scholarly journals Comparison of two stationary stochastic processes using standardized time series

1985 ◽  
Author(s):  
Bor-Chung Chen ◽  
Robert G. Sargent
Keyword(s):  
Time Series ◽  
Stochastic Processes ◽  
Stationary Stochastic Processes

scholarly journals Multifractal products of stochastic processes: construction and some basic properties

2002 ◽  
Vol 34 (4) ◽  
pp. 888-903 ◽  
Author(s):  
Petteri Mannersalo ◽  
Ilkka Norros ◽  
Rudolf H. Riedi
Keyword(s):  
Time Series ◽  
Stochastic Processes ◽  
Power Law ◽  
Special Form ◽  
Multifractal Spectrum ◽  
Nonstationary Process ◽  
Limit Process ◽  
Stationary Stochastic Processes ◽  
Measured Time ◽  
Multifractal Scaling

In various fields, such as teletraffic and economics, measured time series have been reported to adhere to multifractal scaling. Classical cascading measures possess multifractal scaling, but their increments form a nonstationary process. To overcome this problem, we introduce a construction of random multifractal measures based on iterative multiplication of stationary stochastic processes, a special form of T-martingales. We study the ℒ2-convergence, nondegeneracy, and continuity of the limit process. Establishing a power law for its moments, we obtain a formula for the multifractal spectrum and hint at how to prove the full formalism.

scholarly journals Comparison of Stochastic and Machine Learning Methods for Multi-Step Ahead Forecasting of Hydrological Processes

2017 ◽  
Author(s):  
Georgia A. Papacharalampous ◽  
Hristos Tyralis ◽  
Demetris Koutsoyiannis
Keyword(s):  
Machine Learning ◽  
Time Series ◽  
Stochastic Processes ◽  
Real World ◽  
Large Scale ◽  
Simulation Experiment ◽  
Learning Methods ◽  
Machine Learning Methods ◽  
Stationary Stochastic Processes ◽  
First Time

We perform an extensive comparison between 11 stochastic to 9 machine learning methods regarding their multi-step ahead forecasting properties by conducting 12 large-scale computational experiments. Each of these experiments uses 2 000 time series generated by linear stationary stochastic processes. We conduct each simulation experiment twice; the first time using time series of 110 values and the second time using time series of 310 values. Additionally, we conduct 92 real-world case studies using mean monthly time series of streamflow and particularly focus on one of them to reinforce the findings and highlight important facts. We quantify the performance of the methods using 18 metrics. The results indicate that the machine learning methods do not differ dramatically from the stochastic, while none of the methods under comparison is uniformly better or worse than the rest. However, there are methods that are regularly better or worse than others according to specific metrics.

scholarly journals Multifractal products of stochastic processes: construction and some basic properties

2002 ◽  
Vol 34 (04) ◽  
pp. 888-903 ◽  
Author(s):  
Petteri Mannersalo ◽  
Ilkka Norros ◽  
Rudolf H. Riedi
Keyword(s):  
Time Series ◽  
Stochastic Processes ◽  
Power Law ◽  
Special Form ◽  
Multifractal Spectrum ◽  
Nonstationary Process ◽  
Limit Process ◽  
Stationary Stochastic Processes ◽  
Measured Time ◽  
Multifractal Scaling

In various fields, such as teletraffic and economics, measured time series have been reported to adhere to multifractal scaling. Classical cascading measures possess multifractal scaling, but their increments form a nonstationary process. To overcome this problem, we introduce a construction of random multifractal measures based on iterative multiplication of stationary stochastic processes, a special form of T-martingales. We study the ℒ2-convergence, nondegeneracy, and continuity of the limit process. Establishing a power law for its moments, we obtain a formula for the multifractal spectrum and hint at how to prove the full formalism.

Sign in / Sign up

Export Citation Format

Share Document