The Empirical Adaptive Wavelet Decomposition (EAWD): An adaptive decomposition for the variability analysis of observation time series in atmospheric science

Most observational data sequences in geophysics can be interpreted as resulting from the interaction of several physical processes at several time and space scales. As a consequence, measurements time series have often characteristics of non-linearity and non-stationarity and thereby exhibit strong fluctuations at different time-scales. The variability analysis of a time series consists in decomposing it into several mode of variability, each mode representing the fluctuations of the original time series at a specific time-scale. Such a decomposition enables to obtain a time-frequency representation of the original time series and turns out to be very useful to estimate the dimensionality of the underlying dynamics. Decomposition techniques very well suited to non-linear and non-stationary time series have recently been developed in the literature. Among the most widely used of these technics are the empirical mode decomposition (EMD) and the empirical wavelet transformation (EWT). The purpose of this paper is to present a new adaptive filtering method that combines the advantages of the EMD and EWT technics, while remaining close to the dynamics of the original signal made of atmospheric observations, which means reconstructing as close as possible to the original time series, while preserving its variability at different time scales.

Over-whitening or Pre-whitening in Hydro-climatological Trend Analysis?

To meet the basic assumption of classical Mann-Kendall (MK) trend analysis, which requires serially independent time series, a pre-whitening (PW) procedure is proposed to alleviate the serial correlation structure of a given hydro-meteorological time series records for application. The procedure is simply to take the lagged differences in a given time series in the hope that the new time series will have an independent serial correlation coefficient. The whole idea was originally based on the first-order autoregressive AR (1) process, but such a procedure has been documented to damage the trend component in the original time series. On the other hand, the over-whitening procedure (OW) proposes a white noise process superposition of the same length with zero mean and some standard deviation on the original time series to convert it into serially independent series without any damage to the trend component. The stationary white noise addition does not have any trend components. For trend identification, annual average temperature records in New Jersey and Istanbul are presented to show the difference between PW and OW procedures. It turned out that the OW procedure was superior to the PW procedure, which did not cause a loss in the original trend component.

Time-series Imputation Algorithm

Statistical imputation is a field of study that attempts to fill missing data. It is commonly applied to population statistics whose data have no correlation with running time. For a time series, data is typically analyzed using the autocorrelation function (ACF), the Fourier transform to estimate power spectral densities (PSD), the Allan deviation (ADEV), trend extensions, and basically any analysis that depends on uniform time indexes. We explain the rationale for an imputation algorithm that fills gaps in a time series by applying a backward, inverted replica of adjacent live data. To illustrate, four intentional massive gaps that exceed 100% of the original time series are recovered. The L(f) PSD with imputation applied to the gaps is nearly indistinguishable from the original. Also, the confidence of ADEV with imputation falls within 90% of the original ADEV with mixtures of power-law noises. The algorithm in Python is included for those wishing to try it.

Finding the onset of COVID-19 - a correlation analysis with influenza epidemic around the world

Background. COVID-19 showed similar and overlapping symptoms compared with seasonal influenza. It is difficult to distinguish them, especially in the early stage of the outbreak. The confluence of the two diseases might result in considerable morbidity, it is doubtful that whether COVID-19 had already affected the morbidity of influenza earlier than the first report.Methods. We conducted Kolmogorov-Smirnov Test and Kruskal Wallis Test to discover seasonal and regional distributions of influenza and COVID-19. Cluster analysis was utilized to explore possible influence factors. Spearman Test was carried out for analyzing correlations between the two diseases. We employed Arima Model to predict time series of WMI. We proved differences between the forecasted and the original time series of influenza from 2019 to 2021 by Mann-Whitney U Test. Then we observed first abnormal peaks on the time series, tracing back to the onset of COVID-19 affecting influenza compared with the first-report time.Results. WMI and WMC varied significantly in four seasons, five continents and the ten selected countries. Cluster analysis divided the data into two groups according to country, continent, population and morbidity. WMI of China, Israel, Honduras, Morocco and Nigeria were correlated with WMC. The forecasted and the original time series of influenza from 2019 to 2021 were significantly different. Compared with the forecasted one, some abnormal peaks firstly appeared on the original time series of influenza around Dec.31st, 2018 on Austria, Norway, Morocco and Nigeria, Jan.28th, 2019 on South Africa, Apr.8th, 2019 on Marshall Islands, Jul.7th, 2019 on America, Sep.30th, 2019 on China and Israel, Mar.11th, 2020 on Honduras.Conclusions. Winter and autumn were the high incidence season for influenza and COVID-19, respectively. Oceania and Americas owned the highest incidence rate for these two diseases. Human immunity, continents, countries’ policies and population were possible influence factors. Only in Honduras, the first reported COVID-19 case happened concurrently with the abnormal value of the ILI. And in the rest of the included countries, COVID-19 might happen earlier than its first reports. Among these regions, COVID-19 might firstly affect Africa in the first week of 2019.

A Data-Trait-Driven Rolling Decomposition-Ensemble Model for Gasoline Consumption Forecasting

In order to predict the gasoline consumption in China, this paper propose a novel data-trait-driven rolling decomposition-ensemble model. This model consists of five steps: the data trait test, data decomposition, component trait analysis, component prediction and ensemble output. In the data trait test and component trait analysis, the original time series and each decomposed component are thoroughly analyzed to explore hidden data traits. According to these results, decomposition models and prediction models are selected to complete the original time series data decomposition and decomposed component prediction. In the ensemble output, the ensemble method corresponding to the decomposition method is used for final aggregation. In particular, this methodology introduces the rolling mechanism to solve the misuse of future information problem. In order to verify the effectiveness of the model, the quarterly gasoline consumption data from four provinces in China are used. The experimental results show that the proposed model is significantly better than the single prediction models and decomposition-ensemble models without the rolling mechanism. It can be seen that the decomposition-ensemble model with data-trait-driven modeling ideas and rolling decomposition and prediction mechanism possesses the superiority and robustness in terms of the evaluation criteria of horizontal and directional prediction.

Adaptive complementary ensemble EMD and energy-frequency spectra of cryptocurrency prices

In this study, we study the price dynamics of cryptocurrencies using adaptive complementary ensemble empirical mode decomposition (ACE-EMD) and Hilbert spectral analysis. This is a multiscale noise-assisted approach that decomposes any time series into a number of intrinsic mode functions, along with the corresponding instantaneous amplitudes and instantaneous frequencies. The decomposition is adaptive to the time-varying volatility of each cryptocurrency price evolution. Different combinations of modes allow us to reconstruct the time series using components of different timescales. We then apply Hilbert spectral analysis to define and compute the instantaneous energy-frequency spectrum of each cryptocurrency to illustrate the properties of various timescales embedded in the original time series.

The Systematic Bias of Entropy Calculation in the Multi-Scale Entropy Algorithm

Entropy indicates irregularity or randomness of a dynamic system. Over the decades, entropy calculated at different scales of the system through subsampling or coarse graining has been used as a surrogate measure of system complexity. One popular multi-scale entropy analysis is the multi-scale sample entropy (MSE), which calculates entropy through the sample entropy (SampEn) formula at each time scale. SampEn is defined by the “logarithmic likelihood” that a small section (within a window of a length m) of the data “matches” with other sections will still “match” the others if the section window length increases by one. “Match” is defined by a threshold of r times standard deviation of the entire time series. A problem of current MSE algorithm is that SampEn calculations at different scales are based on the same matching threshold defined by the original time series but data standard deviation actually changes with the subsampling scales. Using a fixed threshold will automatically introduce systematic bias to the calculation results. The purpose of this paper is to mathematically present this systematic bias and to provide methods for correcting it. Our work will help the large MSE user community avoiding introducing the bias to their multi-scale SampEn calculation results.

Correlation-aided method for identification and gradation of periodicities in hydrologic time series

Identification of periodicities in hydrological time series and evaluation of their statistical significance are not only important for water-related studies, but also challenging issues due to the complex variability of hydrological processes. In this article, we develop a “Moving Correlation Coefficient Analysis” (MCCA) method for identifying periodicities of a time series. In the method, the correlation between the original time series and the periodic fluctuation is used as a criterion, aiming to seek out the periodic fluctuation that fits the original time series best, and to evaluate its statistical significance. Consequently, we take periodic components consisting of simple sinusoidal variation as an example, and do statistical experiments to verify the applicability and reliability of the developed method by considering various parameters changing. Three other methods commonly used, harmonic analysis method (HAM), power spectrum method (PSM) and maximum entropy method (MEM) are also applied for comparison. The results indicate that the efficiency of each method is positively connected to the length and amplitude of samples, but negatively correlated with the mean value, variation coefficient and length of periodicity, without relationship with the initial phase of periodicity. For those time series with higher noise component, the developed MCCA method performs best among the four methods. Results from the hydrological case studies in the Yangtze River basin further verify the better performances of the MCCA method compared to other three methods for the identification of periodicities in hydrologic time series.

The Importance of Trend-Cycle Analysis for National Statistics Institutes

Seasonal adjustment is a widely applied statistical method. National Statistics Institutes around the world apply seasonal adjustment methods, such as X-12-ARIMA or TRAMO-SEATS, on a regular basis to help users interpret movements in the time series and aid in decision making. The seasonal adjustment process decomposes the original time series into three main components: a trend-cycle, seasonal and irregular. By definition the seasonally adjusted estimates still contain a degree of volatility as they are just a combination of the trend-cycle and irregular. Typically, as an analytical product, the seasonally adjusted estimates are published alongside the time series of the original estimates. In most countries the trend-cycle estimates are not published. Some countries, such as Australia, regularly publish trend-cycle as additional analytical product alongside the original and seasonally adjusted estimates to inform users. This paper presents the case for the regular calculation and production of trend- cycle estimates at National Statistics Institutes to help inform and educate users about the longer term signals in the time series.

Partisan Selectivity in Blame Attribution: Evidence from the COVID-19 Pandemic

Crises and disasters give voters an opportunity to observe the incumbent's response and reward or punish them for successes and failures. Yet even when voters agree on the facts, they tend to attribute responsibility in a group-serving manner, disproportionately crediting their party for positive developments and blaming opponents for negative developments. Using original time series data, we show that partisan disagreement over U.S. President Donald Trump's responsibility for the COVID-19 pandemic quickly emerged alongside the pandemic's onset in March 2020. Three original survey experiments show that the valence of information about the country's performance against the virus contributes causally to such gaps. A Bayesian model of information processing anticipates our findings more closely than do theories of partisan-motivated reasoning. These findings shed new light on the foundations of partisan loyalty, especially among citizens who do not think of themselves as partisans.