arXiv subjects

Sándor Baran

Publications and source records attributed to Sándor Baran.

41 records · Page 3Linked to original sources

arXiv2012

Testing stability in a spatial unilateral autoregressive model

Least squares estimator of the stability parameter $\varrho := |α| + |β|$ for a spatial unilateral autoregressive process $X_{k,\ell}=αX_{k-1,\ell}+βX_{k,\ell-1}+\varepsilon_{k,\ell}$ is investigated. Asymptotic normality with a scaling factor $n^{5/4}$ is shown in the unstable case, i.e., when $\varrho = 1$, in contrast to the AR(p) model $X_k=α_1 X_{k-1}+... +α_p X_{k-p}+ \varepsilon_k$, where the least squares estimator of the stability parameter $\varrho :=α_1 + ... + α_p$ is not asymptotically normal in the unstable, i.e., in the unit root case.

math.ST↗

arXiv2011

Parameter estimation in linear regression driven by a Gaussian sheet

The problem of estimating the parameters of a linear regression model $Z(s,t)=m_1g_1(s,t)+ \cdots + m_pg_p(s,t)+U(s,t)$ based on observations of $Z$ on a spatial domain $G$ of special shape is considered, where the driving process $U$ is a Gaussian random field and $g_1, \ldots, g_p$ are known functions. Explicit forms of the maximum likelihood estimators of the parameters are derived in the cases when $U$ is either a Wiener or a stationary or nonstationary Ornstein-Uhlenbeck sheet. Simulation results are also presented, where the driving random sheets are simulated with the help of their Karhunen-Loève expansions.

math.ST↗

arXiv2011

Parameter estimation in a spatial unit root autoregressive model

Spatial unilateral autoregressive model $X_{k,\ell}=αX_{k-1,\ell}+βX_{k,\ell-1}+γX_{k-1,\ell-1}+ε_{k,\ell}$ is investigated in the unit root case, that is when the parameters are on the boundary of the domain of stability that forms a tetrahedron with vertices $(1,1,-1), \ (1,-1,1),\ (-1,1,1)$ and $(-1,-1,-1)$. It is shown that the limiting distribution of the least squares estimator of the parameters is normal and the rate of convergence is $n$ when the parameters are in the faces or on the edges of the tetrahedron, while on the vertices the rate is $n^{3/2}$.

math.ST↗

arXiv2010

On the variances of a spatial unit root model

The asymptotic properties of the variances of the spatial autoregressive model $X_{k,\ell}=αX_{k-1,\ell}+βX_{k,\ell-1}+γX_{k-1,\ell-1}+ε_{k,\ell}$ are investigated in the unit root case, that is when the parameters are on the boundary of domain of stability that forms a tetrahedron in $[-1,1]^3$. The limit of the variance of $n^{-\varrho}X_{[ns],[nt]}$ is determined, where on the interior of the faces of the domain of stability $\varrho=1/4$, on the edges $\varrho =1/2$, while on the vertices $\varrho =1$.

math.ST↗

arXiv2008

On the least squares estimator in a nearly unstable sequence of stationary spatial AR models

A nearly unstable sequence of stationary spatial autoregressive processes is investigated, when the sum of the absolute values of the autoregressive coefficients tends to one. It is shown that after an appropriate norming the least squares estimator for these coefficients has a normal limit distribution. If none of the parameters equals zero than the typical rate of convergence is n.

math.ST↗