scholarly journals Analysis of the high order ADL(p, q) models used to describe connections between time series

2020 ◽  
Vol 8 (2) ◽  
pp. 7-22 ◽  
Author(s):  
T. R. Kalugin ◽  
A. K. Kim ◽  
D. A. Petrusevich
Keyword(s):  
Time Series ◽  
Statistical Tests ◽  
High Order ◽  
Index Pair ◽  
Time Period ◽  
Production And Consumption ◽  
Consumption Index ◽  
Dynamic Series ◽  
The Mathematical Model ◽  
Index Time Series

In the paper the mathematical models describing connection between two time series are researched. At first each of them is investigated separately, and the ARIMA(p, d, q) model is constructed. These models are based on the time series characteristics obtained during the analysis stage. The connection between two time series is confirmed with the aid of cointegration statistical tests. Then the mathematical model of the connection between series is constructed. The ADL(p, q) model describes this dependence. It’s shown that for the time series under investigation the orders p, q of the ADL(p, q) model are connected with the ARIMA(p, d, q) orders of the  describing each series separately. This step makes the set of the investigated ADL(p, q) models much smaller. In the previous papers it was also shown that the ARIMA(p, d, q) automatical fitting functions in popular packages use limitations on the p, q orders of the time series process: q ≤ 5, p ≤ 5. The wish to use the simplest models is also built in the structure of the Akaike (AIC) and Bayes (BIC) informational criteria. In the paper the maximal values of the ADL(p, q) model orders are supposed to be the orders of the appropriate ARIMA(p, d, q) series. In the previous work it was shown that using high order ARIMA(p, d, q) it is possible to fit the models better. In this paper the experiments on the ADL(p, q) models construction are presented. The wage index and money income index time series pair is researched, and also the gas, water and energy production and consumption index/real agricultural production index pair is investigated. The data in the 2000–2018 time period is taken from the dynamic series of macroeconomic statistics of the Russian Federation.

scholarly journals Statistical Analysis of Discrete-valued Time Series by Parsimonious High-order Markov Chains

2020 ◽  
Vol 49 (4) ◽  
pp. 76-88
Author(s):  
Yuriy Kharin
Keyword(s):  
Time Series ◽  
Statistical Analysis ◽  
Statistical Tests ◽  
Computer Experiments ◽  
High Order ◽  
Parametric Models ◽  
Temporal Data ◽  
Statistical Inferences ◽  
Spatio Temporal ◽  
Theoretical Results

Problems of statistical analysis of discrete-valued time series are considered. Two approaches for construction of parsimonious (small-parametric) models for observed discrete data are proposed based on high-order Markov chains.Consistent statistical estimators for parameters of the developed models and some known models, and also statistical tests on the values of parameters are constructed. Probabilistic properties of the constructed statistical inferences are given. The developed theory is also applied for statistical analysis of spatio-temporal data. Theoretical results are illustrated by computer experiments on real statistical data.

scholarly journals A Neutrosophic Forecasting Model for Time Series Based on First-Order State and Information Entropy of High-Order Fluctuation

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 455 ◽  
Author(s):  
Hongjun Guan ◽  
Zongli Dai ◽  
Shuang Guan ◽  
Aiwu Zhao
Keyword(s):  
Time Series ◽  
Information Entropy ◽  
Stock Exchange ◽  
Time Series Forecasting ◽  
High Order ◽  
Stock Index ◽  
Neutrosophic Set ◽  
Forecasting Model ◽  
Forecasting Models ◽  
Proposed Model

In time series forecasting, information presentation directly affects prediction efficiency. Most existing time series forecasting models follow logical rules according to the relationships between neighboring states, without considering the inconsistency of fluctuations for a related period. In this paper, we propose a new perspective to study the problem of prediction, in which inconsistency is quantified and regarded as a key characteristic of prediction rules. First, a time series is converted to a fluctuation time series by comparing each of the current data with corresponding previous data. Then, the upward trend of each of fluctuation data is mapped to the truth-membership of a neutrosophic set, while a falsity-membership is used for the downward trend. Information entropy of high-order fluctuation time series is introduced to describe the inconsistency of historical fluctuations and is mapped to the indeterminacy-membership of the neutrosophic set. Finally, an existing similarity measurement method for the neutrosophic set is introduced to find similar states during the forecasting stage. Then, a weighted arithmetic averaging (WAA) aggregation operator is introduced to obtain the forecasting result according to the corresponding similarity. Compared to existing forecasting models, the neutrosophic forecasting model based on information entropy (NFM-IE) can represent both fluctuation trend and fluctuation consistency information. In order to test its performance, we used the proposed model to forecast some realistic time series, such as the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX), the Shanghai Stock Exchange Composite Index (SHSECI), and the Hang Seng Index (HSI). The experimental results show that the proposed model can stably predict for different datasets. Simultaneously, comparing the prediction error to other approaches proves that the model has outstanding prediction accuracy and universality.

scholarly journals Mechanical Analysis of the S&P 500 Index Time Series

2021 ◽  
Vol 1814 (1) ◽  
pp. 012004
Author(s):  
Zoran Rajilić ◽  
Nikola Stupar ◽  
Dragana Malivuk Gak
Keyword(s):  
Time Series ◽  
Mechanical Analysis ◽  
Index Time Series

scholarly journals Complexity traits and synchrony of cryptocurrencies price dynamics

2021 ◽  
Author(s):  
Davide Provenzano ◽  
Rodolfo Baggio
Keyword(s):  
Time Series ◽  
Complex Network ◽  
Complex Structures ◽  
Slope Parameter ◽  
Exponential Distributions ◽  
Horizontal Visibility ◽  
Time Period ◽  
Before And After ◽  
Visibility Algorithm ◽  
Similar Complex

AbstractIn this study, we characterized the dynamics and analyzed the degree of synchronization of the time series of daily closing prices and volumes in US$ of three cryptocurrencies, Bitcoin, Ethereum, and Litecoin, over the period September 1,2015–March 31, 2020. Time series were first mapped into a complex network by the horizontal visibility algorithm in order to revel the structure of their temporal characters and dynamics. Then, the synchrony of the time series was investigated to determine the possibility that the cryptocurrencies under study co-bubble simultaneously. Findings reveal similar complex structures for the three virtual currencies in terms of number and internal composition of communities. To the aim of our analysis, such result proves that price and volume dynamics of the cryptocurrencies were characterized by cyclical patterns of similar wavelength and amplitude over the time period considered. Yet, the value of the slope parameter associated with the exponential distributions fitted to the data suggests a higher stability and predictability for Bitcoin and Litecoin than for Ethereum. The study of synchrony between the time series investigated displayed a different degree of synchronization between the three cryptocurrencies before and after a collapse event. These results could be of interest for investors who might prefer to switch from one cryptocurrency to another to exploit the potential opportunities of profit generated by the dynamics of price and volumes in the market of virtual currencies.

scholarly journals Nonlinear analysis of magnetospheric data Part I. Geometric characteristics of the AE index time series and comparison with nonlinear surrogate data

1999 ◽  
Vol 6 (1) ◽  
pp. 51-65 ◽  
Author(s):  
G. P. Pavlos ◽  
M. A. Athanasiu ◽  
D. Kugiumtzis ◽  
N. Hatzigeorgiu ◽  
A. G. Rigas ◽  
...  
Keyword(s):  
Time Series ◽  
State Space ◽  
Null Hypothesis ◽  
Surrogate Data ◽  
Statistical Testing ◽  
Geometrical Parameters ◽  
Geometric Characteristics ◽  
Geometrical Characteristics ◽  
Ae Index ◽  
Index Time Series

Abstract. A long AE index time series is used as a crucial magnetospheric quantity in order to study the underlying dynainics. For this purpose we utilize methods of nonlinear and chaotic analysis of time series. Two basic components of this analysis are the reconstruction of the experimental tiine series state space trajectory of the underlying process and the statistical testing of an null hypothesis. The null hypothesis against which the experimental time series are tested is that the observed AE index signal is generated by a linear stochastic signal possibly perturbed by a static nonlinear distortion. As dis ' ' ating statistics we use geometrical characteristics of the reconstructed state space (Part I, which is the work of this paper) and dynamical characteristics (Part II, which is the work a separate paper), and "nonlinear" surrogate data, generated by two different techniques which can mimic the original (AE index) signal. lie null hypothesis is tested for geometrical characteristics which are the dimension of the reconstructed trajectory and some new geometrical parameters introduced in this work for the efficient discrimination between the nonlinear stochastic surrogate data and the AE index. Finally, the estimated geometric characteristics of the magnetospheric AE index present new evidence about the nonlinear and low dimensional character of the underlying magnetospheric dynamics for the AE index.

Classification of landslide activity based on spaceborne interferometric SAR at the Moselle Valley, Germany

2021 ◽  
Author(s):  
Andre C. Kalia
Keyword(s):  
Time Series ◽  
Clustering Algorithm ◽  
Statistical Tests ◽  
Spatial Density ◽  
Deformation Pattern ◽  
Visual Interpretation ◽  
Landslide Activity ◽  
Spatial Coverage ◽  
Interferometric Sar

<p>Landslide activity is an important information for landslide hazard assessment. However, an information gap regarding up to date landslide activity is often present. Advanced differential interferometric SAR processing techniques (A-DInSAR), e.g. Persistent Scatterer Interferometry (PSI) and Small Baseline Subset (SBAS) are able to measure surface displacements with high precision, large spatial coverage and high spatial sampling density. Although the huge amount of measurement points is clearly an improvement, the practical usage is mainly based on visual interpretation. This is time-consuming, subjective and error prone due to e.g. outliers. The motivation of this work is to increase the automatization with respect to the information extraction regarding landslide activity.</p><p>This study focuses on the spatial density of multiple PSI/SBAS results and a post-processing workflow to semi-automatically detect active landslides. The proposed detection of active landslides is based on the detection of Active Deformation Areas (ADA) and a subsequent classification of the time series. The detection of ADA consists of a filtering of the A-DInSAR data, a velocity threshold and a spatial clustering algorithm (Barra et al., 2017). The classification of the A-DInSAR time series uses a conditional sequence of statistical tests to classify the time series into a-priori defined deformation patterns (Berti et al., 2013). Field investigations and thematic data verify the plausibility of the results. Subsequently the classification results are combined to provide a layer consisting of ADA including information regarding the deformation pattern through time.</p>

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