Testing for correlation structures in short-term variabilities with long-term trends of multivariate time series

2006 ◽  
Vol 74 (4) ◽  
Author(s):  
Tomomichi Nakamura ◽  
Yoshito Hirata ◽  
Michael Small
Keyword(s):  
Time Series ◽  
Multivariate Time Series ◽  
Short Term ◽  
Correlation Structures ◽  
Long Term Trends

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 Tensorized LSTM with Adaptive Shared Memory for Learning Trends in Multivariate Time Series

2020 ◽  
Vol 34 (02) ◽  
pp. 1395-1402
Author(s):  
Dongkuan Xu ◽  
Wei Cheng ◽  
Bo Zong ◽  
Dongjin Song ◽  
Jingchao Ni ◽  
...  
Keyword(s):  
Time Series ◽  
Shared Memory ◽  
Multivariate Time Series ◽  
Temporal Patterns ◽  
Series Data ◽  
Short Term ◽  
Trend Prediction ◽  
Multiple Variables ◽  
Parameter Sharing

The problem of learning and forecasting underlying trends in time series data arises in a variety of applications, such as traffic management, energy optimization, etc. In literature, a trend in time series is characterized by the slope and duration, and its prediction is then to forecast the two values of the subsequent trend given historical data of the time series. For this problem, existing approaches mainly deal with the case in univariate time series. However, in many real-world applications, there are multiple variables at play, and handling all of them at the same time is crucial for an accurate prediction. A natural way is to employ multi-task learning (MTL) techniques in which the trend learning of each time series is treated as a task. The key point of MTL is to learn task relatedness to achieve better parameter sharing, which however is challenging in trend prediction task. First, effectively modeling the complex temporal patterns in different tasks is hard as the temporal and spatial dimensions are entangled. Second, the relatedness among tasks may change over time. In this paper, we propose a neural network, DeepTrends, for multivariate time series trend prediction. The core module of DeepTrends is a tensorized LSTM with adaptive shared memory (TLASM). TLASM employs the tensorized LSTM to model the temporal patterns of long-term trend sequences in an MTL setting. With an adaptive shared memory, TLASM is able to learn the relatedness among tasks adaptively, based upon which it can dynamically vary degrees of parameter sharing among tasks. To further consider short-term patterns, DeepTrends utilizes a multi-task 1dCNN to learn the local time series features, and employs a task-specific sub-network to learn a mixture of long-term and short-term patterns for trend prediction. Extensive experiments on real datasets demonstrate the effectiveness of the proposed model.

scholarly journals Long-Term Data Traffic Forecasting for Network Dimensioning in LTE with Short Time Series

Electronics ◽  
2021 ◽  
Vol 10 (10) ◽  
pp. 1151
Author(s):  
Carolina Gijón ◽  
Matías Toril ◽  
Salvador Luna-Ramírez ◽  
María Luisa Marí-Altozano ◽  
José María Ruiz-Avilés
Keyword(s):  
Time Series ◽  
Deep Learning ◽  
Time Series Analysis ◽  
Data Traffic ◽  
Medium Term ◽  
Short Term ◽  
Traffic Forecasting ◽  
Series Analysis ◽  
Radio Planning

Network dimensioning is a critical task in current mobile networks, as any failure in this process leads to degraded user experience or unnecessary upgrades of network resources. For this purpose, radio planning tools often predict monthly busy-hour data traffic to detect capacity bottlenecks in advance. Supervised Learning (SL) arises as a promising solution to improve predictions obtained with legacy approaches. Previous works have shown that deep learning outperforms classical time series analysis when predicting data traffic in cellular networks in the short term (seconds/minutes) and medium term (hours/days) from long historical data series. However, long-term forecasting (several months horizon) performed in radio planning tools relies on short and noisy time series, thus requiring a separate analysis. In this work, we present the first study comparing SL and time series analysis approaches to predict monthly busy-hour data traffic on a cell basis in a live LTE network. To this end, an extensive dataset is collected, comprising data traffic per cell for a whole country during 30 months. The considered methods include Random Forest, different Neural Networks, Support Vector Regression, Seasonal Auto Regressive Integrated Moving Average and Additive Holt–Winters. Results show that SL models outperform time series approaches, while reducing data storage capacity requirements. More importantly, unlike in short-term and medium-term traffic forecasting, non-deep SL approaches are competitive with deep learning while being more computationally efficient.

scholarly journals Maps, trends, and temperature sensitivities—phenological information from and for decreasing numbers of volunteer observers

2021 ◽  
Author(s):  
Ye Yuan ◽  
Stefan Härer ◽  
Tobias Ottenheym ◽  
Gourav Misra ◽  
Alissa Lüpke ◽  
...  
Keyword(s):  
Climate Change ◽  
Time Series ◽  
Strong Decrease ◽  
Temperature Changes ◽  
Interpolation Accuracy ◽  
Observation Network ◽  
Shiny App ◽  
Long Term Trends ◽  
Autumn And Winter

AbstractPhenology serves as a major indicator of ongoing climate change. Long-term phenological observations are critically important for tracking and communicating these changes. The phenological observation network across Germany is operated by the National Meteorological Service with a major contribution from volunteering activities. However, the number of observers has strongly decreased for the last decades, possibly resulting in increasing uncertainties when extracting reliable phenological information from map interpolation. We studied uncertainties in interpolated maps from decreasing phenological records, by comparing long-term trends based on grid-based interpolated and station-wise observed time series, as well as their correlations with temperature. Interpolated maps in spring were characterized by the largest spatial variabilities across Bavaria, Germany, with respective lowest interpolated uncertainties. Long-term phenological trends for both interpolations and observations exhibited mean advances of −0.2 to −0.3 days year−1 for spring and summer, while late autumn and winter showed a delay of around 0.1 days year−1. Throughout the year, temperature sensitivities were consistently stronger for interpolated time series than observations. Such a better representation of regional phenology by interpolation was equally supported by satellite-derived phenological indices. Nevertheless, simulation of observer numbers indicated that a decline to less than 40% leads to a strong decrease in interpolation accuracy. To better understand the risk of declining phenological observations and to motivate volunteer observers, a Shiny app is proposed to visualize spatial and temporal phenological patterns across Bavaria and their links to climate change–induced temperature changes.

scholarly journals An Efficient Prediction Model for Water Discharge in Schoharie Creek, NY

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Katerina G. Tsakiri ◽  
Antonios E. Marsellos ◽  
Igor G. Zurbenko
Keyword(s):  
New York ◽  
Time Series ◽  
Water Discharge ◽  
Winter Period ◽  
Statistical Methodology ◽  
Summer Period ◽  
Short Term ◽  
Efficient Prediction ◽  
Climatic Time Series

Flooding normally occurs during periods of excessive precipitation or thawing in the winter period (ice jam). Flooding is typically accompanied by an increase in river discharge. This paper presents a statistical model for the prediction and explanation of the water discharge time series using an example from the Schoharie Creek, New York (one of the principal tributaries of the Mohawk River). It is developed with a view to wider application in similar water basins. In this study a statistical methodology for the decomposition of the time series is used. The Kolmogorov-Zurbenko filter is used for the decomposition of the hydrological and climatic time series into the seasonal and the long and the short term component. We analyze the time series of the water discharge by using a summer and a winter model. The explanation of the water discharge has been improved up to 81%. The results show that as water discharge increases in the long term then the water table replenishes, and in the seasonal term it depletes. In the short term, the groundwater drops during the winter period, and it rises during the summer period. This methodology can be applied for the prediction of the water discharge at multiple sites.

Mercury trends and cycling in northern Wisconsin related to atmospheric and hydrologic processes

2019 ◽  
Vol 76 (5) ◽  
pp. 831-846 ◽  
Author(s):  
C.J. Watras ◽  
D. Grande ◽  
A.W. Latzka ◽  
L.S. Tate
Keyword(s):  
Time Series ◽  
Water Cycle ◽  
Water Levels ◽  
Hydrologic Processes ◽  
Littoral Sediments ◽  
Long Term Trends ◽  
Acid Base Status ◽  
Explanatory Mechanism ◽  
Regional Water

Atmospheric deposition is the principal source of mercury (Hg) to remote northern landscapes, but its fate depends on multiple factors and internal feedbacks. Here we document long-term trends and cycles of Hg in the air, precipitation, surface water, and fish of northern Wisconsin that span the past three decades, and we investigate relationships to atmospheric processes and other variables, especially the regional water cycle. Consistent with declining emission inventories, there was evidence of declining trends in these time series, but the time series for Hg in some lakes and most fish were dominated by a near-decadal oscillation that tracked the regional oscillation of water levels. Concentrations of important solutes (SO4, dissolved organic carbon) and the acid–base status of lake water also tracked water levels in ways that cannot be attributed to simple dilution or concentration. The explanatory mechanism is analogous to the “reservoir effect” wherein littoral sediments are periodically exposed and reflooded, altering the internal cycles of sulfur, carbon, and mercury. These climatically driven, near-decadal oscillations confound short or sparse time series and complicate relationships among Hg emissions, deposition, and bioaccumulation.

Warming is Driving Decreases in Snow Fractions While Runoff Efficiency Remains Mostly Unchanged in Snow-Covered Areas of the Western United States

2018 ◽  
Vol 19 (5) ◽  
pp. 803-814 ◽  
Author(s):  
Gregory J. McCabe ◽  
David M. Wolock ◽  
Melissa Valentin
Keyword(s):  
United States ◽  
Time Series ◽  
Winter Precipitation ◽  
Western United States ◽  
Balance Model ◽  
Winter Temperatures ◽  
Long Term Trends ◽  
Monthly Water Balance ◽  
Surface Water Supply

Abstract Winter snowfall and accumulation is an important component of the surface water supply in the western United States. In these areas, increasing winter temperatures T associated with global warming can influence the amount of winter precipitation P that falls as snow S. In this study we examine long-term trends in the fraction of winter P that falls as S (Sfrac) for 175 hydrologic units (HUs) in snow-covered areas of the western United States for the period 1951–2014. Because S is a substantial contributor to runoff R across most of the western United States, we also examine long-term trends in water-year runoff efficiency [computed as water-year R/water-year P (Reff)] for the same 175 HUs. In that most S records are short in length, we use model-simulated S and R from a monthly water balance model. Results for Sfrac indicate long-term negative trends for most of the 175 HUs, with negative trends for 139 (~79%) of the HUs being statistically significant at a 95% confidence level (p = 0.05). Additionally, results indicate that the long-term negative trends in Sfrac have been largely driven by increases in T. In contrast, time series of Reff for the 175 HUs indicate a mix of positive and negative long-term trends, with few trends being statistically significant (at p = 0.05). Although there has been a notable shift in the timing of R to earlier in the year for most HUs, there have not been substantial decreases in water-year R for the 175 HUs.

scholarly journals COASTAL CHANGES AT BETHANY BEACH, DELAWARE

1984 ◽  
Vol 1 (19) ◽  
pp. 112 ◽  
Author(s):  
Jennifer E. Dick ◽  
Robert A. Dalrymple
Keyword(s):  
Coastal Erosion ◽  
Coastal Processes ◽  
Short Term ◽  
Winter Storms ◽  
Barrier Beach ◽  
Commercial Activities ◽  
Long Term Trends ◽  
Coastal Changes ◽  
Summer Homes

The coastal processes affecting Bethany Beach, Delaware were studied and the short-term and long-term trends in coastal changes were determined in order to develop recommendations for protecting Bethany against coastal erosion (Dick and Dalrymple, 1983). Bethany Beach is located on the Delaware Atlantic coastline which is a wide sandy baymouth barrier beach distinguished by highlands at Rehoboth Beach and Bethany Beach. The shoreline is straight, with only minor bulges and indentations (see Figure 1). Bethany Beach is a residential and resort community. Privatelyowned properties front the publicly-owned beach. Construction of new motels and summer homes is anticipated along with the continued growth of commercial activities to accommodate the increased number of visitors. Bethany is protected by a series of nine groins built between 1934 and 1945. Many of these groins have deteriorated, and are flanked at the landward end. Winter storms severely erode the beach and damage shorefront property. The beach is generally narrow (approximately 45 m wide), especially along the southern portion, and is backed by low dunes (about 15-45 m above NGVD). A timber bulkhead extends along most of the backshore.

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