Framework based on multiplicative error and residual analysis to forecast bitcoin intraday-volatility

2021 ◽  
pp. 126613
Author(s):  
Sebastian Tapia ◽  
Werner Kristjanpoller
Keyword(s):  
Residual Analysis ◽  
Multiplicative Error ◽  
Intraday Volatility

scholarly journals The number of maximum primitive sets of integers

2021 ◽  
pp. 1-15
Author(s):  
Hong Liu ◽  
Péter Pál Pach ◽  
Richárd Palincza
Keyword(s):  
Related Problem ◽  
Maximum Size ◽  
Multiplicative Error ◽  
Coprime Integers ◽  
Primitive Sets

Abstract A set of integers is primitive if it does not contain an element dividing another. Let f(n) denote the number of maximum-size primitive subsets of {1,…,2n}. We prove that the limit α = lim n→∞ f(n)1/n exists. Furthermore, we present an algorithm approximating α with (1 + ε) multiplicative error in N(ε) steps, showing in particular that α ≈ 1.318. Our algorithm can be adapted to estimate the number of all primitive sets in {1,…,n} as well. We address another related problem of Cameron and Erdős. They showed that the number of sets containing pairwise coprime integers in {1,…n} is between ${2^{\pi (n)}} \cdot {e^{(1/2 + o(1))\sqrt n }}$ and ${2^{\pi (n)}} \cdot {e^{(2 + o(1))\sqrt n }}$ . We show that neither of these bounds is tight: there are in fact ${2^{\pi (n)}} \cdot {e^{(1 + o(1))\sqrt n }}$ such sets.

Residual analysis in random regressions using SAS and S-PLUS

1999 ◽  
Vol 58 (3) ◽  
pp. 281-282 ◽  
Author(s):  
Sati Mazumdar ◽  
Amy E. Begley ◽  
Patricia R. Houck ◽  
Ying Yang ◽  
Charles F. Reynolds ◽  
...  
Keyword(s):  
Residual Analysis

scholarly journals Can the heterogeneity in stream dissolved organic carbon be explained by contributing landscape elements?

2014 ◽  
Vol 11 (4) ◽  
pp. 1199-1213 ◽  
Author(s):  
A. M. Ågren ◽  
I. Buffam ◽  
D. M. Cooper ◽  
T. Tiwari ◽  
C. D. Evans ◽  
...  
Keyword(s):  
Organic Carbon ◽  
Dissolved Organic Carbon ◽  
Model Development ◽  
Field Measurements ◽  
Mixing Model ◽  
Residual Analysis ◽  
Residence Times ◽  
Stream Network ◽  
Landscape Elements ◽  
Modelling Studies

Abstract. The controls on stream dissolved organic carbon (DOC) concentrations were investigated in a 68 km2 catchment by applying a landscape-mixing model to test if downstream concentrations could be predicted from contributing landscape elements. The landscape-mixing model reproduced the DOC concentration well throughout the stream network during times of high and intermediate discharge. The landscape-mixing model approach is conceptually simple and easy to apply, requiring relatively few field measurements and minimal parameterisation. Our interpretation is that the higher degree of hydrological connectivity during high flows, combined with shorter stream residence times, increased the predictive power of this whole watershed-based mixing model. The model was also useful for providing a baseline for residual analysis, which highlighted areas for further conceptual model development. The residual analysis indicated areas of the stream network that were not well represented by simple mixing of headwaters, as well as flow conditions during which simple mixing based on headwater watershed characteristics did not apply. Specifically, we found that during periods of baseflow the larger valley streams had much lower DOC concentrations than would be predicted by simple mixing. Longer stream residence times during baseflow and changing hydrological flow paths were suggested as potential reasons for this pattern. This study highlights how a simple landscape-mixing model can be used for predictions as well as providing a baseline for residual analysis, which suggest potential mechanisms to be further explored using more focused field and process-based modelling studies.

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