Generic Framework for Downscaling Statistical Quantities at Fine Time-Scales and Its Perspectives towards Cost-Effective Enrichment of Water Demand Records

The challenging task of generating a synthetic time series at finer temporal scales than the observed data, embeds the reconstruction of a number of essential statistical quantities at the desirable (i.e., lower) scale of interest. This paper introduces a parsimonious and general framework for the downscaling of statistical quantities based solely on available information at coarser time scales. The methodology is based on three key elements: (a) the analysis of statistics’ behaviour across multiple temporal scales; (b) the use of parametric functions to model this behaviour; and (c) the exploitation of extrapolation capabilities of the functions to downscale the associated statistical quantities at finer scales. Herein, we demonstrate the methodology using residential water demand records and focus on the downscaling of the following key quantities: variance, L-variation, L-skewness and probability of zero value (no demand; intermittency), which are typically used to parameterise a stochastic simulation model. Specifically, we downscale the above statistics down to a 1 min scale, assuming two scenarios of initial data resolution, i.e., 5 and 10 min. The evaluation of the methodology on several cases indicates that the four statistics can be well reconstructed. Going one step further, we place the downscaling methodology in a more integrated modelling framework for a cost-effective enhancement of fine-resolution records with synthetic ones, embracing the current limited availability of fine-resolution water demand measurements.

Measuring the Topological Time Irreversibility of Time Series With the Degree-Vector-Based Visibility Graph Method

Time irreversibility of a time series, which can be defined as the variance of properties under the time-reversal transformation, is a cardinal property of non-equilibrium systems and is associated with predictability in the study of financial time series. Recent pieces of literature have proposed the visibility-graph-based approaches that specifically refer to topological properties of the network mapped from a time series, with which one can quantify different degrees of time irreversibility within the sets of statistically time-asymmetric series. However, all these studies have inadequacies in capturing the time irreversibility of some important classes of time series. Here, we extend the visibility-graph-based method by introducing a degree vector associated with network nodes to represent the characteristic patterns of the index motion. The newly proposed method is parameter-free and temporally local. The validation to canonical synthetic time series, in the aspect of time (ir)reversibility, illustrates that our method can differentiate a non-Markovian additive random walk from an unbiased Markovian walk, as well as a GARCH time series from an unbiased multiplicative random walk. We further apply the method to the real-world financial time series and find that the price motions occasionally equip much higher time irreversibility than the calibrated GARCH model does.

Time Series Measurement Based on Multiscale High Order Entropy and Roughness Grain Exponents

In multiscale time series analysis, multiscale entropy provides a good framework to quantify the information of time series. Multiscale fractional high-order entropy based on roughness grain exponents (MFHER) is able to identify dynamical, scale dependent and oscillation information. In detail, MFHERcan be seen as a powerful tool to assess the complex characteristics of time series. A set of synthetic time series and an application of real world data financial series are researched. The results show that high order entropy performs well in distinguishing different time series. It has also been found fractional high order entropy is highly sensitive to parameter variation and thus provides a broad perspective to research the complexity of dynamic systems. This study gains an insight into the measurement of MFHER to demonstrate the wide applicability of entropy measures.Aiming at the complexity of network and the uncertainty of internal and external environment, this paper proposes MFHER to quantify the time series information on multiscale time scales. It is of great interests in identifying dynamical properties of nancial series. The results show that the volatility of the sequence is gradually stable when the scale is greater than four. High order entropy can identify the difference among the time series.

Stochastic Modeling of Hydroclimatic Processes Using Vine Copulas

The generation of synthetic time series is important in contemporary water sciences for their wide applicability and ability to model environmental uncertainty. Hydroclimatic variables often exhibit highly skewed distributions, intermittency (that is, alternating dry and wet intervals), and spatial and temporal dependencies that pose a particular challenge to their study. Vine copula models offer an appealing approach to generate synthetic time series because of their ability to preserve any marginal distribution while modeling a variety of probabilistic dependence structures. In this work, we focus on the stochastic modeling of hydroclimatic processes using vine copula models. We provide an approach to model intermittency by coupling Markov chains with vine copula models. Our approach preserves first-order auto- and cross-dependencies (correlation). Moreover, we present a novel framework that is able to model multiple processes simultaneously. This method is based on the coupling of temporal and spatial dependence models through repetitive sampling. The result is a parsimonious and flexible method that can adequately account for temporal and spatial dependencies. Our method is illustrated within the context of a recent reliability assessment of a historical hydraulic structure in central Mexico. Our results show that by ignoring important characteristics of probabilistic dependence that are well captured by our approach, the reliability of the structure could be severely underestimated.

A Multilayer Perceptron Model for Stochastic Synthesis

Time series analysis is a major mathematical tool in hydrology, with the moving average being the most popular model type for this purpose due to its simplicity. During the last 20 years, various studies have focused on an important statistical characteristic, namely the long-term persistence and the simultaneous statistical consistency at all timescales, when different timescales are involved in the simulation. Though these issues have been successfully addressed by various researchers, the solutions that have been suggested are mathematically advanced, which poses a challenge regarding their adoption by practitioners. In this study, a multilayer perceptron network is used to obtain synthetic daily values of rainfall. In order to develop this model, first, an appropriate set of features was selected, and then, a custom cost function was crafted to preserve the important statistical properties in the synthetic time series. This approach was applied to two locations of different climatic conditions that have a long record of daily measurements (more than 100 years for the first and more than 40 years for the second). The results indicate that the suggested methodology is capable of preserving all important statistical characteristics. The advantage of this model is that, once it has been trained, it is straightforward to apply and can be modified easily to analyze other types of hydrologic time series.

The Role of Spectral Complexity in Connectivity Estimation

The study of functional connectivity from magnetoecenphalographic (MEG) data consists of quantifying the statistical dependencies among time series describing the activity of different neural sources from the magnetic field recorded outside the scalp. This problem can be addressed by utilizing connectivity measures whose computation in the frequency domain often relies on the evaluation of the cross-power spectrum of the neural time series estimated by solving the MEG inverse problem. Recent studies have focused on the optimal determination of the cross-power spectrum in the framework of regularization theory for ill-posed inverse problems, providing indications that, rather surprisingly, the regularization process that leads to the optimal estimate of the neural activity does not lead to the optimal estimate of the corresponding functional connectivity. Along these lines, the present paper utilizes synthetic time series simulating the neural activity recorded by an MEG device to show that the regularization of the cross-power spectrum is significantly correlated with the signal-to-noise ratio of the measurements and that, as a consequence, this regularization correspondingly depends on the spectral complexity of the neural activity.

Can hydrological model identifiability be improved? Stress-testing the concept of stochastic calibration

<p>Hydrological calibrations with historical data are often deemed insufficient for deducing safe estimations about a model structure that imitates, as closely as possible, the anticipated catchment behaviour. Ιn order to address this issue, we investigate a promising strategy, using as drivers synthetic time series, which preserve the probabilistic properties and dependence structure of the observed data. The key idea is calibrating a model on the basis of synthetic rainfall-runoff data, and validating against the full observed data sample. To this aim, we employed a proof of concept on few representative catchments, by testing several lumped conceptual hydrological models with alternative parameterizations and across two time-scales, monthly and daily. Next, we attempted to reinforce the validity of the recommended methodology by employing monthly stochastic calibrations in 100 MOPEX catchments. As before, a number of different hydrological models were used, for the purpose of proving that calibration with stochastic inputs is independent of the chosen model. The results highlight that in most cases the new approach leads to stronger parameter identifiability and stable predictive capacity across different temporal windows, since the model is trained over much extended hydroclimatic conditions.</p>

Conditional Simulation of Precipitation Time Series Using Phase Annealing

<p>Precipitation is one of the main inputs for hydrological models. For design purposes observed precipitation at high temporal resolution is often not available. In this case weather generators can be used to simulate realistic precipitation. Synthetic precipitation time series are often produced directly from observed time series using the stochastic methods which are able to reproduce the properties of the observed time series. The main difference and advantage of this research is to generate time series by focusing on the specific properties of the observed time series and trying to obtain these properties indirectly by conducting through investigation on the phases and power spectra and their individual effects using the phase annealing method.</p><p>Phase annealing is mainly based on annealing the phases of precipitation time series which are obtained from Fourier transform in order to meet the desired properties. These are obtained from observed time series and defined in the objective function. The outcome is synthetic time series with altered phases while the power spectrum is kept intact yielding new precipitation time series with properties matching those of the observed time series.</p>