARMAX model, the asymptotic distribution of the residual autocorrelations in the validation data set is given and a χ[sup 2] test for overall residual incorrelation is considered. [ABSTRACT FROM AUTHOR]

Phase response curves (PRCs) are a simple model of how a neuron's spike time is affected by synaptic inputs. PRCs are useful in predicting how networks of neurons behave when connected. One challenge in estimating a neuron's PRCs experimentally is that many neurons do not have stationary firing rates. In this article we introduce a new method to estimate PRCs as a function of firing rate of the neuron. We call the resulting model a parameterized PRC (pPRC). Experimentally, we perturb the neuron applying a current with two parts: 1) a current held constant between spikes but changed at the onset of a spike, used to make the neuron fire at different rates, and 2) a pulse to emulate a synaptic input. A model of the applied constant current and the history is made to predict the interspike interval (ISI). A second model is then made to fit the modulation of the spike time from the expected ISI by the pulsatile stimulus. A polynomial with two independent variables, the stimulus phase and the expected ISI, is used to model the pPRC. The pPRC is validated in a computational model and applied to pyramidal neurons from the CA1 region of the hippocampal slices from rat. The pPRC can be used to model the effect of changing firing rates on network synchrony. It can also be used to characterize the effects of neuromodulators and genetic mutations (among other manipulations) on network synchrony. It can also easily be extended to account for more variables.