论文检索

季节性时间序列模型中非平稳参数设定的检验AI 解读

Let $Y_t$ be an autoregressive process satisfying $Y_t = \alpha_1 Y_{t - 1} + \alpha_2 Y_{t - d} + \alpha_3 Y_{t - d - 1} + e_t$, where $\{e_t\}^\infty_{t = 0}$ is a sequence of $\operatorname{iid}(0, \sigma^2)$ random variables and $d \geq 2$. Such processes have been used as parametric models for seasonal time series. Typical values of $d$ are 2, 4, and 12 corresponding to time series observed semi-annually, quarterly, and monthly, respectively. If $\alpha_1 = 1, \alpha_2 = 1, \alpha_3 = - 1$…

随机差分方程的参数估计AI 解读

Let $Y_t$ satisfy the stochastic difference equation $Y_t = \sum^q_{i=1} \psi_{ti} \alpha_i + \sum^p_{j=1} \gamma_j Y_{t-j} + e_t,$ where the $\{\psi_{ti}\}$ are fixed sequences and (or) weakly stationary time series and the $e_t$ are independent random variables, each with mean zero and variance $\sigma^2$. The form of the limiting distributions of the least squares estimators of $\alpha_i$ and $\gamma_j$ depend upon the absolute value of the largest root of the…

摘要暂缺

摘要暂缺

单整 ARMA 过程样本自相关的渐近分布AI 解读

The behavior of the sample autocorrelation function, r(k), for an integrated autoregressive moving average time series is examined. The nonnormal asymptotic distribution of r(k) is characterized as a function of lag k and the parameters of the process. The validity of the approximation in moderate-sized samples is examined.

摘要暂缺

含单位根的自回归过程估计AI 解读

Let $Y_t$ satisfy the stochastic difference equation $Y_t = \sum^p_{j = 1}\eta_jY_{t - j} + e_t$ for $t = 1, 2, \cdots$, where the $e_t$ are independent identically distributed $(0, \sigma^2)$ random variables and the initial conditions $(Y_{-p + 1}, Y_{-p + 2}, \cdots, Y_0)$ are fixed constants. It is assumed the true, but unknown, roots $m_1, m_2, \cdots, m_p$ of $m^p - \sum^p_{j = 1}\eta_jm^{p - j} = 0$ satisfy $m_1 = m_2 = 1$ and $|m_j| < 1$ for $j = 3, 4, \cdots, p$.…