scholarly journals Time-Delay Identification Using Multiscale Ordinal Quantifiers

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 969
Author(s):  
Miguel C. Soriano ◽  
Luciano Zunino

Time-delayed interactions naturally appear in a multitude of real-world systems due to the finite propagation speed of physical quantities. Often, the time scales of the interactions are unknown to an external observer and need to be inferred from time series of observed data. We explore, in this work, the properties of several ordinal-based quantifiers for the identification of time-delays from time series. To that end, we generate artificial time series of stochastic and deterministic time-delay models. We find that the presence of a nonlinearity in the generating model has consequences for the distribution of ordinal patterns and, consequently, on the delay-identification qualities of the quantifiers. Here, we put forward a novel ordinal-based quantifier that is particularly sensitive to nonlinearities in the generating model and compare it with previously-defined quantifiers. We conclude from our analysis on artificially generated data that the proper identification of the presence of a time-delay and its precise value from time series benefits from the complementary use of ordinal-based quantifiers and the standard autocorrelation function. We further validate these tools with a practical example on real-world data originating from the North Atlantic Oscillation weather phenomenon.

2012 ◽  
Vol 16 (5) ◽  
pp. 1389-1399 ◽  
Author(s):  
P. De Vita ◽  
V. Allocca ◽  
F. Manna ◽  
S. Fabbrocino

Abstract. Thus far, studies on climate change have focused mainly on the variability of the atmospheric and surface components of the hydrologic cycle, investigating the impact of this variability on the environment, especially with respect to the risks of desertification, droughts and floods. Conversely, the impacts of climate change on the recharge of aquifers and on the variability of groundwater flow have been less investigated, especially in Mediterranean karst areas whose water supply systems depend heavily upon groundwater exploitation. In this paper, long-term climatic variability and its influence on groundwater recharge were analysed by examining decadal patterns of precipitation, air temperature and spring discharges in the Campania region (southern Italy), coupled with the North Atlantic Oscillation (NAO). The time series of precipitation and air temperature were gathered over 90 yr, from 1921 to 2010, using 18 rain gauges and 9 air temperature stations with the most continuous functioning. The time series of the winter NAO index and of the discharges of 3 karst springs, selected from those feeding the major aqueducts systems, were collected for the same period. Regional normalised indexes of the precipitation, air temperature and karst spring discharges were calculated, and different methods were applied to analyse the related time series, including long-term trend analysis using smoothing numerical techniques, cross-correlation and Fourier analysis. The investigation of the normalised indexes highlighted the existence of long-term complex periodicities, from 2 to more than 30 yr, with differences in average values of up to approximately ±30% for precipitation and karst spring discharges, which were both strongly correlated with the winter NAO index. Although the effects of the North Atlantic Oscillation (NAO) had already been demonstrated in the long-term precipitation and streamflow patterns of different European countries and Mediterranean areas, the results of this study allow for the establishment of a link between a large-scale atmospheric cycle and the groundwater recharge of carbonate karst aquifers. Consequently, the winter NAO index could also be considered as a proxy to forecast the decadal variability of groundwater flow in Mediterranean karst areas.


2015 ◽  
Vol 15 (3) ◽  
pp. 571-585 ◽  
Author(s):  
E. E. Moreira ◽  
D. S. Martins ◽  
L. S. Pereira

Abstract. In this study, drought in Portugal was assessed using 74 time series of Standardized Precipitation Index (SPI) with a 12-month timescale and 66 years length. A clustering analysis on the SPI Principal Components loadings was performed in order to find regions where SPI drought characteristics are similar. A Fourier analysis was then applied to the SPI time series considering one SPI value per year relative to every month. The analysis focused on the December SPI time series grouped in each of the three identified clusters to investigate the existence of cycles that could be related to the return periods of droughts. The most frequent significant cycles in each of the three clusters were identified and analysed for December and the other months. Results for December show that drought periodicities vary among the three clusters, pointing to a 6-year cycle across the country and a 9.4-year cycle in central and southern Portugal. Both these cycles likely show the influence of the North Atlantic Oscillation (NAO) on the occurrence and severity of droughts in Portugal. Relative to other months it was observed that cycles varied according to the common occurrence of precipitation: for the rainy months – November, December and January – cycles are similar to those for December; for the dry months – May to September – where the lack of precipitation masks the occurrence of drought, the dominant cycles are of short duration and cannot be related to the NAO or other large circulation indices to explain drought variability; for the transition months – February, March, April and October – 6-year and 3-year cycles were identified, the latter being more strongly apparent in central and southern Portugal. NAO influence is again identified relative to the 6-year cycles. The short cycles are apparently associated with positive SPI, thus with wetness, not drought. Overall, results confirm the importance of the NAO as a driving force for dry and wet periods.


2011 ◽  
Vol 7 (3) ◽  
pp. 987-999 ◽  
Author(s):  
A. Koutsodendris ◽  
A. Brauer ◽  
H. Pälike ◽  
U. C. Müller ◽  
P. Dulski ◽  
...  

Abstract. To unravel the short-term climate variability during Marine Isotope Stage (MIS) 11, which represents a close analogue to the Holocene with regard to orbital boundary conditions, we performed microfacies and time series analyses on a ~3200-yr-long record of annually laminated Holsteinian lake sediments from Dethlingen, northern Germany. These biogenic varves comprise two sub-layers: a light sub-layer, which is controlled by spring/summer diatom blooms, and a dark sub-layer consisting mainly of amorphous organic matter and fragmented diatom frustules deposited during autumn/winter. Time series analyses were performed on the thickness of the light and dark sub-layers. Signals exceeding the 95% and 99% confidence levels occur at periods that are near-identical to those known from modern instrumental data and Holocene palaeoclimatic records. Spectral peaks at periods of 90, 25, and 10.5 yr are likely associated with the 88-, 22- and 11-yr solar cycles, respectively. This variability is mainly expressed in the light sub-layer spectra, suggesting solar influence on the palaeoproductivity of the lake. Significant signals at periods between 3 and 5 yr and at ∼6 yr are strongest expressed in the dark sub-layer spectra and may reflect an influence of the El Niño-Southern Oscillation (ENSO) and the North Atlantic Oscillation (NAO) during autumn/winter. Our results suggest that solar forcing and ENSO/NAO-like variability influenced central European climate during MIS 11 similarly to the present interglacial, thus demonstrating the comparability of the two interglacial periods at sub-decadal to decadal timescales.


2003 ◽  
Vol 60 (5) ◽  
pp. 542-552 ◽  
Author(s):  
A F Zuur ◽  
I D Tuck ◽  
N Bailey

Dynamic factor analysis (DFA) is a technique used to detect common patterns in a set of time series and relationships between these series and explanatory variables. Although DFA is used widely in econometric and psychological fields, it has not been used in fisheries and aquatic sciences to the best of our knowledge. To make the technique more widely accessible, an introductory guide for DFA, at an intermediate level, is presented in this paper. A case study is presented. The analysis of 13 landings-per-unit-effort series for Nephrops around northern Europe identified three common trends for 12 of the series, with one series being poorly fitted, but no relationships with the North Atlantic Oscillation (NAO) or sea surface temperature were found. The 12 series could be divided into six groups based on factor loadings from the three trends.


2018 ◽  
Vol 24 (3) ◽  
pp. 984-1003 ◽  
Author(s):  
Aistis RAUDYS ◽  
Židrina PABARŠKAITĖ

Smoothing time series allows removing noise. Moving averages are used in finance to smooth stock price series and forecast trend direction. We propose optimised custom moving average that is the most suitable for stock time series smoothing. Suitability criteria are defined by smoothness and accuracy. Previous research focused only on one of the two criteria in isolation. We define this as multi-criteria Pareto optimisation problem and compare the proposed method to the five most popular moving average methods on synthetic and real world stock data. The comparison was performed using unseen data. The new method outperforms other methods in 99.5% of cases on synthetic and in 91% on real world data. The method allows better time series smoothing with the same level of accuracy as traditional methods, or better accuracy with the same smoothness. Weights optimised on one stock are very similar to weights optimised for any other stock and can be used interchangeably. Traders can use the new method to detect trends earlier and increase the profitability of their strategies. The concept is also applicable to sensors, weather forecasting, and traffic prediction where both the smoothness and accuracy of the filtered signal are important.


Author(s):  
Thomas Önskog ◽  
Christian L. E. Franzke ◽  
Abdel Hannachi

Abstract. The North Atlantic Oscillation (NAO) is the dominant mode of climate variability over the North Atlantic basin and has a significant impact on seasonal climate and surface weather conditions. This is the result of complex and nonlinear interactions between many spatio-temporal scales. Here, the authors study a number of linear and nonlinear models for a station-based time series of the daily winter NAO index. It is found that nonlinear autoregressive models, including both short and long lags, perform excellently in reproducing the characteristic statistical properties of the NAO, such as skewness and fat tails of the distribution, and the different timescales of the two phases. As a spin-off of the modelling procedure, we can deduce that the interannual dependence of the NAO mostly affects the positive phase, and that timescales of 1 to 3 weeks are more dominant for the negative phase. Furthermore, the statistical properties of the model make it useful for the generation of realistic climate noise.


2011 ◽  
Vol 8 (6) ◽  
pp. 11233-11275
Author(s):  
P. De Vita ◽  
V. Allocca ◽  
F. Manna ◽  
S. Fabbrocino

Abstract. Climate change is one of the issues most debated by the scientific community with a special focus to the combined effects of anthropogenic modifications of the atmosphere and the natural climatic cycles. Various scenarios have been formulated in order to forecast the global atmospheric circulation and consequently the variability of the global distribution of air temperature and rainfall. The effects of climate change have been analysed with respect to the risks of desertification, droughts and floods, remaining mainly limited to the atmospheric and surface components of the hydrologic cycle. Consequently the impact of the climate change on the recharge of regional aquifers and on the groundwater circulation is still a challenging topic especially in those areas whose aqueduct systems depend basically on springs or wells, such as the Campania region (Southern Italy). In order to analyse the long-term climatic variability and its influence on groundwater circulation, we analysed decadal patterns of precipitation, air temperature and spring discharges in the Campania region (Southern Italy), coupled with the North Atlantic Oscillation (NAO). The time series of precipitation and air temperature were gathered over 90 yr, in the period from 1921 to 2010, choosing 18 rain gauges and 9 air temperature stations among those with the most continuous functioning as well as arranged in a homogeneous spatial distribution. Moreover, for the same period, we gathered the time series of the winter NAO index (December to March mean) and of the discharges of the Sanità spring, belonging to an extended carbonate aquifer (Cervialto Mount) located in the central-eastern area of the Campania region, as well as of two other shorter time series of spring discharges. The hydrogeological features of this aquifer, its relevance due to the feeding of an important regional aqueduct system, as well as the unique availability of a long-lasting time series of spring discharges, allowed us to consider it as an ideal test site, representative of the other carbonate aquifers in the Campania region. The time series of regional normalised indexes of mean annual precipitation, mean annual air temperature and mean annual effective precipitation, as well as the time series of the normalised annual discharge index were calculated. Different methods were applied to analyse the time series: long-term trend analysis, through smoothing numerical techniques, cross-correlation and Fourier analysis. The investigation of the normalised indexes has highlighted long-term complex periodicities, strongly correlated with the winter NAO index. Moreover, we also found robust correlations among precipitation indexes and the annual discharge index, as well as between the latter and the NAO index itself. Although the effects of the North Atlantic Oscillation had already been proved on long-term precipitation and streamflow patterns of different European countries and Mediterranean areas, the results obtained appear original because they establish a link between a large-scale atmospheric cycle and the groundwater circulation of regional aquifers. Therefore, we demonstrated that the winter NAO index can be considered as an effective proxy to forecast the decadal variability of groundwater circulation in Mediterranean areas and in estimating critical scenarios for the feeding of aqueduct systems.


2011 ◽  
Vol 68 (9) ◽  
pp. 1635-1650 ◽  
Author(s):  
P. Bradford Hubley ◽  
A. Jamie F. Gibson

We developed a Bayesian hierarchical model to estimate annual mortality of repeat-spawning Atlantic salmon, Salmo salar, that distinguishes between mortality rates and the confounding effects of consecutive-year and alternate-year repeat-spawning strategies. The model provides annual estimates of two mortality rates: mortality in the first year (Z1), a time period during which salmon are primarily in freshwater (staging, spawning, and overwintering) followed by a brief period at sea, and mortality in the second year (Z2) when salmon are predominantly at sea. When fit to data for the LaHave River (Nova Scotia, Canada) salmon population, Z1 showed an increasing trend throughout the time series, whereas Z2 also increased but in a single, stepwise manner. Once a time series of mortality rates was separated from the other life-history parameters, we were able to demonstrate how they could be used for examining the influence of environmental conditions by comparing the estimated mortality rate time series with the North Atlantic Oscillation Index (NAOI). This comparison uncovered a statistically significant correlation between the NAOI and the survival in the second year after spawning that would not have been evident had the mortality estimation model not been developed.


2020 ◽  
Author(s):  
Abdel Hannachi ◽  
Thomas Önskog ◽  
Christian Franzke

<p>The North Atlantic Oscillation (NAO) is the dominant mode of climate variability over the North Atlantic basin and has a significant impact on seasonal climate and surface weather conditions. This is the result of complex and nonlinear interactions between many spatio-temporal scales. Here, the authors study a number of linear and nonlinear models for a station-based time series of the daily winter NAO index. It is found that nonlinear autoregressive models including both short and long lags perform excellently in reproducing the characteristic statistical properties of the NAO, such as skewness and fat tails of the distribution and the different time scales of the two phases. As a spinoff of the modelling procedure, we are able to deduce that the interannual dependence of the NAO mostly affects the positive phase and that timescales of one to three weeks are more dominant for the negative phase. The statistical properties of the model makes it useful for the generation of realistic climate noise.</p>


2015 ◽  
Vol 26 ◽  
pp. vii99 ◽  
Author(s):  
Yu Uneno ◽  
Kei Taneishi ◽  
Masashi Kanai ◽  
Akiko Tamon ◽  
Kazuya Okamoto ◽  
...  

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