scholarly journals A Comparison of Hurst Exponent Estimators in Long-range Dependent Curve Time Series

2020 ◽  
Vol 12 (1) ◽  
Author(s):  
Han Lin Shang
Keyword(s):  
Time Series ◽  
Long Range ◽  
Hurst Exponent ◽  
Moving Average ◽  
Estimation Method ◽  
Principal Component ◽  
Functional Principal Component Analysis ◽  
Finite Sample ◽  
Long Run ◽  
Finite Sample Bias

AbstractThe Hurst exponent is the simplest numerical summary of self-similar long-range dependent stochastic processes. We consider the estimation of Hurst exponent in long-range dependent curve time series. Our estimation method begins by constructing an estimate of the long-run covariance function, which we use, via dynamic functional principal component analysis, in estimating the orthonormal functions spanning the dominant sub-space of functional time series. Within the context of functional autoregressive fractionally integrated moving average (ARFIMA) models, we compare finite-sample bias, variance and mean square error among some time- and frequency-domain Hurst exponent estimators and make our recommendations.

scholarly journals Long-Range Dependence in Financial Markets: A Moving Average Cluster Entropy Approach

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 634 ◽  
Author(s):  
Pietro Murialdo ◽  
Linda Ponta ◽  
Anna Carbone
Keyword(s):  
Time Series ◽  
Financial Markets ◽  
Long Range ◽  
Financial Time Series ◽  
Moving Average ◽  
Social Systems ◽  
Long Run ◽  
Characteristic Behaviour ◽  
Correlation Parameters ◽  
Average Cluster

A perspective is taken on the intangible complexity of economic and social systems by investigating the dynamical processes producing, storing and transmitting information in financial time series. An extensive analysis based on the moving average cluster entropy approach has evidenced market and horizon dependence in highest-frequency data of real world financial assets. The behavior is scrutinized by applying the moving average cluster entropy approach to long-range correlated stochastic processes as the Autoregressive Fractionally Integrated Moving Average (ARFIMA) and Fractional Brownian motion (FBM). An extensive set of series is generated with a broad range of values of the Hurst exponent H and of the autoregressive, differencing and moving average parameters p , d , q . A systematic relation between moving average cluster entropy and long-range correlation parameters H, d is observed. This study shows that the characteristic behaviour exhibited by the horizon dependence of the cluster entropy is related to long-range positive correlation in financial markets. Specifically, long range positively correlated ARFIMA processes with differencing parameter d ≃ 0.05 , d ≃ 0.15 and d ≃ 0.25 are consistent with moving average cluster entropy results obtained in time series of DJIA, S&P500 and NASDAQ. The findings clearly point to a variability of price returns, consistently with a price dynamics involving multiple temporal scales and, thus, short- and long-run volatility components. An important aspect of the proposed approach is the ability to capture detailed horizon dependence over relatively short horizons (one to twelve months) and thus its relevance to define risk analysis indices.

scholarly journals Time Series Modelling of The Volume of Overland Timber Export in The Bolgatanga Municipality

2020 ◽  
pp. 124-138
Author(s):  
Henry M. Kpamma ◽  
Silverius K. Bruku ◽  
John A. Awaab
Keyword(s):  
Time Series ◽  
Moving Average ◽  
Preliminary Investigation ◽  
Arima Model ◽  
Estimation Method ◽  
Long Run ◽  
Time Series Modelling ◽  
The Future ◽  
Equilibrium Relationships ◽  
The Right

Aims/ Objectives: This research was carried out with the intention of using time series to model the volume of overland timber exported within Bolgatanga municipalityPlace and Duration of Study: Study of the time series was based on a historical data of the volume of timber exported for twenty consecutive years, from 1999 to 2019 within Bolgatanga municipality.Methodology: The three-stage iterative modeling approach for Box Jenkins was used to match an ARIMA model and to forecast both the amount of timber export and the confiscated lumber. ARIMA method incorporates a cycle of autoregressive and a moving average. The three-stage iterative modeling technique of Box Jenkins which were used are model recognition, parameter estimation and/or diagnostic checks were also made. Results: From the preliminary investigation, the study showed that the amount of timber exported in municipality is skewed to the right, suggesting that much of the amount of timber exported is below the average. This, together with the high volatility in the volume of timber exported, indicates that the amount of timber exported within the municipalities during the twenty-year period was low. The plots from the trends also showed robust variations in the volume of timber exported indicating that timber exporters do not have better grips with the concepts and applications of export technology, hence the erratic nature of the volume of timber exported over the period. The quadratic pattern and the ARIMA (1,1,1) model best represented the amount of timber exported.The analysis further indicated that there will be a further decrease in the amount of timber export from the five years projection into the future. Over the last two decades the Bayesian approach to VAR has gained ground. For a future report, this estimation method will be followed to examine the ”long-run equilibrium relationships” between timber export volumes and climate change.Conclusion: The quadratic pattern and the ARIMA (1,1,1) model best represented the amount of timber exported. There will be a further decrease in the amount of timber export from the five years projection into the future.

Correlating geologic and seismic data with unconventional resource production curves using machine learning

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. O39-O47 ◽  
Author(s):  
Ryan Smith ◽  
Tapan Mukerji ◽  
Tony Lupo
Keyword(s):  
Machine Learning ◽  
Time Series ◽  
Oil And Gas ◽  
Principal Component ◽  
Functional Principal Component Analysis ◽  
Full Time ◽  
Data Types ◽  
Production Time ◽  
Well Production ◽  
Unconventional Resource

Predicting well production in unconventional oil and gas settings is challenging due to the combined influence of engineering, geologic, and geophysical inputs on well productivity. We have developed a machine-learning workflow that incorporates geophysical and geologic data, as well as engineering completion parameters, into a model for predicting well production. The study area is in southwest Texas in the lower Eagle Ford Group. We make use of a time-series method known as functional principal component analysis to summarize the well-production time series. Next, we use random forests, a machine-learning regression technique, in combination with our summarized well data to predict the full time series of well production. The inputs to this model are geologic, geophysical, and engineering data. We are then able to predict the well-production time series, with 65%–76% accuracy. This method incorporates disparate data types into a robust, predictive model that predicts well production in unconventional resources.

Long-Range Dependence of Traffic Flow and Speed of a Motorway: Dynamics and Correlation with Historical Incidents

2017 ◽  
Vol 2616 (1) ◽  
pp. 49-57 ◽  
Author(s):  
Sai Chand ◽  
Gregory Aouad ◽  
Vinayak V. Dixit
Keyword(s):  
Time Series ◽  
Long Range ◽  
Traffic Congestion ◽  
Hurst Exponent ◽  
Fractal Theory ◽  
Urban Traffic ◽  
Spatial And Temporal Variation ◽  
Long Range Dependence ◽  
Incident Rates ◽  
Sydney Australia

Speed and flow of vehicles tend to have several effects on the dynamics of a transport system. Fluctuations of these variables can implicate congestion, can lower predictability, and may even catalyze crashes. A concept of fractal theory called the Hurst exponent—a measure of the long-range dependence (LRD) of a time series—was used to understand the fluctuations in flow and speed of a motorway in Sydney, Australia. The spatial and temporal variation of the LRD for flow ( Hflow) and speed ( Hspeed) at several monitor sites is discussed. Furthermore, the effects of number of lanes on flow and speed predictability are explored. It was observed that the flow predictability of two-lane sections was significantly lower when compared with three-lane and four-lane sections. Conversely, the speed predictability of four-lane sections was considerably higher than that of two-lane and three-lane sections. Finally, traffic congestion was defined with regard to the LRD of speed, and its correlation with historical incident rates was measured. It was ascertained that monitor sites with a historically high proportion of large Hspeed were correlated with unsafe locations. This study could lead to many applications of fractal analysis on highways and urban traffic.

scholarly journals Clustering of Rainfall Stations in RH-24 Mexico Region Using the Hurst Exponent in Semivariograms

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Francisco Gerardo Benavides-Bravo ◽  
F-Javier Almaguer ◽  
Roberto Soto-Villalobos ◽  
Víctor Tercero-Gómez ◽  
Javier Morales-Castillo
Keyword(s):  
Time Series ◽  
Long Range ◽  
Hurst Exponent ◽  
Historical Data ◽  
Regional Frequency Analysis ◽  
Long Range Dependence ◽  
National Commission ◽  
Long Range Correlations ◽  
Rainfall Variations ◽  
Regional Frequency

An important topic in the study of the time series behavior and, in particular, meteorological time series is the long-range dependence. This paper explores the behavior of rainfall variations in different periods, using long-range correlations analysis. Semivariograms and Hurst exponent were applied to historical data in different pluviometric stations of the Río Bravo-San Juan watershed, at the hydrographic RH-24 Mexico region. The database was provided by the Water National Commission (CONAGUA). Using the semivariograms, the Hurst exponent was obtained and used as an input to perform a cluster analysis of rainfall stations. Groups of homogeneous samples that might be useful in a regional frequency analysis were obtained through the process.

The Multi-Dependent Hurst Exponent in Traffic Time Series

2010 ◽  
Vol 20-23 ◽  
pp. 346-351
Author(s):  
Ke Qiang Dong ◽  
Peng Jian Shang ◽  
Hong Zhang
Keyword(s):  
Time Series ◽  
Long Range ◽  
Hurst Exponent ◽  
Short Range ◽  
A Priori ◽  
Correlated Data ◽  
Nonstationary Time Series ◽  
Traffic Time Series ◽  
Correlation Exponent ◽  
Correlation Properties

We propose a new method called the multi-dependent Hurst exponent to investigate the correlation properties of the nonstationary time series. The method is validated with the artificial series including both short-range correlated data and long-range correlated data. The results indicate that the multi-dependent Hurst exponents fluctuate around the a-priori known correlation exponent H. Application to traffic time series is also presented, and comparison is made between the artificial time series and traffic time series.

scholarly journals GAUSSIAN INFERENCE IN AR(1) TIME SERIES WITH OR WITHOUT A UNIT ROOT

2008 ◽  
Vol 24 (3) ◽  
pp. 631-650 ◽  
Author(s):  
Peter C.B. Phillips ◽  
Chirok Han
Keyword(s):  
Time Series ◽  
Central Limit ◽  
Unit Root ◽  
Initial Conditions ◽  
Finite Sample ◽  
Linear Processes ◽  
Limit Theory ◽  
Sample Bias ◽  
Dynamic Panels ◽  
Finite Sample Bias

This paper introduces a simple first-difference-based approach to estimation and inference for the AR(1) model. The estimates have virtually no finite-sample bias and are not sensitive to initial conditions, and the approach has the unusual advantage that a Gaussian central limit theory applies and is continuous as the autoregressive coefficient passes through unity with a uniform $\sqrt{n}$ rate of convergence. En route, a useful central limit theorem (CLT) for sample covariances of linear processes is given, following Phillips and Solo (1992, Annals of Statistics, 20, 971–1001). The approach also has useful extensions to dynamic panels.

scholarly journals Forecasting the COVID-19 Epidemic By Integrating Symptom Search Behavior Into Predictive Models: Infoveillance Study (Preprint)

2021 ◽  
Author(s):  
Alessandro Rabiolo ◽  
Eugenio Alladio ◽  
Esteban Morales ◽  
Andrew Ian McNaught ◽  
Francesco Bandello ◽  
...  
Keyword(s):  
Time Series ◽  
Predictive Models ◽  
Web Application ◽  
Moving Average ◽  
Time Lag ◽  
Search Behavior ◽  
Principal Component ◽  
Google Trends ◽  
Time Range ◽  
Prediction Ability

BACKGROUND Previous studies have suggested associations between trends of web searches and COVID-19 traditional metrics. It remains unclear whether models incorporating trends of digital searches lead to better predictions. OBJECTIVE The aim of this study is to investigate the relationship between Google Trends searches of symptoms associated with COVID-19 and confirmed COVID-19 cases and deaths. We aim to develop predictive models to forecast the COVID-19 epidemic based on a combination of Google Trends searches of symptoms and conventional COVID-19 metrics. METHODS An open-access web application was developed to evaluate Google Trends and traditional COVID-19 metrics via an interactive framework based on principal component analysis (PCA) and time series modeling. The application facilitates the analysis of symptom search behavior associated with COVID-19 disease in 188 countries. In this study, we selected the data of nine countries as case studies to represent all continents. PCA was used to perform data dimensionality reduction, and three different time series models (error, trend, seasonality; autoregressive integrated moving average; and feed-forward neural network autoregression) were used to predict COVID-19 metrics in the upcoming 14 days. The models were compared in terms of prediction ability using the root mean square error (RMSE) of the first principal component (PC1). The predictive abilities of models generated with both Google Trends data and conventional COVID-19 metrics were compared with those fitted with conventional COVID-19 metrics only. RESULTS The degree of correlation and the best time lag varied as a function of the selected country and topic searched; in general, the optimal time lag was within 15 days. Overall, predictions of PC1 based on both search terms and COVID-19 traditional metrics performed better than those not including Google searches (median 1.56, IQR 0.90-2.49 versus median 1.87, IQR 1.09-2.95, respectively), but the improvement in prediction varied as a function of the selected country and time frame. The best model varied as a function of country, time range, and period of time selected. Models based on a 7-day moving average led to considerably smaller RMSE values as opposed to those calculated with raw data (median 0.90, IQR 0.50-1.53 versus median 2.27, IQR 1.62-3.74, respectively). CONCLUSIONS The inclusion of digital online searches in statistical models may improve the nowcasting and forecasting of the COVID-19 epidemic and could be used as one of the surveillance systems of COVID-19 disease. We provide a free web application operating with nearly real-time data that anyone can use to make predictions of outbreaks, improve estimates of the dynamics of ongoing epidemics, and predict future or rebound waves.

Sign in / Sign up

Export Citation Format

Share Document