Spaced Time Series Data Research Articles

Time Series Analysis on the Damage Report of the Northern Kyushu Heavy Rainfall in July 2017

After a natural disaster occurs, the production and sharing of damage reports are extremely important for a disaster response site. However, one of the problems is that the data shared by the damage reports cannot clearly indicate when the damage situation could be grasped because such data change day by day. Accordingly, in this study, the data of the damage reports of the Headquarters for Disaster Control are treated as unequally spaced time series data to evaluate the changing conditions of the data quantitatively. For this purpose, a case is examined for the Headquarters for Disaster Control of Fukuoka Prefecture at the time of the Northern Kyushu Heavy Rainfall event in July 2017. As a result of the examination, it is indicated that the quantitative evaluation would be possible for 1) analysis on timing when the data of the damage reports are updated, 2) analysis on the characteristics of time series of the report data, and 3) visualization of the progress of the damage report service.

Space–time series clustering: Algorithms, taxonomy, and case study on urban smart cities

This paper provides a short overview of space–time series clustering, which can be generally grouped into three main categories such as: hierarchical, partitioning-based, and overlapping clustering. The first hierarchical category is to identify hierarchies in space–time series data. The second partitioning-based category focuses on determining disjoint partitions among the space–time series data, whereas the third overlapping category explores fuzzy logic to determine the different correlations between the space–time series clusters. We also further describe solutions for each category in this paper. Furthermore, we show the applications of these solutions in an urban traffic data captured on two urban smart cities (e.g., Odense in Denmark and Beijing in China). The perspectives on open questions and research challenges are also mentioned and discussed that allow to obtain a better understanding of the intuition, limitations, and benefits for the various space–time series clustering methods. This work can thus provide the guidances to practitioners for selecting the most suitable methods for their used cases, domains, and applications.

Infilling the missing values of groundwater level using time and space series: case of Nantong City, east coast of China

Dynamic monitoring data of the groundwater level form an important basis to understand the current state of groundwater development and utilization, which is required to plan its sustainable exploitation. The dynamic data of groundwater level are typical space-time series data with the characteristics of nonlinear strong space-time correlation. However, because of the influences of human or natural factors, long-term monitoring data of the groundwater level are often incomplete to varying degrees. Consequently, the efficiency and accuracy of traditional data in-filling methods for the missing groundwater level data are low. Additionally, restoration methods based on spatio-temporal geostatistics and machine learning are not sufficiently comprehensive to consider spatio-temporal correlations, which results in low restoration accuracy. Therefore, this study was based on an analysis of the characteristics and the missing status of the groundwater level dynamic monitoring data of the pore confined aquifer III of Nantong City, east coast of China. Both the universal Kriging (UK) interpolation method and the support vector regression (SVR) method were used for spatial missing correction and temporal missing correction, respectively. A separable spatial-temporal missing correction coupling model of groundwater level monitoring data was constructed and named UK-SVR. The reliabilities and accuracies of UK-SVR, UK, SVR, and K-nearest neighbor were evaluated by a cross-validation algorithm. The results showed that UK-SVR achieved higher accuracy than other single data-infilling models.

Signal Pre-Selection for Monitoring and Prediction of Vehicle Powertrain Component Aging

Predictive maintenance has become important for avoiding unplanned downtime of modern vehicles. With increasing functionality the exchanged data between Electronic Control Units (ECU) grows simultaneously rapidly. A large number of in-vehicle signals are provided for monitoring an aging process. Various components of a vehicle age due to their usage. This component aging is only visible in a certain number of in-vehicle signals. In this work, we present a signal selection method for in-vehicle signals in order to determine relevant signals to monitor and predict powertrain component aging of vehicles. Our application considers the aging of powertrain components with respect to clogging of structural components. We measure the component aging process in certain time intervals. Owing to this, unevenly spaced time series data is preprocessed to generate comparable in-vehicle data. First, we aggregate the data in certain intervals. Thus, the dynamic in-vehicle database is reduced which enables us to analyze the signals more efficiently. Secondly, we implement machine learning algorithms to generate a digital model of the measured aging process. With the help of Local Interpretable Model-Agnostic Explanations (LIME) the model gets interpretable. This allows us to extract the most relevant signals and to reduce the amount of processed data. Our results show that a certain number of in-vehicle signals are sufficient for predicting the aging process of the considered structural component. Consequently, our approach allows to reduce data transmission of in-vehicle signals with the goal of predictive maintenance.

Discrete‐Time Approximation of a Cogarch(p,q) Model and its Estimation

In this article, we construct a sequence of discrete‐time stochastic processes that converges in the Skorokhod metric to a COGARCH(p,q) model. The result is useful for the estimation of the COGARCH(p,q) on irregularly spaced time series data. The proposed estimation procedure is based on the maximization of a pseudo log‐likelihood function and is implemented in the yuima package.

Prediction of GWL with the help of GRACE TWS for unevenly spaced time series data in India : Analysis of comparative performances of SVR, ANN and LRM

Prediction of Ground Water Level (GWL) is extremely important for sustainable use and management of ground water resource. The motivations for this work is to understand the relationship between Gravity Recovery and Climate Experiment (GRACE) derived terrestrial water change (ΔTWS) data and GWL, so that ΔTWS could be used as a proxy measurement for GWL. In our study, we have selected five observation wells from different geographic regions in India. The datasets are unevenly spaced time series data which restricts us from applying standard time series methodologies and therefore in order to model and predict GWL with the help of ΔTWS, we have built Linear Regression Model (LRM), Support Vector Regression (SVR) and Artificial Neural Network (ANN). Comparative performances of LRM, SVR and ANN have been evaluated with the help of correlation coefficient (ρ) and Root Mean Square Error (RMSE) between the actual and fitted (for training dataset) or predicted (for test dataset) values of GWL. It has been observed in our study that ΔTWS is highly significant variable to model GWL and the amount of total variations in GWL that could be explained with the help of ΔTWS varies from 36.48% to 74.28% (0.3648⩽R2⩽0.7428). We have found that for the model GWL∼ΔTWS, for both training and test dataset, performances of SVR and ANN are better than that of LRM in terms of ρ and RMSE. It also has been found in our study that with the inclusion of meteorological variables along with ΔTWS as input parameters to model GWL, the performance of SVR improves and it performs better than ANN. These results imply that for modelling irregular time series GWL data, ΔTWS could be very useful.

Discrete Time Approximation of a COGARCH(p,q) Model and its Estimation (Preliminary Version)

In this paper, we construct a sequence of discrete time stochastic processes that converges in probability and in the Skorokhod metric to a COGARCH(p,q) model. The result is useful for the estimation of the continuous model defined for irregularly spaced time series data. The estimation procedure is based on the maximization of a pseudo log-likelihood function and is implemented in the yuima package.

Classification and clustering with continuous time Bayesian network models

Classification and clustering of streaming data are relevant in finance, computer science, and engineering while they are becoming increasingly important in medicine and biology. Streaming data are analyzed with algorithms and models capable to represent dynamics, sequences and time. Dynamic Bayesian networks and hidden Markov models are commonly used to analyze streaming data. However, they are concerned with evenly spaced time series data and thus suffer from several limitations. Indeed, it is not clear how timestamps should be discretized even if some approaches to mitigate this problem have been recently made available. In this paper we describe the class of continuous time Bayesian networks classifiers and develop algorithms for their parametric and structural learning to solve classification and clustering of multivariate discrete state continuous time trajectories. Numerical experiments on synthetic and real world data are used to compare the performance of continuous time Bayesian network models to that achieved by dynamic Bayesian networks. In particular, post-stroke rehabilitation data is used for the classification task while urban traffic data from continuous time loop is used for the clusteirng task. The achieved results confirm the effectiveness of the proposed approaches.

The risk–return tradeoff: A COGARCH analysis of Merton's hypothesis

We analysed daily returns of the CRSP value weighted and equally weighted indices over 1953–2007 in order to test for Merton's theorised relationship between risk and return. Like some previous studies we used a GARCH stochastic volatility approach, employing not only traditional discrete time GARCH models but also using a COGARCH — a newly developed continuous-time GARCH model which allows for a rigorous analysis of unequally spaced data. When a risk–return relationship symmetric to positive or negative returns is postulated, a significant risk premium of the order of 7–8% p.a., consistent with previously published estimates, is obtained. When the model includes an asymmetry effect, the estimated risk premium, still around 7% p.a., becomes insignificant. These results are robust to the use of a value weighted or equally weighted index. The COGARCH model properly allows for unequally spaced time series data. As a sidelight, the model estimates that, during the period from 1953 to 2007, the weekend is equivalent, in volatility terms, to about 0.3–0.5 regular trading days.

Using the Existing Spectral Clutter Filter With the Nonuniformly Spaced Time Series Data in Weather Radar

The National Weather Service (NWS) has a network of weather surveillance Doppler radars, WSR-88D, that is routinely upgraded to reflect current technological and engineering advances. During the last decade, the staggered pulse repetition time (SPRT) was proposed to mitigate range/velocity ambiguity in WSR-88D; however, it could not be used at lowest elevation tilts due to the inability to filter ground clutter from the nonuniformly spaced time series. A complicated spectral procedure was developed to address this issue, but the procedure was derived for a specific set of data acquisition parameters and used a lookup table to provide a value for the clutter spectrum width. Attempts to use SPRT with different sets of acquisition parameters always led to the degradation of filtering. It is proposed here that the clutter spectrum width be estimated by using Gaussian model adaptive processing (GMAP) that is currently used by NWS for uniformly sampled time series. GMAP is an adaptive ground clutter filter that performs an iterative fit of a Gaussian curve to the spectral coefficients identified as being due to ground clutter. GMAP cannot be used directly with the SPRT spectrum because of multiple clutter replicas that are due to staggered nonuniform sampling. However, the elements of GMAP can be exploited and used in the SPRT procedure. This letter presents how the elements of GMAP can be used with the SPRT data to provide successful clutter filtering at lowest elevation tilts.

GARCH modelling in continuous time for irregularly spaced time series data

The discrete time GARCH methodology which has had such a profound influence on the modelling of heteroscedasticity in time series is intuitively well motivated in capturing many “stylised facts” concerning financial series, and is now almost routinely used in a wide range of situations, often including some where the data are not observed at equally spaced intervals of time. But such data is more appropriately analysed with a continuous time model which preserves the essential features of the successful GARCH paradigm. One such possible extension is the diffusion limit of Nelson [22], but this is problematic in that the discrete time GARCH model and its continuous time diffusion limit are not statistically equivalent (Wang [28]). As an alternative, Kluppelberg et al. [14] recently introduced a continuous time version of the GARCH (the “COGARCH” process) which is constructed directly from a background driving Levy process. The present paper shows how to fit this model to irregularly spaced time series data using discrete time GARCH methodology, by approximating the COGARCH with an embedded sequence of discrete time GARCH series which converges to the continuous time model in a strong sense (in probability, in the Skorokhod metric), as the discrete approximating grid grows finer. This property is also especially useful in certain other applications such as options pricing. The way is then open to using, for the COGARCH, similar statistical techniques to those already worked out for GARCH models, and to illustrate this, an empirical investigation using stock index data is given.

Air–sea CO 2 exchange in a subtropical estuarine-coral reef system, Kaneohe Bay, Oahu, Hawaii

The present study represents the first time-series evaluation of air–sea CO 2 exchange for a coastal marine system of a subtropical high island of the Pacific. From September 2003 through September 2004, surface water total alkalinity (TA) and dissolved inorganic carbon (DIC) data were collected bimonthly throughout the Kaneohe Bay estuarine-coral reef system. The partial pressure of carbon dioxide ( pCO 2) and the air–sea CO 2 exchange flux were calculated using TA, DIC, atmospheric CO 2 at sea level, and five wind speed relationships for gas transfer velocity. pCO 2 values were above the atmospheric level (average: 378 μatm) throughout Kaneohe Bay (400–500 μatm) and Kaneohe Stream waters (600–1300 μatm) during baseline conditions. pCO 2 levels above atmospheric in bay water were driven mainly by calcification while pCO 2 levels above atmospheric in stream water were driven mainly by remineralization of terrestrial organic matter. pCO 2 values above the atmospheric level were observed in surface water that extended almost 4 km beyond the boundary of the bay indicating that processes inside the bay such as calcification affect the inorganic carbon properties of the surrounding near shore open ocean. Precipitation from storm events in the Kaneohe watershed increases stream and land runoff that brings excess nutrients to bay waters. These excess nutrients stimulate phytoplankton blooms which draw down CO 2 in Kaneohe Bay water through photosynthesis. Despite the significant effects of the storms, Kaneohe Bay was a net annual source of CO 2 to the atmosphere of − 0.046 Gmol C year − 1 (− 0.55 kton C year − 1 ) with an area-specific flux of − 1.45 mol C m − 2 year − 1 (− 17.4 g C m − 2 year − 1 ). The source of CO 2 in Kaneohe Bay could be stronger on a long-term basis since dry years may be stronger net annual sources than wet years such as this study period. As shown by Kaneohe Bay data, the dynamic nature of estuarine systems makes closely spaced time-series data imperative for characterizing accurately the inorganic carbon system and the net annual air–sea exchange flux of CO 2.

MTIE and TDEV Analysis of Unevenly Spaced Time Series Data

This work investigates how uneven data spacing affects the computations of MTIE (maximum time interval error) and TDEV (time deviation). MTIE and TDEV are evaluated with unevenly spaced data in five different power-law noise types.Each simulated data set has 3600 evenly spaced data points spaced one second apart.Dat a points are then removed from each file according to the parameter p. Each data point in a file is removed with probability p and retained with probability (1 – p). For the unevenly spaced data files, the average spacing is recomputed.Then MTIE and TDEV were calculated for data files with different p values.The simulated results show that the difference among the performance of various p values is not significant when the observation time exceeds 100 seconds. Additionally, the discrepancy between the computation results of evenly (p = 0) and slightly unevenly (0>p>0.1) spaced data files is often negligible.Therefore, the effect of slightly unevenly spaced data on computations of MTIE and TDEV can be ignored.Based on these results, the telecommunications synchronization measurement can be performed using a simple model, which does not require a clock recovery device to recover the timing signal from the data bits.Instead, the network data signal can be input directly to the time interval counter (TIC).The measured data are often unevenly spaced as the data bits of “1” and “0” are not distributed regularly. However, this novel measurement model can still be validated using previous results.

Method of running parabolae: Spectral and statistical properties of the smoothing function

Analytic expressions in a general form are derived for the expectation of functions related to the smoothing the astronomical signals using local approximations with additional weights. No restrictions are made on distribution of the times of the signal. Applications are made for polynomial fits of orders 0 and 2 and weights and . These variable weights ensure that the smoothing function will be both continuous and differentiable, which is important for determining the extrema and the shape of the variations. Special attention is paid to evenly spaced time series data, which if their number is large enough will allow one to obtain analytic expressions for the main functions.

Forecasting the frequency of changes in quoted foreign exchange prices with the autoregressive conditional duration model

This paper applies the Autorecressive Conditional Duration model to Foreign Exchange quotes arriving on Reuters screens. The Autoregressive Conditional Duration model, developed in Engle and Russell (1995) [Engle, R., Russell, J., 1995. Autoregressive conditional duration; a new model for irregularly spaced time series data, University of California, San Diego, unpublished manuscript.], is a new statistical model for the analysis of data that does not arrive in equal time intervals. When Dollar/Deutschmark data are examined, it is clear that many of the price quotes are simply noisy repeats of the previous quote. By systematically thinning the sample, a measure of the time between price changes is developed. These price durations are modeled with the ACD to obtain estimates of the instantaneous intensity of price changes. This measure is related to standard measures of volatility but is formulated in a way that incorporates the information in the irregular sampling intervals. A simple market microstructure model implies that the bid-ask spread should have predictive power for the volatility which is supported by the data. A model of price leadership however, is not supported.

Noise analysis of unevenly spaced time series data

Two-way satellite time and frequency transfer (TWSTFT) data are typically recorded on Monday, Wednesday and Friday. This produces an unevenly spaced time series on which it is difficult to perform an accurate two-sample variance analysis. We have investigated the effect of uneven data spacing on the computation of σx(τ) [1-2]. Evenly spaced simulated data sets were generated for noise processes ranging from white phase modulation to random walk frequency modulation. σx(τ) was then calculated for each noise type. Data were subsequently removed from each simulated data set to create two unevenly spaced sets with average intervals of 2,8 and 3,6 days. These sparse sets correspond to typical TWSTFT data patterns. σx(τ) was then calculated for each sparse data set using two different approaches. First, the missing data points were replaced by linear interpolation and σx(τ) calculated from this now full data set. The second approach ignored the fact that the data were unevenly spaced and calculated σx(τ) as if the data were equally spaced with average spacing of 2,8 or 3,6 days. The impact of uneven data spacing on the results of these two approaches is significant and is discussed. Finally, techniques are presented for correcting errors caused by uneven data spacing in simulated TWSTFT data sets, and the appropriate technique is applied to a real data set.

Researches for Modeling Water Quality of Tidal Rivers

This paper deals with system identification by statistical method for modeling dynamically water quality of tidal rivers by using the nonstationary time series of the observations of the water quality parameters (NBOD, CBOD and DO) and the time series of the observations of the hydraulic parameters (V, Q and A). For this purpose, a difference model with time-varying coefficients is derived with the concentration of the water quality parameters as nonstationary spacetime series data. The time-varying coefficients of the model are then divided into two parts, time-varying and time-invariant, the former consists of some hydraulic parameters and the later is then used for parameter estimation.In the second part of this paper, a noise model is also derived. It is a linear time-varying model. The noise process is not wide-sense stationary. According to the measured data of hydraulic parameters of a tidal river, we analyse the time-varying part and then obtain its varying range. Further the tidal period can be decomposed into a set of subsequences according to its different phases. From each of them we can obtain a noise model which is linear time-invariant. And we then conclude that the noise process is mean value ergodic. From an analysis of the noise behavior, it is found that the time series analysis method can be used for modeling the water quality of tidal rivers. Allen’s PSS criterion is then used for choosing the model and determining the estimated parameters. This is exactly that Tamura’s NICE (Nonstationary Statistical System Identification Method for River Quality Modeling) is applied to tidal rivers.The paper further proposes a method for determining the model and modifying its parameter valuesComputer simulation shows that the proposed method is realizable and recommended for modeling the water quality of tidal rivers (Snangnai Huang-Pu River).

A Method of Estimating Space-Time Spectra from Polar-Orbiting Satellite Data

Abstract Space-time spectral formulas are modified to estimate wavenumber-frequency spectra correctly from space-time series data sampled at the same local time but at different hours of a day by a polar-orbiting satellite. It is shown that a significant error occurs in the wavenumber-frequency spectra of the space-time series for wave periods less than 10 days. This error can be eliminated without time interpolation by taking a space-Fourier transform with respect to the frequency-shifted wavenumbers measured at the same local time.