Time Series Phenomena Research Articles

Threshold integer-valued autoregressive model with serially dependent innovation

ABSTRACT Nonlinearity in count time series is commonly encountered in practice. To better explain the nonlinear phenomena in count time series, this article introduces a new threshold INAR(1) model using the idea of serially dependent innovation. The proposed model contains some existing INAR(1) models as special cases and establishes a connection between the threshold INAR(1) model and the threshold INARCH(1) model. The basic probabilistic and statistical properties of the new model are investigated. Model parameters, including the threshold variable, are estimated by the conditional least squares, modified quasi-likelihood and conditional maximum likelihood methods. Asymptotic properties and numerical results of the estimates are also studied. An application to the monthly trading volume of stock B in Shanghai Stock Exchange is conducted to show the practicability of the proposed model.

MultiStream EvolveCluster

This paper proposes a novel multi-stream clustering algorithm, MultiStream EvolveCluster (MS-EC), that can be used for continuous and distributed monitoring and analysis of evolving time series phenomena. It can maintain evolving clustering solutions separately for each stream/view and consensus clustering solutions reflecting evolving interrelations among the streams. Each stream behavior can be analyzed by different clustering techniques using a distance measure and data granularity that is specially selected for it. The properties of the MultiStream EvolveCluster algorithm are studied and evaluated with respect to different consensus clustering techniques, distance measures, and cluster evaluation measures in synthetic and real-world smart building datasets. Our evaluation results show a stable algorithm performance in synthetic data scenarios. In the case of real-world data, the algorithm behavior demonstrates sensitivity to the individual streams’ data quality and the used consensus clustering technique.

Crop Water Requirements with Changing Climate in an Arid Region of Saudi Arabia

Agriculture is critical for a country’s population growth and economic expansion. In Saudi Arabia (SA), agriculture relies on groundwater, seasonal water, desalinated water, and recycled water due to a lack of surface water resources, a dry environment, and scanty rainfall. Estimating water consumption to plan crop water requirements (CWR) in changing environments is difficult due to a lack of micro-level data on water consumption, particularly in agricultural systems. High-resolution satellite data combined with environmental data provides a valuable tool for computing the CWR. This study aimed to estimate the CWR with a greater spatial and temporal resolution and localized field data and environmental variables. Obtaining this at the field level is appropriate, but geospatial technology can produce repeatable, time-series phenomena and align with environmental data for wider coverage regions. The CWR in the study area has been investigated through two methods: firstly, based on the high-resolution PlanetScope (PS) data, and secondly, using the FAO CROPWAT model v8.0. The analysis revealed that evapotranspiration (ETo) showed a minimum response of 2.22 mm/day in January to a maximum of 6.13 mm/day in July, with high temperatures (42.8). The humidity reaches a peak of 51%, falling to a minimum in June of 15%. Annual CWR values (in mm) for seven crops studied in the present investigation, including date palm, wheat, citrus, maize, barley, clover, and vegetables, were 1377, 296, 964, 275, 259, 1077, 214, respectively. The monthly averaged CWR derived using PS showed a higher correlation (r = 0.83) with CROPWAT model results. The study was promising and highlighted that such analysis is decisive and can be implemented in any region by using Machine Learning and Deep Learning for in-depth insights.

Model Selection and Post Selection to Improve the Estimation of the ARCH Model

The Autoregressive Conditionally Heteroscedastic (ARCH) model is useful for handling volatilities in economical time series phenomena that ARIMA models are unable to handle. The ARCH model has been adopted in many applications that contain time series data such as financial market prices, options, commodity prices and the oil industry. In this paper, we propose an improved post-selection estimation strategy. We investigated and developed some asymptotic properties of the suggested strategies and compared with a benchmark estimator. Furthermore, we conducted a Monte Carlo simulation study to reappraise the relative characteristics of the listed estimators. Our numerical results corroborate with the analytical work of the study. We applied the proposed methods on the S&P500 stock market daily closing prices index to illustrate the usefulness of the developed methodologies.

Legacy Survey of Space and Time cadence strategy evaluations for active galactic nucleus time-series data in Wide-Fast-Deep field

ABSTRACT Machine learning is a promising tool to reconstruct time-series phenomena, such as variability of active galactic nuclei (AGNs), from sparsely sampled data. Here, we use three Continuous Autoregressive Moving Average (CARMA) representations of AGN variability – the Damped Random Walk (DRW) and (over/under)Damped Harmonic Oscillator – to simulate 10-yr AGN light curves as they would appear in the upcoming Vera Rubin Observatory Legacy Survey of Space and Time (LSST), and provide a public tool to generate these for any survey cadence. We investigate the impact on AGN science of five proposed cadence strategies for LSST’s primary Wide-Fast-Deep (WFD) survey. We apply for the first time in astronomy a novel Stochastic Recurrent Neural Network (SRNN) algorithm to reconstruct input light curves from the simulated LSST data, and provide a metric to evaluate how well SRNN can help recover the underlying CARMA parameters. We find that the light-curve reconstruction is most sensitive to the duration of gaps between observing season, and that of the proposed cadences, those that change the balance between filters, or avoid having long gaps in the g band perform better. Overall, SRNN is a promising means to reconstruct densely sampled AGN light curves and recover the long-term structure function of the DRW process (SF∞) reasonably well. However, we find that for all cadences, CARMA/SRNN models struggle to recover the decorrelation time-scale (τ) due to the long gaps in survey observations. This may indicate a major limitation in using LSST WFD data for AGN variability science.

Immunology-Based Sustainable Portfolio Management

Immunological principles can be used to build a sustainable investment portfolio. The theory of immunology states that information about recognized pathogens is stored in the memory of the immune system. Information about previous illnesses can be helpful when the pathogen re-enters the body. Real-time analysis of 11 automated financial trading datasets confirmed this phenomenon in financial time series. Therefore, in order to increase the sustainability of the portfolio, we propose to train the portfolio with the most similar segments of historical data. The segment size and offset may vary depending on the data set and time.

A New Bivariate Random Coefficient INAR(1) Model with Applications

Excess zeros is a common phenomenon in time series of counts, but it is not well studied in asymmetrically structured bivariate cases. To fill this gap, we first considered a new first-order, bivariate, random coefficient, integer-valued autoregressive model with a bivariate innovation, which follows the asymmetric Hermite distuibution with five parameters. An attractive advantage of the new model is that the dependence between series is achieved by innovative parts and the cross-dependence of the series. In addition, the time series of counts are modeled with excess zeros, low counts and low over-dispersion. Next, we established the stationarity and ergodicity of the new model and found its stochastic properties. We discuss the conditional maximum likelihood (CML) estimate and its asymptotic property. We assessed finite sample performances of estimators through a simulation study. Finally, we demonstrate the superiority of the proposed model by analyzing an artificial dataset and a real dataset.

Forecasting Non-Stationary Time Series with the Multiscale Autoregressive (MAR) Model Approach Using the Haar Wavelet Filter at the Rupiah Exchange Rate Against the Dollar

Time series data is a collection of a phenomenon that occurs based on a fixed or at the same time index. Time series phenomena often exhibit non-stationary behavior. One of the time series analyses for non-stationary data is the Multiscale Autoregressive Model (MAR). The MAR model chosen is a model that meets the assumptions of normality and white noise. The predictors used in MAR modeling are wavelet coefficients and scales which are the result of decomposition using Maximal Overlap Discrete Wavelet Transform (MODWT), MODWT functions to decompose data based on the level of each wavelet filter (family). The wavelet filters used in this study are Haar. In this study, the model generated from the data that was stationary first was more accurate than the data that was not stationary first.

The impact of temporal variability in light-climate on time-averaged primary production and a phytoplankton bloom in a well-mixed estuary

Phytoplankton primary production (PP) in turbid estuaries is often limited by light-availability. Two important factors altering light-climate are solar irradiance at the water surface and exponential light-extinction coefficient within the water column. Additionally, the depth of the water body changes the light-climate and corresponding PP by altering the ratio of the euphotic and mixing depth in a well-mixed estuary. These three parameters are highly variable yet are often assumed to be constant by both experimental scientists and modelers because of a lack of data or to reduce complexity. Because assuming constant parameters introduces an error, we utilize an idealized model of depth-integrated primary production to analyze the (individual) impact of temporal variability in these three parameters. We only consider the main tidal and solar constituents in temporal variability of the forcings and apply a second-order moment approximation to analyze the bias introduced to time-averaged PP estimates by neglecting temporal fluctuations. We demonstrate that the sign and magnitude of this bias are system-specific and depend on two non-dimensional parameters that characterize the system. The first is equivalent to the ratio of mixing and photic depth. The second accounts for typical incident irradiance and the photosynthetic parameters of the phytoplankton population present. To demonstrate the applicability of our approach, we apply the model to two cases in the Scheldt estuary (Belgium) in the brackish and freshwater part. In the first application, we study the impact of fluctuations on phytoplankton in dynamic equilibrium, where biomass is assumed to be constant. We show that variability in solar irradiance has the largest impact on time-averaged PP in dynamic equilibrium, resulting in a 30 percent decrease compared to time-invariant forcing. By comparing with a numerical integrator, we show that a second-order moment approximation correctly predicts the order of magnitude of the impact of temporal variability of the individual parameters. In the second application, we study the impact of fluctuations on unbounded exponential phytoplankton growth. Also here, fluctuations in solar irradiance have the largest impact and lead to a significant decrease in exponential growth. In this case study, we show that temporal fluctuations delay the onset of the biomass by two weeks and decrease the biomass by a factor 14 after two weeks compared to time invariant forcing. Additionally, we show that the temporal fluctuations induce low-frequency variability in phytoplankton biomass with similar periodicity as the spring-neap cycle, making it difficult to observe these phenomena in real-world time series.

Detection of Extreme Phenomena in the Stable Boundary Layer over the Amazonian Forest

We apply different methods for detection of extreme phenomena (EP) in air-turbulent time series measured in the nocturnal boundary layer above the Amazon forest. The methods used were: (a) a Morlet complex wavelet transform, which is often used in analysis of non-linear application processes. Through the use of the wavelet, it is possible to observe a phase singularity that involves a strong interaction between an extensive range of scales; (b) recurrence plot tests, which were used to identify a sudden change between different stable atmospheric states. (c) statistical analysis of early-warning signals, which verify simultaneous increases in the autocorrelation function and in the variance in the state variable; and (d) analysis of wind speed versus turbulent kinetic energy to identify different turbulent regimes in the stable boundary layer. We found it is adequate to use a threshold to classify the cases of strong turbulence regime, as a result of the occurrence of EP in the tropical atmosphere. All methods used corroborate and indicate synergy between events that culminate in what we classify as EP of the stable boundary layer above the tropical forest.

Neural-based time series forecasting of loss of coolant accidents in nuclear power plants

In the last few years, deep learning in neural networks demonstrated impressive successes in the areas of computer vision, speech and image recognition, text generation, and many others. However, sensitive engineering areas such as nuclear engineering benefited less from these efficient techniques. In this work, deep learning expert systems are utilized to model and predict time series progression of a design-basis nuclear accident, featuring a loss of coolant accident. Two major findings are accomplished in this work. First, the ability to train expert systems with high accuracy, which could help nuclear power plant operators to figure out plant responses during the accident. Second, building fast, efficient, and accurate deep models to simulate nuclear phenomena, which could be valuable to nuclear computational science. In this work, large amount of time series data is obtained from simulation tools by simulating different conditions of the base-case/nominal accident scenario. Four critical outputs/responses are monitored during the accident (e.g. temperature, pressure, break flow rate, water level). Two approaches are adopted in this work. The first approach is to use feedforward deep neural networks (DNN) to fit all time steps and outputs in a single model. The second approach is to use long short-term memory (LSTM) to fit all time steps together for each reactor response separately. Both DNN and LSTM demonstrate very good performance in predicting the test and base-case scenarios, with accuracy as low as 92% and as high as 99%, where these test scenarios are unknown to the expert systems and are not included in the model training. In addition, both approaches demonstrate a significant reduction in computational costs, as the deep expert system is able to accurately predict the accident 100,000 times faster than the original simulation tool. Given sufficient data, the methodology adopted in this study demonstrates that DNN/LSTM expert systems can be used as a decision support system to model advanced time series phenomena within nuclear power plants with high accuracy and negligible computational costs.

Прогнозирование суточных цен на ОРЭМ РФ с помощью модели ARFIMA

The long memory phenomenon in time series of daily spot prices in the Russian electricity market is investigated. The forecasting performance of the ARFIMA model is assessed by cross-validation. The empirical results confirmed the presence of long memory in electricity prices and the best prediction accuracy of the ARFIMA model.

Testing Day of the Week Effect on Precious Metals Market

Market efficiency assumes that asset prices should be characterized by randomness and unpredictability, so that potential market participants are not able to generate above-average profits. This means that there should be no seasonal phenomenon in time series, which clearly projects a certain pattern of behavior of financial assets. The paper is an attempts to verify some specific seasonal effect called “the day of the week” on the precious metals market. The selection of this area is not accidental. Precious metals are an alternative to classic capital investments, especially in the case of financial and economic crises. In addition, the literature shows a gap in this area in terms of dynamics analysis on commodity markets, if compared to capital market. The analysis of day of the week effect was carried out taking into account both conditional mean and conditional variance. Results are not clear and strongly depends on the type of precious metal.

Evaluating an animated and static time series map of District Six: A visual and cognitive approach

Visualization of spatial information is an important aspect in the representation of map displays. Maps today are visually adapted to a variety of mediums in displaying spatial information temporally and as time series phenomena. GIS technology has incorporated tools for analysing these spatio-temporal trends. However map users are overwhelmed by the amount of information in these map displays and therefore experience cognitive overload. In this study we find that static and animated maps have their respective advantages in the visualization of the map reader by placing participants through a structured set of questions. All these facets exist in the visual and cognitive realm of the map reader. District Six is a unique area that has experienced significant spatial change in the last century, mainly attributed to its political history. This has been depicted in a conventional static and animated time series map representation which has been designed to facilitate the understanding of the spatial change that occurred during this unique period of history. In this paper a methodology has been investigated and implemented in the design of the map, by enhancing the map reader’s experience in visualising time series spatial data. We conclude further that visual intention and attention are cognitive facets that collectively strengthen the map reader’s ability in learning spatial information.

Localization in covariance matrices of coupled heterogenous Ornstein-Uhlenbeck processes.

We define a random-matrix ensemble given by the infinite-time covariance matrices of Ornstein-Uhlenbeck processes at different temperatures coupled by a Gaussian symmetric matrix. The spectral properties of this ensemble are shown to be in qualitative agreement with some stylized facts of financial markets. Through the presented model formulas are given for the analysis of heterogeneous time series. Furthermore evidence for a localization transition in eigenvectors related to small and large eigenvalues in cross-correlations analysis of this model is found, and a simple explanation of localization phenomena in financial time series is provided. Finally we identify both in our model and in real financial data an inverted-bell effect in correlation between localized components and their local temperature: high- and low-temperature components are the most localized ones.

On the multifractal effects generated by monofractal signals

We study quantitatively the level of false multifractal signal one may encounter while analyzing multifractal phenomena in time series within multifractal detrended fluctuation analysis (MF-DFA). The investigated effect appears as a result of finite length of used data series and is additionally amplified by the long-term memory the data eventually may contain. We provide the detailed quantitative description of such apparent multifractal background signal as a threshold in spread of generalized Hurst exponent values Δh or a threshold in the width of multifractal spectrum Δα below which multifractal properties of the system are only apparent, i.e. do not exist, despite Δα≠0 or Δh≠0. We find this effect quite important for shorter or persistent series and we argue it is linear with respect to autocorrelation exponent γ. Its strength decays according to power law with respect to the length of time series. The influence of basic linear and nonlinear transformations applied to initial data in finite time series with various levels of long memory is also investigated. This provides additional set of semi-analytical results. The obtained formulas are significant in any interdisciplinary application of multifractality, including physics, financial data analysis or physiology, because they allow to separate the ‘true’ multifractal phenomena from the apparent (artificial) multifractal effects. They should be a helpful tool of the first choice to decide whether we do in particular case with the signal with real multiscaling properties or not.

Capturing the Zero: A New Class of Zero-Augmented Distributions and Multiplicative Error Processes

We propose a novel approach to model serially dependent positive-valued variables which realize a non-trivial proportion of zero outcomes. This is a typical phenomenon in financial time series observed at high frequencies, such as cumulated trading volumes. We introduce a flexible point-mass mixture distribution and develop a semiparametric specification test explicitly tailored for such distributions. Moreover, we propose a new type of multiplicative error model based on a zero-augmented distribution, which incorporates an autoregressive binary choice component and thus captures the (potentially different) dynamics of both zero occurrences and of strictly positive realizations. Applying the proposed model to high-frequency cumulated trading volumes of both liquid and illiquid NYSE stocks, we show that the model captures the dynamic and distributional properties of the data well and is able to correctly predict future distributions. Copyright The Author, 2013. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com, Oxford University Press.

Trending time-varying coefficient market models

In this paper we study time-varying coefficient (beta coefficient) models with a time trend function to characterize the nonlinear, non-stationary and trending phenomenon in time series and to explain the behavior of asset returns. The general local polynomial method is developed to estimate the time trend and coefficient functions. More importantly, a graphical tool, the plot of the kth-order derivative of the parameter versus time, is proposed to select the proper order of the local polynomial so that the best estimate can be obtained. Finally, we conduct Monte Carlo experiments and a real data analysis to examine the finite sample performance of the proposed modeling procedure and compare it with the Nadaraya–Watson method as well as the local linear method.

Development of an Open-Source Toolbox for the Analysis and Visualization of Remotely Sensed Time Series

The GEONETCast data-dissemination system delivers free multi-source raw satellite images and processed products to users worldwide; from these data, users can construct long time series to study dynamic phenomena. To explore these dynamics, using an animation with few controls is common practice. But animations easily produce information overload leading to change blindness, a problem that can be addressed in various ways. We present a combination of analytical and visual functionalities to better support visual exploration of animated time series. Analytical pre-processing functions include slicing and tracking of objects of interest. Results of the slicing and the tracking are input to the visualization environment, which is further enriched by tools to make various time, attribute, and area selections and by options to visually enhance selections relative to their surroundings, visualize the path of moving objects, and multiple layers. The resulting toolbox is dedicated to visual exploration and analysis of dynamic phenomena in time series. A case study demonstrates, with a use scenario, how it works. Early exposure of some visualization functions to users has already led to improvements, but more extensive testing will follow after further enrichment of the toolbox. Directions of future research are described.

Capturing the Zero: A New Class of Zero-Augmented Distributions and Multiplicative Error Processes

We propose a novel approach to model serially dependent positive-valued variables which realize a non-trivial proportion of zero outcomes. This is a typical phenomenon in financial time series observed at high frequencies, such as cumulated trading volumes. We introduce a flexible point-mass mixture distribution and develop a semiparametric specification test explicitly tailored for such distributions. Moreover, we propose a new type of multiplicative error model (MEM) based on a zero-augmented distribution, which incorporates an autoregressive binary choice component and thus captures the (potentially different) dynamics of both zero occurrences and of strictly positive realizations. Applying the proposed model to high-frequency cumulated trading volumes of both liquid and illiquid NYSE stocks, we show that the model captures the dynamic and distributional properties of the data well and is able to correctly predict future distributions.