相关论文: Propagation of Memory Parameter from Durations to …
In this work we propose a new class of long-memory models with time-varying fractional parameter. In particular, the dynamics of the long-memory coefficient, $d$, is specified through a stochastic recurrence equation driven by the score of…
Earlier we proposed the stochastic point process model, which reproduces a variety of self-affine time series exhibiting power spectral density S(f) scaling as power of the frequency f and derived a stochastic differential equation with the…
This article deals with detection of nonconstant long memory parameter in time series. The null hypothesis presumes stationary or nonstationary time series with constant long memory parameter, typically an I(d) series with d>-.5. The…
We consider Stochastic Volatility processes with heavy tails and possible long memory in volatility. We study the limiting conditional distribution of future events given that some present or past event was extreme (i.e. above a level which…
We establish new results for estimation and inference in financial durations models, where events are observed over a given time span, such as a trading day, or a week. For the classical autoregressive conditional duration (ACD) models by…
We study the asymptotic behaviour of different statistics for time series exhibiting long memory and nonstationarity. For processes with memory parameter $d\in(-1/2,3/2)$, we derive the joint limiting distribution of discrete Fourier…
We propose a constructive approach to building temporal point processes that incorporate dependence on their history. The dependence is modeled through the conditional density of the duration, i.e., the interval between successive event…
Agents' heterogeneity is recognized as a driver mechanism for the persistence of financial volatility. We focus on the multiplicity of investment strategies' horizons, we embed this concept in a continuous time stochastic volatility…
This note develops a stochastic model of asset volatility. The volatility obeys a continuous-time autoregressive equation. Conditions under which the process is asymptotically stationary and possesses long memory are characterised.…
We present a simple game model where agents with different memory lengths compete for finite resources. We show by simulation and analytically that an instability exists at a critical memory length, and as a result, different memory lengths…
The propagator for the activity in a broad class of self-organized critical models obeys an imaginary-time Schr\"odinger equation with a nonlocal, history-dependent potential representing memory. Consequently, the probability for an…
This paper investigates the continuous-time limit of score-driven models with long memory. By extending score-driven models to incorporate infinite-lag structures with coefficients exhibiting heavy-tailed decay, we establish their weak…
This paper introduces the Markov-Switching Multifractal Duration (MSMD) model by adapting the MSM stochastic volatility model of Calvet and Fisher (2004) to the duration setting. Although the MSMD process is exponential $\beta$-mixing as we…
In this paper, change-point problems for long memory stochastic volatility models are considered. A general testing problem which includes various alternative hypotheses is discussed. Under the hypothesis of stationarity the limiting…
We propose to describe the dynamics of phase transitions in terms of a non-stationary Generalized Langevin Equation for the order parameter. By construction, this equation is non-local in time, i.e.~it involves memory effects whose…
Motivated by studies on the recurrent properties of animal and human mobility, we introduce a path-dependent random walk model with long range memory for which not only the mean square displacement (MSD) can be obtained exactly in the…
Autoregressive conditional duration (ACD) models are primarily used to deal with data arising from times between two successive events. These models are usually specified in terms of a time-varying conditional mean or median duration. In…
In this paper, we show that the adaptive multidimensional increment ratio estimator of the long range memory parameter defined in Bardet and Dola (2012) satisfies a central limit theorem (CLT in the sequel) for a large semiparametric class…
The diffusion equation is extended by including spatial-temporal memory in such a manner that the conservation of the concentration is maintained. The additional memory term gives rise to the formation of non-trivial stationary solutions.…
Long memory or long range dependency is an important phenomenon that may arise in the analysis of time series or spatial data. Most of the definitions of long memory of a stationary process $X=\{X_1, X_2,\cdots,\}$ are based on the…