Time Series Analysis - Univariate Box-Jenkins ARIMA Models（时间序列预测的ARIMA模型）

Models in Time Series Analysis enable the user to generate:

forecasts

of a (dependent) time series that is based upon the information of its own past,

explain

events that occurred in the past, and provide insight into the dynamical

interrelationships

between variables.

时间序列的分析模型可以用于：基于以前的数据预测时间序列，解释过去事件，深入的分析变量间的动态关系。

In the following sections we describe the development of

Autoregressive Integrated Moving Average

models (short: ARIMA),

Transfer Function-Noise

models, and

Multivariate Time Series Models

according to the methodologies proposed by

Box and Jenkins

and many other scientists.

下面我们根据

Box and Jenkins

和一些其他科学家的研究讲述：ARIMA模型；Transfer Function-Noise 模型；

Multivariate Time Series 模型；

For obvious reasons these methodologies can only apply to time series. Above that, the steps or intervals of the time series under investigation are always supposed to be

equally spaced

in time (which is an important restriction).

因为显而易见的原因，这些模型只能用于时间序列。更重要的是对于时间序列的研究，我们是基于这样一个前提的：时间序列的间隔是等长的。

Furthermore we assume that each observation of the time series has the same expectation function, standard deviation, and probability distribution function.

此外，我们还假定，这些时间序列有这相同的期望函数，标准偏差和相同的概率分别函数；

Since the Box-Jenkins methodology uses Maximum Likelihood Estimation (MLE), it is obvious that a distribution has to be assumed about the error term. In practice we will assume a

white noise

error component, which is a sequence of uncorrelated stochastic variables with a fixed (normal) distribution, a mathematical expectation of zero, and constant variance.

由于使用了最大概似法（MLE），显然需要假定一个错误量。实践中我们使用了白噪音作为错误的组成，它是由一系列不相关随机变量组成，有着正规的分布，数学期望为0和不变的常量（？？）。