Multifractal spectrum of branching random walks on free groups
Consider a symmetric branching random walk on a free group $\mathbb{F}$ in the transient regime $1 0$ for $1<r<R$, whereas $α(R)=0$.
math.PR↗
arXiv subjects
Shuwen Lai
Publications and source records attributed to Shuwen Lai.
Self-normalized tests for multistep conditional predictive ability
This paper proposes self-normalized tests for multistep conditional predictive ability in forecast comparison. By normalizing the sample mean of the transformed loss differential using functionals of its cumulative sum (CUSUM) process, specifically an adjusted-range normalizer for scalars and a matrix normalizer for vectors, our approach avoids direct estimation of the long-run covariance matrix. Consequently, it eliminates the need for the ad hoc bandwidth, kernel, and lag-truncation choices required by traditional methods. We establish the asymptotic theory for these statistics, deriving pivotal null limiting distributions and proving test consistency. Monte Carlo simulations show that the proposed tests effectively mitigate the finite-sample size distortions associated with traditional heteroskedasticity and autocorrelation consistent (HAC) methods, while retaining strong empirical power against conditional predictability alternatives.
math.ST↗
Sample Path Large Deviations for Random Walks on Regular Trees
This paper investigates the large deviation problem in the sample path space of the nearest-neighbor random walks on regular trees. We establish the sample path large deviation principle for the law of the distance from a nearest random walk on a regular tree to the root with a good convex rate function. Furthermore, we derive an implicit expression for the rate function via the Fenchel-Legendre transform of the log-moment generating function.
math.PR↗