Name
Title | ||
|---|---|---|
The limit theorem for dependent random variables with applications to autoregression models. |
Abstract | ||
|---|---|---|
This paper studies the autoregression models of order one, in a general time series setting that allows for weakly dependent
innovations. Let {X
t
} be a linear process defined by X
t
= Σ
k=0∞ψ
k
ɛ
t−k
, where {ψ
k
, k ≥ 0} is a sequence of real numbers and {ɛ
k
, k = 0, ±1, ±2, …} is a sequence of random variables. Two results are proved in this paper. In the first result, assuming that
{ɛ
k
, k ≥ 1} is a sequence of asymptotically linear negative quadrant dependent (ALNQD) random variables, the authors find the limiting
distributions of the least squares estimator and the associated regression t statistic. It is interesting that the limiting distributions are similar to the one found in earlier work under the assumption
of i.i.d. innovations. In the second result the authors prove that the least squares estimator is not a strong consistency
estimator of the autoregressive parameter α when {ɛ
k
, k ≥ 1} is a sequence of negatively associated (NA) random variables, and ψ
0 = 1, ψ
k
= 0, k ≥ 1. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1007/s11424-011-8119-z | J. Systems Science & Complexity |
Keywords | Field | DocType |
negatively associated,autoregression models,unit root test.,least squares estimator,unit root test,alnqd,random variable,generation time,strong consistency,autoregressive model | Least squares,Autoregressive model,Random variable,Mathematical optimization,Combinatorics,Regression,Mathematical analysis,t-statistic,Strong consistency,Real number,Mathematics,Estimator | Journal |
Volume | Issue | ISSN |
24 | 3 | 1559-7067 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
8 | ||