Fitting Time Series Research Articles

Penalized Maximum Likelihood Estimation of Semiparametric Generalized Linear Models with Application to Climate Temperature Data

Global temperature change is an important indicator of climate change. Climate time series data are characterized by trend, seasonal/cyclical as well as irregular components. Adequately modeling these components cannot be overemphasized. In this paper, we have proposed an approach of modeling temperature data using semiparametric additive generalized linear model. We have derived a penalized maximum likelihood estimation of the additive component of the semiparametric generalized linear models, that is, of regression coefficients and smooth functions. A statistical modeling with real time series data set was conducted on temperature data. The study has provided indications on the gain of using semiparametric modeling in situations where a signal component can be additively decomposed in to trend, cyclical and irregular components. Thus, we recommend semiparametric additive penalized models as an option to fit time series data sets in modelling the different component with different functions to adequately explain the relation inherent in data.

Automatic distortion-suppressed time series fitting method for irregular sampled NDVI

ABSTRACT Time series Normalized Difference Vegetation Index (NDVI) fitting, which describes the discrete time series observations with a mathematical model, can remove the residual noise, fill in the missing data, and produce a noise-free continuous time series; therefore, numerous time series fitting methods have been developed, but most of them focused on regularly sampled, noise-suppressed data, as NDVI time series derived from medium-spatial remote sensing images has irregular sampled and distortion-intensive characteristic, limiting the applicability of traditional methods. To address this problem, an automatic distortion-suppressed time series fitting method for irregular sampled NDVI is proposed in this paper. First, the observation quality is evaluated: (I) the observations on a fully clear image are identified as clear observations. (II) According to the prior knowledge that the NDVI is underestimated, the observations in the upper convex hull and above the line of two temporal-adjacent clear observations (identified by fully clear image and upper convex) are labelled as clear observations. (III) As the temporal evolution of NDVI is a slow and continuous process, deep-V observations, which has experienced an abrupt decrease and increase consecutively, are identified as noisy observations. Second, different weights are assigned to observations based on the quality assessment result, and the NDVI time series is weighted fitted. To highlight the observations above the fitting line and suppress those below the fitting line, the weights are updated according to the direction and distance between the actual observation and fitting prediction value. Then, fitting and reweighting processes are repeated until a stable fitting result is obtained. We use images acquired by the Multi-Spectral Imager (MSI) onboard Sentinel-2 satellite in Shouxian, Anhui Province to construct NDVI time series and test the method. The result demonstrates that our method can suppress the distortion and realize time series fitting automatically, compared with the state of art method, our method can obtain reasonably overestimation of the NDVI, providing an alternative for fitting irregular sampled NDVI.

A modified BDS test

The BDS test is a test for detecting whether a random sequence is i.i.d. (independent and identically distributed). It has been used in economics and finance to examine whether a fitted time series model is adequate by examining whether the residual sequence is nearly i.i.d. Though the BDS test is widely used in the literature, it has a weakness of over-rejecting the null hypothesis even though the sample size T is as large as (100,1000). In this study, we propose a modified BDS test (MBDS test) by removing some terms from the correlation integral, which is the foundation of the BDS test. Theoretical calculations and simulation results show that the MBDS test efficiently corrects the bias of the BDS test.

Spatially and temporally complete Landsat reflectance time series modelling: The fill-and-fit approach

Statistical time series models are increasingly being used to fit medium resolution time series provided by satellite sensors, such as Landsat, for terrestrial monitoring. Cloud and shadows, combined with low satellite repeat cycles, reduce surface observation availability. In addition, only a single year of data can be used where there is high inter-annual variation, for example, over many croplands. These factors reduce the ability to fit time series models and reduce model fitting accuracy. In solution, we propose a novel fill-and-fit (FF) approach for application to medium resolution satellite time series. In the ‘fill’ step, gaps are filled using a recently published algorithm developed to fill large-area gaps in satellite time series using no other satellite data. In the ‘fit’ step, a linear harmonic model is fitted to the gap-filled time series. The FF approach, and the conventional harmonic model fitting without gap filling, termed the F approach, are demonstrated using seven months of Landsat-7 and -8 surface reflectance Analysis Ready Data (ARD) over agricultural regions in North Dakota, Minnesota, Michigan, and Kansas. Synthetic model-predicted reflectance for days through the growing season are examined, and assessed quantitatively by comparison with an independent Landsat surface reflectance data set. The six Landsat reflective band root-mean-square difference (RMSD) between the predicted and the independent reflectance, considering millions of pixel observations for each ARD tile, show that the FF approach is more accurate than the F approach. The mean FF RMSD values varied from 0.025 to 0.026 for the four tiles, whereas the mean F RMSD values varied from 0.026 to 0.047. These mean FF RMSD values are <0.03 which is comparable to the uncertainty specification for the Landsat 8 OLI TOA reflectance, but greater than the atmospheric correction uncertainty in any Landsat 8 OLI band. The greatest RMSD values were found over the Minnesota tile and occurred due to a long period of missing data early in the growing season, and the smallest RMSD values were found for the Kansas tile because of the high availability of clear surface observations. The F approach could not be applied where there were insufficient clear surface observations to fit the model, and where the model was applied, the fitting was often sensitive to issues including gaps in the Landsat time series and the presence of undetected cloud- and shadow-contaminated observations. The FF approach could be applied to every ARD tile pixel location and the predicted reflectance was spatially-coherent and natural looking. Examples are shown that illustrate the potential of using FF predicted synthetic reflectance time series for land surface monitoring.

Virtual topography measurement with transfer functions derived by fitted time series models

The deviations between the actual geometry of a workpiece and the measured geometry are defined by the transfer function of the surface topography measuring instrument used. When the transfer characteristics of a measuring instrument are known, they can, for example, be used for the estimation of measuring results by performing virtual measurements and can subsequently be applied for the estimation of the measurement uncertainty. A technique that has been increasingly applied for the determination of the transfer function of topography measuring devices is the approach based on physical modeling. Here, mathematical models apply simplifications of the complex physical relationships to describe the transfer characteristics of measuring devices. Another method used in practice is the application of material measures for the direct measurement of transfer properties. Within this paper, an alternative approach developed by the authors that applies the ARMA model is further investigated and optimized with regard to its practical applicability. This model was described in a previous publication (Keksel et al 2018 Meas. Sci. Technol. 29 095012) and combines the advantages of theoretical modeling and the experimental determination of transfer characteristics. Within the present work, the approach is further optimized and it is demonstrated that the description of measuring devices by the ARMA model delivers reasonable results for various measuring principles that can be used for a precise virtual prediction of measurement results.

Numerical investigation on the power of parametric and nonparametric tests for trend detection in annual maximum series

Abstract. The need to fit time series characterized by the presence of a trend or change points has generated increased interest in the investigation of nonstationary probability distributions in recent years. Considering that the available hydrological time series can be recognized as the observable part of a stochastic process with a definite probability distribution, two main topics can be tackled in this context: the first is related to the definition of an objective criterion for choosing whether the stationary hypothesis can be adopted, whereas the second regards the effects of nonstationarity on the estimation of distribution parameters and quantiles for an assigned return period and flood risk evaluation. Although the time series trend or change points are usually detected using nonparametric tests available in the literature (e.g., Mann–Kendall or CUSUM test), the correct selection of the stationary or nonstationary probability distribution is still required for design purposes. In this light, the focus is shifted toward model selection criteria; this implies the use of parametric methods, including all of the issues related to parameter estimation. The aim of this study is to compare the performance of parametric and nonparametric methods for trend detection, analyzing their power and focusing on the use of traditional model selection tools (e.g., the Akaike information criterion and the likelihood ratio test) within this context. The power and efficiency of parameter estimation, including the trend coefficient, were investigated via Monte Carlo simulations using the generalized extreme value distribution as the parent with selected parameter sets.

Ecosystem modelling of data-limited fisheries: How reliable are Ecopath with Ecosim models without historical time series fitting?

Long-term time series data are not available for many of the African Great Lakes. This precludes fitting ecosystem model parameters to time series data, and we do not know how reliable non-fitted models are compared to fitted ones in terms of predicting consequences of alternative management strategies. To investigate this, we generate a historical Ecopath with Ecosim (EwE) model for Lake Victoria (East Africa), fitted to time series data (1980–2015), and a present-day EwE model (representing average conditions for the period 2010–2015). We do scenario simulations using the present-day model and the comparable 2015 end-state of the historical model, and test if incorporating information on short-term biomass trends by adjusting biomass accumulation (BA) parameter in the present-day model increases its reliability. We find that there are differences in model predictions, but those differences can be lessened by adjusting BA terms in the present-day model to reflect biomass trends from short-term empirical data. We also compare the models with and without fitted vulnerability parameters. The models generally give comparable results for the dominant commercial fisheries at low fishing pressure; when fishing mortality is increased, the models give variable predictions. This study adds to the current understanding of the limitations of EwE models that are not challenged to reproduce long-term historical fishery responses to perturbations. We conclude that for the less productive groups, as well as groups that suffer heavy mortality (either due to predation or fisheries), it may be appropriate to use negative BA as first draft assumption in present-day models.

Modelling of malaria incidence in Akure, Nigeria: negative binomial approach

The connections between malaria incidence and climate variability have been studied in recent time using some mathematical and statistical models. Many of the statistical models in literature focused on time series approach based on Box–Jenkins methodology. However, fitting time series model based on the Box–Jenkins methodology may be challenging. Most malaria incidence data are count and are over-dispersed. In this study, negative binomial models were formulated for fitting malaria incidence in Akure—one of the epidemic cities in Nigeria. In particular, negative binomial models were formulated for each of the number of outpatient individuals, number of inpatient individuals and mortality count as a function of some climate variables. It was found that an increase in minimum temperature and relative humidity at lag 1 significantly increased the chance of malaria transmission and thereby leads to an increase in the number of inpatient and outpatient individuals, as well as the total number of malaria cases. The minimum temperature, rainfall amount and relative humidity of the study area have a significant impact on the increase of number of inpatient and outpatient individuals while mortality count depends on the total number of reported malaria cases. The findings from this study is to offer in-depth understanding on climate-malaria incidence linkages in Akure, Nigeria.

Discovery of Time Series Motifs on Intel Many-Core Systems

A motif is a pair of subsequences of a longer time series, which are very similar to each other. Motif discovery is applied in a wide range of subject areas involving time series: medicine, biology, entertainment, weather prediction, and others. In this paper, we propose a novel parallel algorithm for motif discovery using Intel MIC (Many Integrated Core) accelerators in the case when time series fit in the main memory. We perform parallelization through thread-level parallelism and OpenMP technology. The algorithm employs a set of matrix data structures to store and index the subsequences of a time series and to provide an efficient vectorization of computations on the Intel MIC platform. The experimental evaluation shows the high scalability of the proposed algorithm.

Sinusoidal wave fit indexing of irreversible displacements for crackmeters monitoring of rockfall areas: test at Pietra di Bismantova (Northern Apennines, Italy)

Temperature changes affect crackmeters monitoring on a daily and a seasonal basis. This is due to rock mass thermal dilatancy and to instrumental matters. The consequent widening closing cycles can mask small irreversible displacements that might be precursors of rock failures. Recently, Weber et al. (Cryosphere 11:567–583, 2017) have proposed a linear fit method between temperature and fracture opening in order to compute the irreversibility index as a metrics to rank irreversible displacements. However, such an approach requires temperature sensors coupled to crackmeters. In order to overcome these limits, we propose an alternative method for deriving a normalised Z-score irreversibility index. It is based on sinusoidal wave fit of cracks opening time series only; thus, it does not require temperature monitoring. The methodology has been tested using data recorded by a wireless sensor network installed at La Pietra di Bismantova rock slab composed of 14 crackmeters and thermometers monitoring potentially unstable rock masses. A comparison of results obtained using the method of Weber et al. (Cryosphere 11:567–583, 2017) and the sinusoidal approach shows that the latter is much less sensitive to the duration of the moving window used to derive the irreversibility index, making it a much more flexible tool for indexing irreversible displacements over short time periods. Moreover, as rapid high–magnitude temperature changes can also be the causal factor of irreversible displacements, their statistical relation with peaks of the Z-score irreversibility index has been investigated. Results have shown that, depending on which crack is examined, correlations between irreversibility peaks and antecedent extreme temperature variations are more or less relevant. In conclusion, we believe that the Z-score sinusoidal wave fit irreversibility index (ZSFI) can represent a useful metrics for indexing irreversible displacements in unstable blocks using crackmeters’ datasets affected by temperature cycles at the daily and seasonal scale.

Improved Spring Vegetation Phenology Calculation Method Using a Coupled Model and Anomalous Point Detection

High temporal resolution remote sensing satellite data can be used to collect vegetation phenology observations over regional and global scales. Logistic and polynomial functions are the most widely used methods for fitting time series normalized difference vegetation index (NDVI) derived from the Moderate Resolution Imaging Spectroradiometer (MODIS). Furthermore, the maximum in the curvature of the fitted curve is usually considered as the spring green-up date. However, the existing green-up date calculation methods have low accuracy for sparse vegetation. This paper proposes an improved green-up date calculation method using a coupled model and anomalous point detection (CMAPD). This model is based on a combination of logistic and polynomial functions, which is used to fit time series vegetation index. Anomalous values were identified using the nearest neighbor algorithm, and these values were corrected by the combination of growing degree-days (GDD) and land use type. Then, the trends and spatial patterns of green-up date was analyzed in the Sanjiangyuan area. The results show that the coupled model fit the time series data better than a single logistic or polynomial function. Besides, the anomalous point detection method properly controlled the green-up date within the local threshold, and could reflect green-up date more accurately. In addition, a weak statistically significant advance trend for average vegetation green-up date was observed from 2000 to 2016. However, in 10.4% of the study area, the the green-up date has significant advanced. Regression analysis showed that the green-up date is correlated to elevation: the green-up date is clearly later at higher elevations.

A Dynamical and Zero-Inflated Negative Binomial Regression Modelling of Malaria Incidence in Limpopo Province, South Africa.

Recent studies have considered the connections between malaria incidence and climate variables using mathematical and statistical models. Some of the statistical models focused on time series approach based on Box–Jenkins methodology or on dynamic model. The latter approach allows for covariates different from its original lagged values, while the Box–Jenkins does not. In real situations, malaria incidence counts may turn up with many zero terms in the time series. Fitting time series model based on the Box–Jenkins approach and ARIMA may be spurious. In this study, a zero-inflated negative binomial regression model was formulated for fitting malaria incidence in Mopani and Vhembe―two of the epidemic district municipalities in Limpopo, South Africa. In particular, a zero-inflated negative binomial regression model was formulated for daily malaria counts as a function of some climate variables, with the aim of identifying the model that best predicts reported malaria cases. Results from this study show that daily rainfall amount and the average temperature at various lags have a significant influence on malaria incidence in the study areas. The significance of zero inflation on the malaria count was examined using the Vuong test and the result shows that zero-inflated negative binomial regression model fits the data better. A dynamical climate-based model was further used to investigate the population dynamics of mosquitoes over the two regions. Findings highlight the significant roles of Anopheles arabiensis on malaria transmission over the regions and suggest that vector control activities should be intense to eradicate malaria in Mopani and Vhembe districts. Although An. arabiensis has been identified as the major vector over these regions, our findings further suggest the presence of additional vectors transmitting malaria in the study regions. The findings from this study offer insight into climate-malaria incidence linkages over Limpopo province of South Africa.

Development of a first order integrated moving average model corrupted with a Markov modulated convex combination of autoregressive moving average errors

ABSTRACTWith a view to providing a tool to accurately model time series processes which may be corrupted with errors such as measurement, round-off and data aggregation, this study developed an integrated moving average (IMA) model with a transition matrix for the errors resulting in a convex combination of two ARMA errors. Datasets on interest rates in the United States and Nigeria were used to demonstrate the application of the formulated model. Basic tools such as the autocovariance function, maximum likelihood method, Newton–Raphson iterative method and Kolmogorov–Smirnov test statistic were employed to examine and fit the formulated specification to data. Test results showed that the proposed model provided a generalisation and a more flexible specification than the existing models of AR error and ARMA error in fitting time series processes in the presence of errors.

Application of the LASSO algorithm for fitting the multiexponential data of the NMR relaxometry

The problem of time series fitting by the sum of several exponentials with different decay parameters often arises analyzing the data of a physical experiment. In particular, such a problem arises determining the nuclear transverse relaxation times from the spin-echo decay NMR data. Mathematically, the problem can be formulated as a solution of the Fredholm integral equation of the first kind with an exponential kernel, or an equivalent system of linear equations. To solve this equation, various regularization methods are used, based on the L2-norm in most cases. We report the application of the L1-regularization for the problem, using the LASSO algorithm. A comparison was made between the results of L1- and L2-regularization on model time series, which were the sum of several exponential decays with noise. Also the L1- and L2-regularization were applied to analyze the 1H NMR experimental data of the spin-echo decays of n-hexane adsorbed in the porous volume of aluminium poor MFI-type zeolites known as ZSM-5. It was found out that the L1-regularization is effective method for determination of the transverse relaxation times from NMR data.

Prescription Drug Monitoring Program: Registration and Use by Prescribers and Pharmacists Before and After Legal Mandatory Registration, California, 2010-2017.

To estimate the effect of California's prescription drug monitoring program's (PDMP) registration mandate on use of the PDMP. We evaluated the effect of California's mandatory PDMP registration law by fitting time series models on the percentage of clinicians registered for California's PDMP and the percentage of clinicians who were active PDMP users (users who created ≥ 1 patient prescription reports in a given month) from 2010 through 2017. We also compared PDMP use among early PDMP adopters (clinicians who registered > 8 months before the mandatory registration deadline) versus late adopters (clinicians who registered ≤ 8 months before the deadline). Mandatory registration was associated with increases in active PDMP users: 53.5% increase for prescribers and 17.9% for pharmacists. Early adopters were 4 times more likely to be active PDMP users than were late adopters. Mandatory registration was associated with increases in PDMP registration and use, but most new registrants did not become active users. Public Health Implications. Mandatory PDMP registration increases PDMP use but does not result in widespread PDMP usage by all clinicians prescribing controlled substances.

Using a Positive Deviance Approach to Influence the Culture of Patient Safety Related to Infection Prevention.

BackgroundHealth care–associated infections (HAIs) are a socio-technical problem. We evaluated the impact of a social change intervention on health care personnel (HCP), called “positive deviance” (PD), on patient safety culture related to infection prevention among HCP.MethodsThis observational study was done in 6 medical wards at an 800-bed public academic hospital in the United States. Three of these wards were randomly assigned to receive PD intervention on HCP. After a retrospective 6-month baseline period, PD was implemented over 9 months, followed by 9 months of follow-up. Patient safety culture and social networks among HCP were surveyed at 6, 15, and 24 months. Rates of HAI were measured among patients.ResultsThe measured patient safety culture was steady over time at 69% aggregate percent positive responses in wards with PD vs decline from 79% to 75% in wards without PD (F statistic 10.55; P = .005). Social network maps suggested that nurses, charge nurses, medical assistants, ward managers, and ward clerks play a key role in preventing infections. Fitted time series of monthly HAI rates showed a decrease from 4.8 to 2.8 per 1000 patient-days (95% confidence interval [CI], 2.1 to 3.5) in wards without PD, and 5.0 to 2.1 per 1000 patient-days (95% CI, –0.4 to 4.5) in wards with PD.ConclusionsA positive deviance approach appeared to have a significant impact on patient safety culture among HCP who received the intervention. Social network analysis identified HCP who are likely to help disseminate infection prevention information. Systemwide interventions independent of PD resulted in HAI reduction in both intervention and control wards.

On Time Domain Analysis of Malaria Morbidity in Nigeria

That malaria contributes substantially to the poor health situation in Africa is an understatement. To help government in the continuous provision of necessary measures needful to curb increasing spread of the parasites, there is a need to build an appropriate time domain model which can be used to forecast the future rate of spread. As a result of this, ARIMA model was built for analyzing the secondary data collected on the incidence of malaria. It was discovered that the data was not stationary and stationarity was achieved through 2nd order differencing. The ACF and PACF of the differenced data suggested possible models for selection. AIC and MSE were used to select the models that really provided a best fit for the time series. From various ARIMA models generated, ARIMA model was found to best fit the malaria data. Ljung-Box test and Shapiro-Wilk test met all necessary conditions for independence and normality. The model was used for forecast and it was observed that there is going to be a steady increase in malaria prevalence.

Safety performance evaluation in a steel industry: A short-term time series approach

BackgroundThe aim of the present study was to assess the safety performance in a steel industry and predicting the occurrence of incidents using Customized Predictive Risk Index (CPRI) technique. Materials and methods350 unsafe observations were recorded and scored based on risk factors of probability of danger, frequency of work exposure, number of persons at risk, and severity of consequence. Risk Index (RI) of each observation was calculated through geometric average of risk factors. Optimum forecasting time series model of RI was determined using the smallest value of Akaike information criterion (AIC) to predict the CPRI trend and forecast the occurrence of incidents with a 95% confidence interval. Descriptive analysis was conducted using SPSS 22.00 and incident forecasting based on CPRI trend was conducted using forecast package for R 3.3.1. ResultsAutoregressive of 6 consecutive observations (AR-6) was chosen as the optimum model to fit time series data and define CPRI (AC = 1226.58). Most incidents occurred when the CPRI value was exceeds five and this range was determined as action zone and forecasting criteria for predicting the occurrence of incidents. ConclusionCustomized Predictive Risk Index (CPRI), developed in this study could be used as a leading indicator for safety performance in steel industry. Ensuring the managers about the functionality of leading indicators to assess safety performance could be facilitated with comparing the results achieved by models with the real data.

Deep learning: A guide for practitioners in the physical sciences

Machine learning is finding increasingly broad applications in the physical sciences. This most often involves building a model relationship between a dependent, measurable output, and an associated set of controllable, but complicated, independent inputs. We present a tutorial on current techniques in machine learning—a jumping-off point for interested researchers to advance their work. We focus on deep neural networks with an emphasis on demystifying deep learning. We begin with background ideas in machine learning and some example applications from current research in plasma physics. We discuss supervised learning techniques for modeling complicated functions, beginning with familiar regression schemes, and then advancing to more sophisticated deep learning methods. We also address unsupervised learning and techniques for reducing the dimensionality of input spaces. Along the way, we describe methods for practitioners to help ensure that their models generalize from their training data to as-yet-unseen test data. We describe classes of tasks—predicting scalars, handling images, and fitting time-series—and prepare the reader to choose an appropriate technique. We finally point out some limitations to modern machine learning and speculate on some ways that practitioners from the physical sciences may be particularly suited to help.

Ablation dynamics during laser interstitial thermal therapy for mesiotemporal epilepsy.

IntroductionThe recent emergence of laser interstitial thermal therapy (LITT) as a frontline surgical tool in the management of brain tumors and epilepsy is a result of advances in MRI thermal imaging. A limitation to further improving LITT is the diversity of brain tissue thermoablative properties, which hinders our ability to predict LITT treatment-related effects. Utilizing the mesiotemporal lobe as a consistent anatomic model system, the goal of this study was to use intraoperative thermal damage estimate (TDE) maps to study short- and long-term effects of LITT and to identify preoperative variables that could be helpful in predicting tissue responses to thermal energy.MethodsFor 30 patients with mesiotemporal epilepsy treated with LITT at a single institution, intraoperative TDE maps and pre-, intra- and post-operative MRIs were co-registered in a common reference space using a deformable atlas. The spatial overlap of TDE maps with manually-traced immediate (post-ablation) and delayed (6-month) ablation zones was measured using the dice similarity coefficient (DSC). Then, motivated by simple heat-transfer models, ablation dynamics were quantified at amygdala and hippocampal head from TDE pixel time series fit by first order linear dynamics, permitting analysis of the thermal time constant (τ). The relationships of these measures to 16 independent variables derived from patient demographics, mesiotemporal anatomy, preoperative imaging characteristics and the surgical procedure were examined.ResultsTDE maps closely overlapped immediate ablation borders but were significantly larger than the ablation cavities seen on delayed imaging, particularly at the amygdala and hippocampal head. The TDEs more accurately predicted delayed LITT effects in patients with smaller perihippocampal CSF spaces. Analyses of ablation dynamics from intraoperative TDE videos showed variable patterns of lesion progression after laser activation. Ablations tended to be slower for targets with increased preoperative T2 MRI signal and in close proximity to large, surrounding CSF spaces. In addition, greater laser energy was required to ablate mesial versus lateral mesiotemporal structures, an effect associated with laser trajectory and target contrast-enhanced T1 MRI signal.ConclusionsPatient-specific variations in mesiotemporal anatomy and pathology may influence the thermal coagulation of these tissues. We speculate that by incorporating demographic and imaging data into predictive models we may eventually enhance the accuracy and precision with which LITT is delivered, improving outcomes and accelerating adoption of this novel tool.