Time-dependent Intrinsic Correlation Research Articles

A Spatial Correlation Identification Model for Coherent Structure Extraction and Three-Dimensional Visualization

Multi-scale coherent structures have been observed in ocean currents, which are induced by the interaction of shear flows with different velocities. Understanding the spatial configuration and scale characteristics of coherent structures will promote the explanation of physical ocean phenomena. Considering the self-similarity, we propose a spatial correlation identification model for coherent structure extraction and three-dimensional visualization based on the wavelet transform and time-dependent intrinsic correlation method. The spatial and scale distributions of coherent structures are related to the dissipation rate variation. Most large-scale coherent structures, with the largest length scale of 13 m, are found to exist in stable fluid, such as the water column below 50 m. However, small-scale structures are found in chaotic fluids, such as the upper layer. Furthermore, we found that coherent structures of different scales coexist simultaneously in the same depth range, indicating a simultaneous multi-scale structure pattern for turbulent flow investigations.

Saltwater intrusion in the Po River Delta (Italy) during drought conditions: Analyzing its spatio-temporal evolution and potential impact on agriculture

Saltwater intrusion along rivers is a complex process controlled by multiple factors and thus fluctuates with a highly nonlinear nature and time-varying characteristics. It is challenging to monitor saltwater intrusion. The objective of this study was to clarify the spatial-temporal variation of saltwater intrusion and its potential impact on agriculture in the Po River Delta (Italy). 2006 was the most severe year of saltwater intrusion in the period we considered. 2022 was even worse, but the data are still under processing. In this study, the Hilbert-Huang transform (HHT) and rescaled range (R/S) were used to identify the multi-time scales and change trends of the salinity and discharge in 2006. After that, the time-dependent intrinsic correlation (TDIC) was used to depict intrinsic relationships between salinity and discharge at different time scales. The results showed that discharge and salinity exhibited behaviours of positive long-range correlation during different periods. The temporal series of salinity and discharge was decomposed into six intrinsic mode functions (IMF) and residuals based on the ensemble empirical mode decomposition (EEMD). The sum of variance contribution rates of IMF1 (4 days), IMF2 (10 days), and IMF3 (12.1 days) of salinity was more than 75%. All measured TDICs have highlighted strong correlations between salinity and discharge. Furthermore, we used spatial interpolation techniques to map salinity data along rivers. This allowed the investigation of dynamic changes in saltwater intrusion patterns during periods of severe drought. Outcomes show a significant negative correlation between salinity and normalized difference vegetation index (NDVI), indicating that the study area's agricultural greening was affected by saltwater intrusion.

Multiscale Correlation Analysis between Wind Direction and Meteorological Parameters in Guadeloupe Archipelago

In this paper, the wind direction (WD) behaviour with respect to the variability of other meteorological parameters (i.e., rainfall (R), temperature (T), relative humidity (Rh), solar radiation (SR) and wind speed (U)) was studied in a multi-scale way. To carry out this study, the Hilbert–Huang transform (HHT) framework was applied to a Guadeloupe archipelago dataset from 2016 to 2021. Thus, the time-dependent intrinsic correlation (TDIC) analysis based on multivariate empirical mode decomposition (MEMD) was performed. For time scales between ∼3 days and ∼7 months, the localized positive and negative correlations between WD and the meteorological parameters have been identified. The alternation between these correlations was more significant for T and Rh. With regard to SR and U, there was a dominance of a negative correlation with WD. We assumed that the micro-climate previously identified in the literature for the study area plays a key role in these behaviours. A strong positive correlation between WD and R was found from ∼7 months to ∼2.5 years. At the annual scale, the relationships between WD and all meteorological parameters were long range and no significant transition in correlation was observed showing the impact of the Earth’s annual cycle on climatic variables. All these results clearly show the influence of R-T-Rh-SR-U on WD over different time scales.

Study of the Dynamical Relationships between PM2.5 and PM10 in the Caribbean Area Using a Multiscale Framework

The Caribbean basin is a geographical area with a high prevalence of asthma due to mineral dust. As such, it is crucial to analyze the dynamic behavior of particulate pollutants in this region. The aim of this study was to investigate the relationships between particulate matter with aerodynamic diameters less than or equal to 2.5 and 10 μm (PM2.5 and PM10) using Hilbert–Huang transform (HHT)-based approaches, including the time-dependent intrinsic correlation (TDIC) and time-dependent intrinsic cross-correlation (TDICC) frames. The study utilized datasets from Puerto Rico from between 2007 and 2010 to demonstrate the relationships between two primary particulate matter concentration datasets of air pollution across multiple time scales. The method first decomposes both time series using improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) to obtain the periodic scales. The Hilbert spectral analysis identified two dominant peaks at a weekly scale for both PM types. High amplitude contributions were sustained for long and continuous time periods at seasonal to intra-seasonal scales, with similar trends in spectral amplitude observed for both types of PM except for monthly and intra-seasonal scales of six months. The TDIC method was used to analyze the resulting modes with similar periodic scales, revealing the strongest and most stable correlation pattern at quarterly and annual cycles. Subsequently, lagged correlations at each time scale were analyzed using the TDICC method. For high-frequency PM10 intrinsic mode functions (IMFs) less than a seasonal scale, the value of the IMF at a given time scale was found to be dependent on multiple antecedent values of PM2.5. However, from the quarterly scale onward, the correlation pattern of the PM2.5-PM10 relationship was stable, and IMFs of PM10 at these scales could be modeled by the lag 1 IMF of PM2.5. These results demonstrate that PM2.5 and PM10 concentrations are dynamically linked during the passage of African dust storms.

Tillage-induced microtopography alters time-dependent intrinsic correlation of runoff and sediment yield

Tillage practices change microtopography and hydrological process, which significantly affects soil erosion. The objective of this study is understanding storm-driven microtopography development under different tillage practices and its effects on runoff and soil erosion. A series of simulated rainfall experiments with an intensity of 2.0 mm min−1 were implemented on three 4 m by 0.8 m soil boxes on a 15° slope with different tillage-induced microreliefs including smooth slope (SS), artificial digging (AD), and ridge tillage (RT). The Hilbert-Huang transform (HHT) was used to detect the change trends of runoff and sediment yield, and the time-dependent intrinsic correlation (TDIC) was used to depict intrinsic runoff-sediment relations. The results showed the soil roughness were SS < AD < RT during different rill erosive stages. AD and RT slopes reduced runoff by 11.5–64.5% compared with the SS slope during water erosion. AD and RT slopes also reduced sediment yield by 13.3–83.4% during interrill erosion process, but the sediment yield increased by 59.2–132.1% during rill erosion. Runoff and sediment yield had multi-scale temporal variation characteristics. Ensemble empirical mode decomposition (EEMD) was adapted to decompose the runoff and sediment yield data into different intrinsic mode functions (IMFs). For the high-frequency components (IMF1-IMF3), rougher microrelief led to increase in the periods of runoff and sediment yield, while the trend of the low-frequency components (IMF4-IMF5) was opposite to that of the high-frequency components. This phenomenon was mainly related to the spatial structure of microtopography. Tillage-induced microtopography altered the associations of runoff with sediment yield in different time scales. This study provided new insights into revealing the mechanism of tillage erosion in sloping farmland.

A multivariate EMD-LSTM model aided with Time Dependent Intrinsic Cross-Correlation for monthly rainfall prediction

Accurate prediction of rainfall is a complex problem because of the large number of controlling factors, complex interrelationships between them and the multiscaling behaviour of the process. Because of the multiscaling behaviour of the problem, the use of hybrid modelling involving decomposition techniques is preferable over strenuous physical models and standalone driven techniques for accurate rainfall predictions. This study proposes a novel hybrid modelling framework integrating Long Short Term Memory (LSTM) and Multivariate Empirical Mode Decomposition (MEMD) aided with Time Dependent Intrinsic Cross-Correlation (TDICC) analysis algorithm for monthly rainfall predictions. The application of the proposed model is demonstrated for monthly rainfall prediction of 2005–2015 period at All India spatial domain considering El-Niño Southern Oscillation(ENSO), Indian Ocean Dipole(IOD) and five antecedent values of rainfall are the input variables. The proposed framework first uses MEMD to obtain a set of orthogonal components namely Intrinsic Mode Functions (IMFs) identifying and aligning the common scales embedded in the multiple input variables considered. Subsequently, scale specific rainfall information are predicted by incorporating them on relevant IMFs and their significant lags identified through TDIC and TDICC analyses. Final aggregation of predicted rainfall components from different scales gives the monthly rainfall of a generic time step ahead. The efficacy of the proposed MEMD-TDICC-LSTM framework is compared with five other hybrid models such as MEMD-TDIC-ANN, MEMD-TDICC-ANN, MEMD-ACO-ANN, MEMD-ACO-LSTM and MEMD-TDIC-LSTM, which used Time Dependent Intrinsic Correlation (TDIC) and Ant Colony Optimization (ACO) for predictor selection and Artificial Neural Network (ANN) as modelling tool. The study has used different graphical representations and ten different statistical performance evaluation measures for the prediction of validation period, it is observed that the proposed model could achieve a predictive skill of 0.98, Nash-SutcliffeEfficiency (NSE) of 0.95 and Index of Agreement (IA) of 0.91 which is better than all the five remaining models. The capability of MEMD-TDICC-LSTM model to predict the extremes is also confirmed by using the bar graph for the drought year rainfall of 2009 and is observed that the model is successful in capturing the extremes with an annual rainfall 975.16 mm closer to observed value 927.3 mm. MEMD algorithm facilitates the inclusion of multiple large scale climatic oscillations as inputs and their multi time scale decomposition, TDICC helps to fix the relevant inputs at different time scales and the LSTM functions as the robust modelling tool. Further, the framework using this specific combination resulted in substantial reduction in modelling complexity and faster execution, as the approach considers only the most relevant and significant inputs in the process.

Multiscale analysis of the dynamic relationship between particulate matter ([formula omitted]) and meteorological parameters using CEEMDAN: A focus on “Godzilla” African dust event

This study investigates the dynamic relationship between particulate matter with less than 10μm aerodynamic diameter (PM10) and meteorological parameters (i.e., solar radiation (SR), air temperature (T), wind speed and direction (U and D), rainfall (R), relative humidity (Rh), and visibility (V)), while using time-dependent intrinsic correlation (TDIC) analysis based on complete ensemble empirical mode decomposition with adaptive noise. The TDIC analysis captured both negative and positive correlations between PM10 and the meteorological parameters at all examined time scales; nevertheless, as high PM10 concentrations were mainly related to synoptic scale sources, the correlations were more significant for a mean time period ranging from 1 to 7 d. In the high dust season (i.e., from May to September), results showed that dust outbreaks have a major impact on climate. Trends differ among meteorological parameters: At daily scale, positive (negative) correlations were found between PM10 and SR, T, U, and V (R and Rh), while correlation strength may change with increasing time scale. In addition, transition periods between the low (i.e., from October to April) and high dust season, but also before and after the passages of rainy events, were identified by the TDIC analysis. The impact of the largest African dust storm in the last 50 years on climate has also been identified locally at a time scale between 1 and 4 d, which corresponds to the duration of its passage.

Short-Term Load Forecasting and Temperature Load Extraction Based on CEEMDAN and TDIC

With the intensification of urbanization in various countries worldwide, the temperature load which is greatly affected by ambient temperature, such as summer cooling loads and winter heating loads, accounts for a rising proportion of the total urban load. It causes an increasing peak-to-valley load difference. However, due to the complex composition and strong randomness of the load, it is necessary to study the multi-scale and multi-period correlation between temperature. Based on this, the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) is used to decompose the temperature and load into multi-scale components. The time-dependent intrinsic correlation (TDIC) is proposed to analyze the local correlation between temperature and load in multiple periods under a multi-scale framework, and obtain the dynamic change characteristics of the correlation between temperature and load. Based on the TDIC analysis results, a suitable sample period for short-term load forecasting (STLF) and input temperature data can be selected. Finally, extreme learning machine optimized by particle swarm optimization (PSO-ELM) is used to forecast each component of the load. The proposed STLF method is validated on real-time data from the Pennsylvania-New Jersey-Maryland (PJM) Company in the United States. The proposed method has greatly reduced in both mean absolute percentage error (MAPE) and root mean square error (RMSE) compared with other traditional methods, and the temperature load that fluctuates with temperature in the day to be forecasted is extracted.

Correlations between crude oil and stocks prices of renewable energy and technology companies: A multiscale time-dependent analysis

The study on the dynamic relationships between crude oil, stock prices of renewable energy and technology companies has aroused increasingly interest in the literature. This work novelly proposes the application of a time-dependent intrinsic correlation (TDIC) method to investigate the interconnection by quantitatively establishing its linkage between these three markets. TDIC is a Hilbert-Huang transform-based correlation tool in which the sliding window size for running correlation calculation can be adaptively adjusted by the instantaneous period of intrinsic mode function (IMFs) with characteristic scale. The time-varying associations between the West Texas Intermediate crude oil futures, the WilderHill Clean Energy Index and the NYSE Arca Technology Index are clarified and discussed in the short, medium and long-term. The findings show that the long-term (one year and above) correlation between pairwise markets is higher than the short-term (within one week) on average, which, in turn, is greater than the medium-term. A decreasing dependence of renewable energy on crude oil particularly after European debt crisis is detected. Besides, the relatively greater connection effects of negative changes than positive changes are revealed. These results are crucial for investors and policymakers to have flexible investment portfolio and risk management strategies in energy and financial markets.

Investigation of local correlations between particulate matter ([formula omitted]) and air temperature in the Caribbean basin using Ensemble Empirical Mode Decomposition

This study investigates the relationship between particulate matter that have an aerodynamic diameter less than 10 µm diameter (PM10) and air temperature (T) in the Caribbean basin. To conduct this analysis, eleven years of daily time series recorded in Guadeloupe archipelago were used. Firstly, the stationarity threshold of both time series is quantified using the infinite moving average. Then, statistical analyses were performed using the conditional mean and the joint probability density function method. Both methods used showed a dependence between PM10 and T particularly during the high dust season, i.e. from May to September. From a dynamical point of view, the coherence function highlighted a global correlation information between PM10 and T in the frequency domain. To capture possible localized correlation information, both time series are studied in a multiscale way using a new cross-correlation technique classically based on Empirical Mode Decomposition (EMD) termed the Time-Dependent Intrinsic Correlation (TDIC) analysis. After computing EMD and Ensemble Empirical Mode Decomposition (EEMD) methods, a mode-mixing problem is detected in EMD frame. Consequently, for the first time in air pollution field, a combination of EEMD and TDIC is performed. The achieved results show that the strength and nature of association between PM10 and T vary with time scales and time spells. We found that PM10 from African and marine aerosols are strongly correlated to T respectively for large and small periodicities. One also observed that extreme weather events such as heavy rainfall, hurricanes or drought induce a strong anti-correlation.

An investigation on drought teleconnection with indian ocean dipole and el-nino southern oscillation for peninsular india using time dependent intrinsic correlation

Drought is an obscure climatic state that has socioeconomic repercussions on power generation, agricultural production, forestry, tourism and construction. In this study, an Ensemble Empirical Mode Decomposition (EEMD) based Time Dependent Intrinsic Correlation (TDIC) analysis was conducted to assess the impacts of Indian Ocean Dipole(IOD) and El Niño-Southern Oscillation (ENSO) to drought events of Peninsular region in India. Standardized Precipitation Index (SPI) at three different time scales (SPI-3, SPI-6 and SPI-12) are considered for analysis. The teleconnections IOD and ENSO on the three indices are evaluated independently using TDIC method and the detection and attribution was made from the obtained correlation plots. From the detailed analysis, short term drought (SPI-3) is found to have better correlation with both IOD and ENSO. It is also interpreted that high frequency modes of SPI-3 have more association to IOD while low frequency modes show more correlation to ENSO. Thereby, IOD experiences a lagged influence on ENSO relation to rainfall. The IMF3 and IMF7 of SPI-12 also show positive association that can be added to existing data for efficient prediction of drought events. Similarly, for ENSO IMF1, IMF6 and IMF7 of SPI-6 and IMF6 and IMF7 of SPI-12 can also be used for determining the drought accurately.

Development of a noise-assisted multivariate empirical mode decomposition framework for characterizing PM 2.5 air pollution in Taiwan and its relation to hydro-meteorological factors

To better understand air pollution problems, the relationships between PM2.5 and hydro-meteorological variables are studied using a state-of-the-art multivariate nonlinear and non-stationary filtering method, noise-assisted multivariate empirical mode decomposition (NAMEMD), and the time-dependent intrinsic correlation (TDIC) algorithm. Three characteristic scales (annual, diurnal and semi-diurnal) are shown to be significant to PM2.5 characterization, based on using NAMEMD filtering. Temporal fluctuations of local correlations among PM2.5 and hydro-meteorological variables are presented. On diurnal and semi-diurnal scales, seasonal variation of the local correlation between temperature and humidity is observed. A combined wind speed and direction analysis can be conducted using the NAMEMD-based algorithm. The pollutant roses that are generated from the reconstructed wind directions reveal the sources of PM2.5 on different scales. PM2.5 is found to be related to land breeze at the diurnal scale and to winter monsoons at the annual scale. The scale-dependent wind direction that contributes to the increase of PM2.5 can be identified.

Fine interrelation between track irregularities and vehicle responses: multi-scale time-dependent correlation analysis

Track irregularities are perhaps the main excitations of vehicle–track systems and cause dynamic wheel–rail responses, but track irregularities and vehicle responses do not always correspond to each other. In this study, the interrelations between track irregularities and vehicle responses in a multi-scale framework were investigated using measured data. Firstly, the track irregularity and vehicle response data were separated into modes on different time scales using multivariate empirical mode decomposition, and the energy distribution of each wavelength component was determined. Then, the local correlations between irregularity–response mode pairs were examined via time-dependent intrinsic correlation (TDIC) analysis. The irregularity–response interrelation was not always unique, but rather varied in both time scale and time domain, and positive–negative correlation reversals frequently occurred, causing a low overall correlation and coherence. TDIC analysis can elucidate the wavelengths and positions of track irregularities that affect vehicle responses.

Multiscale Dynamic Correlation Analysis of Wind-PV Power Station Output Based on TDIC

The stochastic characteristics of wind power and photovoltaic (PV) make the resource allocation of power system difficult. Therefore, it is necessary to consider the correlation between the power generation of wind and PV power stations to avoid resource waste and guarantee system power supply, while the traditional correlation analysis method cannot accurately describe the multiscale and time-varying characteristics of the correlation. In this article, based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), the time series of the wind and PV power generation was decomposed into multiscale components. Moreover, the time-dependent intrinsic correlation (TDIC) is introduced to excavate the local correlation of the power generation time series under the framework of a multi-time scale, the dynamic change of a correlation is captured by analyzing the TDIC plots. The analysis shows that the strength and nature of the association between wind and PV vary with time scales and time spells, reflecting rich, dynamic characteristics. The correlation variation of different scale components in local time is of great significance to power system operation, planning, and resource optimal allocation.

Vortex statistics of a cylinder wake flow close to the wall based on IB-LBM

In this paper, statistical behaviors of vortex in the wake flow of a circular cylinder placed near a plane wall in the two-dimensional (2D) channel are investigated by Immersed Boundary Lattice Boltzmann Method. Although vortices shed from the cylinder periodically, there are very complicated interactions between vortices and the solid wall. The gap ratios [Formula: see text] are considered in three cases [Formula: see text] to study vortex statistic behaviors when flow is in steady state. It can be seen that a single row of coherent structures in the same sign varies to dipole vortex shedding as [Formula: see text] increases. The results of vortex statistics by the conditional analysis, which are based on a new and accurate vortex identification criteria called Liutex, show the algebraic number density [Formula: see text], where [Formula: see text] is vortex area. The relationship between the vortex circulation [Formula: see text] and vortex area [Formula: see text] is [Formula: see text] and the one between the kinetic energy of vortex [Formula: see text] and [Formula: see text] is [Formula: see text] in the range where [Formula: see text]. Moreover, it has been found that vortices contain about 30% of the total energy of the flow which is almost conserved as Re varies by studying the energy ratio [Formula: see text] of all vortices to the entire flow field. The statistic behaviors of energy spectrums show that the spectrums contain an inertial range in which [Formula: see text] not only in the coherent structure field but also in the background field. More features of the vortex structure in the wake flow have been described by the empirical mode decomposition (EMD). There is a linear relationship between the frequency and the mode of the form [Formula: see text] e[Formula: see text] in the semi-log coordinates. The period of each mode [Formula: see text] e[Formula: see text] in the semi-log coordinates. The time-dependent intrinsic correlation (TDIC) shows that there is a strong negative correlation relationship between the pressure and the flow velocity in the complex attachment vortex.

Multiscale modelling of monthly streamflows using MEMD-GP coupled approach

ABSTRACTThis study presented multiscale characterization of monthly streamflow time series using Multivariate Empirical Mode Decomposition (MEMD) and developed an innovative approach for streamflow prediction by coupling MEMD with Genetic Programming (GP). Firstly, the possible hydro-climatic teleconnection of monthly streamflows of Mahanadi river basin in India with two large-scale climate oscillations of ElNiño Southern Oscillation (ENSO) and Equatorial Indian Ocean Oscillation (EQUINOO) is investigated by applying MEMD based Time-Dependent Intrinsic Correlation (TDIC) analysis. The TDIC analysis showed that the association between large-scale climate oscillations and streamflows is not unique always, but both the nature and strength of the association varies with time scales and over the time domain. Based on this finding, the study proposed MEMD-GP coupled approach for streamflow prediction, in which different modes corresponding to different process scales obtained by the MEMD are predicted separately using GP; and summation of these predicted modes provides the monthly streamflow at the station. A statistical performance evaluation based on multiple criteria showed that the proposed approach performs better than the multiple linear regression, M5 model tree and GP models for monthly streamflow prediction including extreme low and high flows, due to its unique capability to include the significant predictors at different time scales.

Multi-scale time dependent correlation between synchronous measurements of ground-level ozone and meteorological parameters in the Caribbean Basin

Ground-level ozone (O3) is a major air pollutant which is strongly links to weather conditions. To our knowledge, there are few analysis of O3 behavior in Caribbean region. The aim of this paper is to study the correlation between O3 and meteorological parameters (i.e., solar radiation, temperature, relative humidity and wind speed) in a multi-scale way. Firstly, we estimate their Fourier power spectra and consider their scaling properties in the physical space. The power spectra computed follows a power law behavior for all datasets. Thereafter, the multiple scale dynamics and the correlations between simultaneous measurements of O3 and meteorological parameters was analyzed using the Empirical Mode Decomposition (EMD) based methods. After EMD decomposition of each time series, we investigate their local correlations using a new cross-correlation technique termed Time Dependent Intrinsic Correlation method (TDIC). The time evolution and the scale dependence of their correlation are determined at different time scales and for different intrinsic modes functions. All measured TDICs have highlighted strong correlations between O3 and meteorological parameters. The impact of weather conditions (e.g., drought, rainfall, windy period) have been locally observed on O3 formation for all the time scales. This study shows that TDIC method is a powerful tool for perform multi-scale cross-correlation analysis in air pollution field.

Multiscale running correlation analysis of water quality datasets of Noyyal River, India, using the Hilbert–Huang Transform

This study performs the multiscale decomposition of six water quality parameters from Elunuthimangalam station in Noyyal River, a water quality hotspot in Southern India, using the complete ensemble empirical mode decomposition with adaptive noise method. Then, the intrinsic mode functions (IMFs) obtained are subjected to normalized Hilbert transform-direct quadrature-coupled framework for their time–frequency characterization. The time–frequency–amplitude spectra revealed that the dominant frequency is dynamic in characteristics and the marginal spectra successfully captured the significant high anthropogenic interventions in the form of pollutant disposals in the study area. Then, an in-depth examination of the association of different water quality parameters such as pH, temperature, dissolved oxygen (DO), biochemical oxygen demand (BOD) and total hardness (TH) with electrical conductivity (EC) is done through a running correlation method, namely time-dependent intrinsic correlation (TDIC) in which the sliding window size is adaptively fixed based on instantaneous frequencies estimated by HT. The TDIC analysis revealed that with the exception of TH, the association of water quality parameters with EC in different time scales is not alike in both nature and strength. Also the well-debated DO–temperature and DO–BOD relationships displayed diverse correlation properties in different time scales and over the time domain.

Recurrence duration statistics and time-dependent intrinsic correlation analysis of trading volumes: A study of Chinese stock indices

The trading volume in stock markets is known as an important variable which reflects the liquidity of the financial markets and therefore is regarded to be greatly important for the measurement of market liquidity risk. In this work, a new concept called recurrence duration is introduced for study of daily trading volumes, which is inspired by idea of the volatility duration that was proposed and studied in our previous work. The recurrence duration is thought as the shortest passing time that the following days’ trading volume takes to exceed or go below the current trading volume which is time-varying. Similar to the volatility duration distribution of the price returns, the power-law function could describe the empirical probability distribution of recurrence durations of trading volumes, and their tail distributions can be fitted by two stretched exponential functions. Further, the correlation relationships of trading volumes between Chinese stock indices as well as the correlations of recurrence durations are investigated. One approach employed is a recently proposed method, time-dependent intrinsic correlation (TDIC), which is based on the empirical mode decomposition (EMD) to decompose nonlinear and nonstationary signals into the intrinsic mode functions (IMFs), the instantaneous periods of which are used then in determination of the sizes of sliding windows to compute the running correlation coefficients for the multiscale signals. The empirical results reveal rich patterns of correlations for both trading volumes and recurrence durations at different scales for different modes. Another approach is the widely-used DCCA cross-correlation coefficient, by which the level of cross-correlation is measured for both original series and IMF modes of the stock indices.

Empirical forecasting and Indian Ocean dipole teleconnections of south–west monsoon rainfall in Kerala

Rainfall is a vital hydrologic variable that has a direct and significant impact on the economic development of monsoon-dominated state of Kerala in southern India. An effective approach providing accurate prediction of rainfall makes it possible to take preventive and mitigation measures against natural disasters. In this study, the ensemble empirical mode decomposition (EEMD)–artificial neural networks (ANN)–multiple linear regression (MLR) hybrid approach is used to forecast the south–west monsoon (SWM) rainfall of Kerala. The EEMD of SWM rainfall of Kerala resulted in a set of orthogonal components of specific periodic scale. The non-linear components are identified and separately modeled using ANN and rest of the components are modeled using linear regression to get their values at a specific time t. Finally, the predicted modes are recombined to get the forecasts of a generic time t. The SWM rainfalls of 1871–1972 are used for model calibration and forecasts are made sequentially for 1973–2014 period, which clearly demonstrated its efficacy in handling non-linear part of SWM rainfall data with a predictive skill of 0.65 for validation data. Further, by considering a dataset of 1961–2014 period, this study has investigated the possible teleconnection of SWM rainfall of Kerala with the Indian Ocean dipole (IOD) using the cross-correlation and EEMD-based time-dependent intrinsic correlation (TDIC) analyses. Apart from the strong correlation in the trend component, the analysis has proved the dominancy of negative association of IOD with SWM of Kerala in different process scales with strong positive association at localized time spells. The forecasting strategy demonstrated in the study and the evidence of IOD–SWM rainfall link are an amendment to the efforts for improving the predictability of SWM rainfall in Kerala.