Nonstationary Stochastic Modelling of Multivariate Long-Term Wind and Wave Data

2005 ◽  
Author(s):  
Christos N. Stefanakos ◽  
Konstandinos A. Belibassakis
Keyword(s):  
Time Series ◽  
Standard Deviation ◽  
Multivariate Time Series ◽  
Stochastic Modelling ◽  
Mean Value ◽  
Wave Data ◽  
Available Information ◽  
Periodic Components ◽  
Box Cox Transformation

In the present work, a nonstationary stochastic model, which is suitable for the analysis and simulation of multivariate time series of wind and wave data, is being presented and validated. This model belongs to the class of periodically correlated stochastic processes with yearly periodic mean value and standard deviation (periodically correlated or cyclostationary stochastic process). First, the time series is appropriately transformed to become Gaussian using the Box-Cox transformation. Then, the series is decomposed, using an appropriate seasonal standardization procedure, to a periodic (deterministic) mean value and a (stochastic) residual time series multiplied by a periodic (deterministic) standard deviation. The periodic components are estimated using appropriate time series of monthly data. The residual stochastic part, which is proved to be stationary, is modelled as a VARMA process. This way the initial process can be given the structure of a multivariate periodically correlated process. The present methodology permits a reliable reproduction of available information about wind and wave conditions, which is required for a number of applications.

The Long-Term Wind and Wave Spectra of the Mediterranean Sea

2005 ◽  
Author(s):  
Christos N. Stefanakos
Keyword(s):  
Time Series ◽  
Standard Deviation ◽  
Stochastic Processes ◽  
Mediterranean Sea ◽  
Mean Value ◽  
Residual Time ◽  
Wave Data ◽  
The Mediterranean ◽  
Periodic Components

It is a well-known fact that long-term time series of wind and wave data are modelled as nonstationary stochastic processes with yearly periodic mean value and standard deviation (periodically correlated or cyclostationary stochastic processes). Using this model, the initial nonstationary series are decomposed to a seasonal (periodic) mean value m(t) and a residual time series W(t) multiplied by a seasonal (periodic) standard deviation s(t), of the form Y(t) = m(t) + s(t)W(t). The periodic components m(t) and s(t) are estimated using mean monthly values, and the residual time series W(t) is examined for stationarity. For this purpose, spectral densities of W(t) are obtained from different seasonal segments, calculated and compared with each other. It is shown that W(t) can indeed be considered stationary, and thus Y(t) can be considered periodically correlated. This analysis has been applied to model wind and wave data from several locations in the Mediterranean Sea. It turns out that the spectrum of W(t) is very weakly dependent on the site, a fact that might be useful for the geographic parameterization of wind and wave climate.

scholarly journals Estimación Espectral de Series de Tiempo de Absorbancia Uv-Vis para el Monitoreo de Calidad de Aguas

Ingeniería ◽  
2017 ◽  
Vol 22 (2) ◽  
pp. 211
Author(s):  
Leonardo Plazas-Nossa ◽  
Miguel Antonio Ávila Angulo ◽  
Andres Torres
Keyword(s):  
Time Series ◽  
Fourier Transform ◽  
Multivariate Time Series ◽  
Treatment Plant ◽  
Visible Range ◽  
Wide Sense ◽  
Sample Number ◽  
San Fernando ◽  
Study Sites ◽  
Box Cox Transformation

Context: Signals recorded as multivariate time series by UV-Vis absorbance captors installed in urban sewer systems, can be non-stationary, yielding complications in the analysis of water quality monitoring. This work proposes to perform spectral estimation using the Box-Cox transformation and differentiation in order to obtain stationary multivariate time series in a wide sense. Additionally, Principal Component Analysis (PCA) is applied to reduce their dimensionality.Method: Three different UV-Vis absorbance time series for different Colombian locations were studied: (i) El-Salitre Wastewater Treatment Plant (WWTP) in Bogotá; (ii) Gibraltar Pumping Station (GPS) in Bogotá; and (iii) San-Fernando WWTP in Itagüí. Each UV-Vis absorbance time series had equal sample number (5705). The esti-mation of the spectral power density is obtained using the average of modified periodograms with rectangular window and an overlap of 50%, with the 20 most important harmonics from the Discrete Fourier Transform (DFT) and Inverse Fast Fourier Transform (IFFT).Results: Absorbance time series dimensionality reduction using PCA, resulted in 6, 8 and 7 principal components for each study site respectively, altogether explaining more than 97% of their variability. Values of differences below 30% for the UV range were obtained for the three study sites, while for the visible range the maximum differences obtained were: (i) 35% for El-Salitre WWTP; (ii) 61% for GPS; and (iii) 75% for San-Fernando WWTP.Conclusions: The Box-Cox transformation and the differentiation process applied to the UV-Vis absorbance time series for the study sites (El-Salitre, GPS and San-Fernando), allowed to reduce variance and to eliminate ten-dency of the time series. A pre-processing of UV-Vis absorbance time series is recommended to detect and remove outliers and then apply the proposed process for spectral estimation.Language: Spanish.

scholarly journals A Multivariate Forecasting Model for the COVID-19 Hospital Census Based on Local Infection Incidence

2021 ◽  
Author(s):  
Hieu M. Nguyen ◽  
Philip Turk ◽  
Andrew McWilliams
Keyword(s):  
Time Series ◽  
Multivariate Time Series ◽  
Healthcare Systems ◽  
Leading Indicators ◽  
Short Term ◽  
Correction Model ◽  
Vector Error Correction ◽  
Infection Incidence ◽  
Vector Error

AbstractCOVID-19 has been one of the most serious global health crises in world history. During the pandemic, healthcare systems require accurate forecasts for key resources to guide preparation for patient surges. Fore-casting the COVID-19 hospital census is among the most important planning decisions to ensure adequate staffing, number of beds, intensive care units, and vital equipment. In the literature, only a few papers have approached this problem from a multivariate time-series approach incorporating leading indicators for the hospital census. In this paper, we propose to use a leading indicator, the local COVID-19 infection incidence, together with the COVID-19 hospital census in a multivariate framework using a Vector Error Correction model (VECM) and aim to forecast the COVID-19 hospital census for the next 7 days. The model is also applied to produce scenario-based 60-day forecasts based on different trajectories of the pandemic. With several hypothesis tests and model diagnostics, we confirm that the two time-series have a cointegration relationship, which serves as an important predictor. Other diagnostics demonstrate the goodness-of-fit of the model. Using time-series cross-validation, we can estimate the out-of-sample Mean Absolute Percentage Error (MAPE). The model has a median MAPE of 5.9%, which is lower than the 6.6% median MAPE from a univariate Autoregressive Integrated Moving Average model. In the application of scenario-based long-term forecasting, future census exhibits concave trajectories with peaks lagging 2-3 weeks later than the peak infection incidence. Our findings show that the local COVID-19 infection incidence can be successfully in-corporated into a VECM with the COVID-19 hospital census to improve upon existing forecast models, and to deliver accurate short-term forecasts and realistic scenario-based long-term trajectories to help healthcare systems leaders in their decision making.Author summaryDuring the COVID-19 pandemic, healthcare systems need to have adequate resources to accommodate demand from COVID-19 cases. One of the most important metrics for planning is the COVID-19 hospital census. Only a few papers make use of leading indicators within multivariate time-series models for this problem. We incorporated a leading indicator, the local COVID-19 infection incidence, together with the COVID-19 hospital census in a multivariate framework called the Vector Error Correction model to make 7-day-ahead forecasts. This model is also applied to produce 60-day scenario forecasts based on different trajectories of the pandemic. We find that the two time-series have a stable long-run relationship. The model has a good fit to the data and good forecast performance in comparison with a more traditional model using the census data alone. When applied to different 60-day scenarios of the pandemic, the census forecasts show concave trajectories that peak 2-3 weeks later than the infection incidence. Our paper presents this new model for accurate short-term forecasts and realistic scenario-based long-term forecasts of the COVID-19 hospital census to help healthcare systems in their decision making. Our findings suggest using the local COVID-19 infection incidence data can improve and extend more traditional forecasting models.

scholarly journals A pragmatic re-engineering approach to extend short observation time series by climate anomaly gridding

2021 ◽  
Author(s):  
Ole Einar Tveito
Keyword(s):  
Time Series ◽  
Mean Value ◽  
Observation Time ◽  
Data Series ◽  
Climate Anomaly ◽  
Data Set ◽  
Actual Problem ◽  
Climate Gradients ◽  
Observation Series

<p>For many purposes, including the estimation of climate normals, requires long, continuous  and preferably homogeneous time series. Many observation series do not meet these requirements, especially due to modernisation and automation of the observation network. Despite the lack of long series there is still a need to provide climate parameters representing a longer time period than available. An actual problem is the calculation of new standard climate normals for the 1991-2020 period, where normal values need to be assigned also for observation series not meeting the requirements of WMO to estimate climate normals from observations. </p><p>One possible approach to estimate monthly time series is to extract value from gridded climate anomaly fields. In this study this approach is applied to complete time series that will be the basis for calculation of long term reference values.</p><p>The calculation of the long term time series is a two step procedure. First monthly anomaly grids based on homogenised data series are produced. The homogenized series provide more stable and reliable spatial estimates than applying non homogenised data. The homogenised data set is also complete ensuring a spatially consistent input throughout the analysis period 1991-2020.</p><p>The monthly anomalies for the location of the series to be complete are extracted from the gridded fields. By combining the interpolated anomalies with the observations the long term mean value can be estimated. The study shows that this approach provides reliable estimates of long term values, even with just a few events for calibration. The precision of the estimates depend more on the representativity of the grid estimates than length of the observation series. At locations where the anomaly grids represent the spatial climate variability well, stable estimates are achieved. On the other hand will the estimates at locations where the anomaly grids are less accurate due to sparse data coverage or steep climate gradients lead to estimates with a larger variability, and  thus more uncertain estimates. </p>

Exploring long-term urban cycles with multivariate time-series analysis

2021 ◽  
pp. 239980832110581
Author(s):  
Luca Salvati
Keyword(s):  
Time Series ◽  
Life Cycle ◽  
Time Series Analysis ◽  
Population Growth ◽  
Multivariate Time Series ◽  
Metropolitan Region ◽  
Series Analysis ◽  
Multivariate Time Series Analysis ◽  
Non Linear

European cities underwent long-term socioeconomic transformations resulting in a shift from centralized demographic growth typical of late industrialization to a more recent (and spatially uncoordinated) de-concentration of population and economic activities. While abandoning traditional compact models and moving toward settlement dispersion, population growth in urban areas was assumed to follow a “life cycle” constituted of four developmental stages (urbanization, suburbanization, counter-urbanization, and re-urbanization). We studied anomalies in the City Life Cycle (CLC) of a large metropolitan region (Athens, Greece) with the aim at achieving a less mechanistic interpretation of long-term population growth in complex social contexts. Using population data that cover more than 170 years (1848–2020) and multivariate time-series analysis, a non-linear growth history was delineated, with sequential accelerations and decelerations characteristic of the first CLC stage (urbanization). Considering the classical division in three radio-centric districts (core, ring, and agglomeration), different development stages coexisted since World War II. Heterogeneous suburbanization processes mixed up with late urbanization and weaker impulses of counter-urbanization and re-urbanization. The empirical results of time-series analysis confirm the non-linear expansion of Athens, shedding further light on long-term mechanisms of metropolitan development and informing management policies of urban growth.

Application of Fuzzy Time Series Techniques in Wind and Wave Data Forecasting

2014 ◽  
Author(s):  
Christos N. Stefanakos ◽  
Orestis Schinas ◽  
Grim Eidnes
Keyword(s):  
Time Series ◽  
Stock Prices ◽  
Mean Squared Error ◽  
Offshore Structures ◽  
Fuzzy Time Series ◽  
Great Success ◽  
Peak Period ◽  
Wave Data ◽  
Forecasting Performance

This work explores the applicability of widely known fuzzy time series forecasting techniques for the prediction of wind and wave data. These techniques have extensively been used with great success to the forecasting of stock prices. In the present work, long-term time series of wind speed, significant wave height, and peak period are examined and used for the verification of the forecasting performance of the fuzzy models. To examine the forecasting accuracy, the root mean squared error (RMSE) is used as an evaluation criterion to compare the forecasting performance of the listing models. As the importance of quality of wind and wave data increases, effective forecasting could further benefit designers of offshore structures and environmental researchers.

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