
Weak convergence of the sequential empirical copula processes under longrange dependence
We consider nonparametric estimation for multivariate copulabased stati...
read it

Differential Entropy Rate Characterisations of Long Range Dependent Processes
A quantity of interest to characterise continuousvalued stochastic proc...
read it

Refinements of BarndorffNielsen and Shephard model: an analysis of crude oil price with machine learning
A commonly used stochastic model for derivative and commodity market ana...
read it

Strong Law of Large Numbers for Functionals of Random Fields With Unboundedly Increasing Covariances
The paper proves the Strong Law of Large Numbers for integral functional...
read it

Quantifying Long Range Dependence in Language and User Behavior to improve RNNs
Characterizing temporal dependence patterns is a critical step in unders...
read it

Director Field Model of the Primary Visual Cortex for Contour Detection
We aim to build the simplest possible model capable of detecting long, n...
read it

A Statistical Investigation of Long Memory in Language and Music
Representation and learning of longrange dependencies is a central chal...
read it
On almost sure limit theorems for detecting longrange dependent, heavytailed processes
Marcinkiewicz strong law of large numbers, n^1/p∑_k=1^n (d_k d)→ 0 almost surely with p∈(1,2), are developed for products d_k=∏_r=1^s x_k^(r), where the x_k^(r) = ∑_l=∞^∞c_kl^(r)ξ_l^(r) are twosided linear process with coefficients {c_l^(r)}_l∈ℤ and i.i.d. zeromean innovations {ξ_l^(r)}_l∈ℤ. The decay of the coefficients c_l^(r) as l→∞, can be slow enough for {x_k^(r)} to have long memory while {d_k} can have heavy tails. The longrange dependence and heavy tails for {d_k} are handled simultaneously and a decoupling property shows the convergence rate is dictated by the worst of longrange dependence and heavy tails, but not their combination. The results provide a means to estimate how much (if any) longrange dependence and heavy tails a sequential data set possesses, which is done for real financial data. All of the stocks we considered had some degree of heavy tails. The majority also had longrange dependence. The Marcinkiewicz strong law of large numbers is also extended to the multivariate linear process case.
READ FULL TEXT
Comments
There are no comments yet.