Confidence Regions for Parameters in Stationary Time Series Models With Gaussian Noise

This article develops two new empirical likelihood methods for long-memory time series models based on adjusted empirical likelihood and mean empirical likelihood. By application of Whittle likelihood, one obtains a score function that can be viewed as the estimating equation of the parameters of the long-memory time series model. An empirical likelihood ratio is obtained which is shown to be asymptotically chi-square distributed. It can be used to construct confidence regions. By adding pseudo samples, we simultaneously eliminate the non-definition of the original empirical likelihood and enhance the coverage probability. Finite sample properties of the empirical likelihood confidence regions are explored through Monte Carlo simulation, and some real data applications are carried out.

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.

Estimation of AR (2) Model with Dependent Errors for Unbounded Stationary and Nonstationary Time Series

In this paper the GLS and the ML estimators, the variance-covariance matrix, the unbiased for the GLS and the ML estimators of parameters of AR (2) model with constant in case of dependent errors have been derived, the simulation results shown that the values of MSE and Thiel’s U in case of unbounded stationary time series for all sample size T are less than the values of MSE and Thiel’s U in case of unbounded nonstationary time series which approved that the results for unbounded stationary times series are better than the results for unbounded nonstationary times series, and the simulation results for unbounded nonstationary time series shown that by using the measurement of MSE the best case among of all cases of nonstationary which gives the smallest values of MSE is case four when the first and the second conditions of stationary conditions for AR (2) model are exists, while by using the measurement of Thiel’s U the best case among of all cases of nonstationary which gives the smallest values of Thiel’s U is case six when the second and the third conditions of stationary conditions for AR (2) model are exists.

The impact of world oil and food price shocks on the interdependence of Brazil and Russia: SVAR-DCC-GARCH model

This study seeks to identify the extent to which global oil and food price volatilities affected the interdependence of the Brazilian and Russian economies in the period from 1996 to 2021. The ARCH/GARCH framework was used to model the volatility of oil and food prices. The Structural Vector Autoregressive (SVAR) approach was used to ascertain the sensitivity of key economic indicators to oil and food shocks. The Impulse Response Function (IRF) was used to trace short-term effects over a period of 12 months. Subsequently, the multivariate dynamic conditional correlation DCC-GARCH model, created by Engle & Sheppard (2001), was used to model time-varying correlations of paired macroeconomic variables. This study contributes to the empirical literature in two fundamental ways. Firstly, it pairs the two largest oil and food producers in the BRICS bloc. Secondly, unlike some earlier studies, the applied methodology ensures the effectiveness of the results by using stationary time series data. The results show that Brazil and Russia have long-run spillover effects for all macroeconomic variables in response to both oil and food price shocks. Furthermore, money supply and exchange rate variables exhibited declining positive correlation coefficients during the global financial crisis of 2008–2009, but peaked in early 2020 due to the Covid-19 pandemic. As a corollary of the main findings, the researchers recommend that investors should diversify their portfolios beyond these two economies in order to minimize the risk of contagion during severe global crises.

A Machine Learning Pipeline for Forecasting Time Series in the Banking Sector

The problem of forecasting time series is very widely debated. In recent years, machine learning algorithms have been very prolific in this area. This paper describes a systematic approach to building a machine learning predictive model for solving optimization problems in the banking sector. A literature analysis on applying such methods in this particular area is presented. As a direct result of the described research, a universal scenario for forecasting various non-stationary time series in automatic mode was developed. The developed scenario for solving specific banking tasks to improve business efficiency, including optimizing demand for ATMs, forecasting the load on the call center and cash center, is considered. A machine learning methodology in economics that can yield robust and reproducible results and can be reused in solving other similar tasks is described. The methodology described in the article was tested on three cases and showed the ability to generate models that are superior in accuracy to similar predictive models described in the literature by at least three percentage points. This article will be helpful to specialists dealing with the problem of forecasting economic time series and students and researchers due to a large number of links to systematic literature reviews on this topic.

Analysis of spatiotemporal variations of drought and its correlations with remote sensing-based indices via wavelet analysis and clustering methods

Beside in situ observations, satellite-based products can provide an ideal data source for spatiotemporal monitoring of drought. In this study, the spatiotemporal pattern of drought was investigated for the northwest part of Iran using ground- and satellite-based datasets. First, the Standardized Precipitation Index series were calculated via precipitation data of 29 sites located in the selected area and the CPC Merged Analysis of Precipitation satellite. The Maximal Overlap Discrete Wavelet Transform (MODWT) was used for obtaining the temporal features of time series, and further decomposition was performed using Ensemble Empirical Mode Decomposition (EEMD) to have more stationary time series. Then, multiscale zoning was done based on subseries energy values via two clustering methods, namely the self-organizing map and K-means. The results showed that the MODWT–EEMD–K-means method successfully identified homogenous drought areas. On the other hand, correlation between the satellite sensor data (i.e. the Normalized Difference Vegetation Index, the Vegetation Condition Index, the Vegetation Healthy Index, and the Temperature Condition Index) was evaluated. The possible links between central stations of clusters and satellite-based indices were assessed via the wavelet coherence method. The results revealed that all applied satellite-based indices had significant statistical correlations with the ground-based drought index within a certain period.

Increasing the sensitivity of real-time method for diagnostic of autogenerators phase synchronization based on their non-stationary time series

Purpose of this work is to of the research – Increasing the sensitivity of a method for diagnosing phase synchronization of autogenerators based on their non-stationary time series in real time, and also a comparison of the statistical properties of the proposed modification of the method with the well-known method for diagnostics of loop synchronization, which has proven itself in the analysis of experimental data. Methods.The paper compares the probabilities of the appearance of an error of the second kind of the developed modified method for diagnostics of phase synchronization with the probabilities of occurrence of an error of the second kind of the known method at equal values of sensitivity. When comparing the methods, generated test time realizations with a priori known boundaries of the phase synchronization sections are used, which repeat the statistical properties of the experimental data. It also compares the computational complexity of the two methods. Results. A modification of the method for diagnosing phase synchronization of autonomic regulation circuits in real time is proposed. It is shown that the proposed modification provides similar values of sensitivity and probability of appearance of errors of the second kind as the previously proposed approach. The developed method has less computational complexity than the previously proposed method. The values of free parameters corresponding to different values of sensitivity and probability of appearance of errors of the second kind are obtained. Conclusion. The area of application of the developed method with modification is formulated. The low computational complexity of the proposed method, as well as the possibility of switching devices to integer computations in calculations, makes it possible to use it for wearable registrations performing calculations in real time, based on small-sized low-power processors that do not support floating-point arithmetic operations.

The significance of neural inter-frequency power correlations

It is of great interest in neuroscience to determine what frequency bands in the brain have covarying power. This would help us robustly identify the frequency signatures of neural processes. However to date, to the best of the author’s knowledge, a comprehensive statistical approach to this question that accounts for intra-frequency autocorrelation, frequency-domain oversampling, and multiple testing under dependency has not been undertaken. As such, this work presents a novel statistical significance test for correlated power across frequency bands for a broad class of non-stationary time series. It is validated on synthetic data. It is then used to test all of the inter-frequency power correlations between 0.2 and 8500 Hz in continuous intracortical extracellular neural recordings in Macaque M1, using a very large, publicly available dataset. The recordings were Current Source Density referenced and were recorded with a Utah array. The results support previous results in the literature that show that neural processes in M1 have power signatures across a very broad range of frequency bands. In particular, the power in LFP frequency bands as low as 20 Hz was found to almost always be statistically significantly correlated to the power in kHz frequency ranges. It is proposed that this test can also be used to discover the superimposed frequency domain signatures of all the neural processes in a neural signal, allowing us to identify every interesting neural frequency band.