发表机构
Geneva Graduate Institute（日内瓦高等研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对离散采样或时间聚合下的AR(p)过程，推导了其参数识别集，证明并数值验证了关于误差项方差及自回归参数点识别的相关猜想。
AI 中文摘要
本文研究每q个周期观测一次的AR(p)过程，观测形式可为瞬时值（存量变量）或采样区间内的总和（流量变量）。在相当温和的假设下，推导了一般滞后阶数p∈ℕ和采样频率q∈ℕ的识别集，界定了其基数，并提供了计算所有候选点及确定其是否属于识别集的方法。分析支持以下猜想：(i)误差项方差可点识别；(ii)时间聚合下自回归参数可点识别；(iii)离散采样下，奇数采样频率时自回归参数可点识别，偶数采样频率时则可识别至交替符号。本文在部分设定下证明了该猜想，并通过更广泛的数值计算进行了验证。
英文摘要
I consider an AR($p$) process that is observed every $q$ periods, either as a snapshot (stock variable) or as a sum over the sampling interval (flow variable). I first characterize the resulting ARMA process followed by observables. Under fairly mild assumptions, I then derive the identified set for general lag lengths $p \in \mathbb{N}$ and sampling frequencies $q \in \mathbb{N}$, I bound its cardinality, and I provide an algorithm to compute all candidate points and determine their membership in the identified set. My exact but implicit characterization supports the following conjecture that I prove in some settings and verify numerically more broadly: (i) the error term-variance is point-identified, (ii) under temporal aggregation, the autoregressive parameters are point-identified, and (iii) under discrete sampling they are point-identified for odd $q$ and identified up to alternating sign for even $q$. My analysis supplements existing inference results that show consistency and asymptotic Normality of the Gaussian Maximum Likelihood estimator conditional on point-identification. Holding the number of observations fixed, I show that its precision does not necessarily decrease with $q$.
