autoregressive series

简明释义

1. 自回归级数; 2. 自回归序列;

英英释义

例句

1.An autoregressive series can help identify patterns in economic indicators over time.

一个自回归序列可以帮助识别经济指标随时间变化的模式。

2.In time series analysis, we often model the data as an autoregressive series to capture its temporal dependencies.

在时间序列分析中，我们通常将数据建模为自回归序列以捕捉其时间依赖性。

3.To forecast future sales, we used an autoregressive series model based on historical sales data.

为了预测未来的销售，我们使用了基于历史销售数据的自回归序列模型。

4.The stock prices exhibited characteristics of an autoregressive series, indicating that past prices influence future prices.

股票价格表现出自回归序列的特征，表明过去的价格影响未来的价格。

5.The researcher found that the climate data could be effectively modeled as an autoregressive series.

研究人员发现气候数据可以有效地建模为自回归序列。

作文

In the field of statistics and time series analysis, understanding the concept of an autoregressive series is crucial for forecasting and modeling data. An autoregressive series refers to a type of time series where the current value is based on its previous values. This relationship is established through a mathematical model that uses past observations to predict future outcomes. For instance, if we consider a time series representing monthly sales figures, the sales for the current month may depend on the sales figures from previous months. The autoregressive series model captures this dependency by regressing the current observation on its own lagged values.The fundamental idea behind an autoregressive series is that past events can provide valuable information about future events. This concept is particularly useful in various fields such as economics, finance, and environmental studies, where historical data plays a significant role in decision-making processes. By analyzing an autoregressive series, researchers can identify patterns and trends that help them make informed predictions.To illustrate the workings of an autoregressive series, let’s consider a simple example. Suppose we have a dataset of daily temperatures over a month. If we want to predict tomorrow's temperature, we might look at the temperatures from the previous days. A common approach is to use an autoregressive series model, which could take into account the temperatures from the last three days to forecast the next day’s temperature. Mathematically, this can be expressed as:T(t) = c + φ1 * T(t-1) + φ2 * T(t-2) + φ3 * T(t-3) + ε(t)In this equation, T(t) is the temperature on day t, c is a constant, φ1, φ2, and φ3 are the coefficients that represent the influence of the previous temperatures, and ε(t) is the error term. This model illustrates how the current observation is influenced by its past values, which is the essence of an autoregressive series.One of the key advantages of using an autoregressive series model is its simplicity and effectiveness in capturing temporal dependencies. However, it is important to note that the model assumes that the underlying process remains stationary, meaning that the statistical properties do not change over time. If the series exhibits trends or seasonality, additional techniques may be required to account for these factors.Moreover, the choice of the order of the autoregressive series model, often denoted as AR(p), where p represents the number of lagged observations included, is critical. Selecting the appropriate order can significantly affect the model’s performance. Techniques such as the Akaike Information Criterion (AIC) or Bayesian Information Criterion (BIC) can assist in determining the optimal order by balancing model fit and complexity.In conclusion, the concept of an autoregressive series serves as a foundational element in time series analysis. By leveraging past observations to inform future predictions, it provides a powerful tool for understanding dynamic systems. Whether in business forecasting or climate modeling, mastering the principles of autoregressive series can enhance our ability to make data-driven decisions and improve our predictive accuracy.

在统计学和时间序列分析领域，理解自回归序列的概念对于预测和建模数据至关重要。自回归序列指的是一种时间序列，其中当前值基于其先前的值。这种关系通过一个数学模型建立，该模型利用过去的观察值来预测未来的结果。例如，如果我们考虑一个代表月销售数字的时间序列，则当前月份的销售额可能依赖于前几个月的销售数字。自回归序列模型通过将当前观察值回归到其自身的滞后值上来捕捉这种依赖性。自回归序列背后的基本思想是，过去的事件可以为未来的事件提供有价值的信息。这个概念在经济学、金融学和环境研究等多个领域特别有用，因为历史数据在决策过程中发挥着重要作用。通过分析自回归序列，研究人员可以识别出帮助他们做出明智预测的模式和趋势。为了说明自回归序列的工作原理，让我们考虑一个简单的例子。假设我们有一个代表一个月内每日气温的数据集。如果我们想预测明天的气温，我们可能会查看前几天的气温。一个常见的方法是使用自回归序列模型，它可能考虑过去三天的气温来预测下一天的气温。在数学上，这可以表示为：T(t) = c + φ1 * T(t-1) + φ2 * T(t-2) + φ3 * T(t-3) + ε(t)在这个方程中，T(t)是第t天的气温，c是一个常数，φ1、φ2和φ3是表示先前气温影响的系数，而ε(t)是误差项。这个模型说明了当前观察值如何受到过去值的影响，这正是自回归序列的本质。使用自回归序列模型的一个主要优点是其简单性和有效性，能够捕捉时间依赖性。然而，需要注意的是，该模型假设基础过程保持平稳，这意味着统计特性不会随时间变化。如果序列表现出趋势或季节性，可能需要额外的技术来考虑这些因素。此外，自回归序列模型的阶数选择，通常表示为AR(p)，其中p代表包含的滞后观察值的数量，是至关重要的。选择适当的阶数可以显著影响模型的性能。诸如赤池信息量准则（AIC）或贝叶斯信息量准则（BIC）等技术可以帮助确定最佳阶数，通过平衡模型拟合和复杂性。总之，自回归序列的概念作为时间序列分析的基础元素，为利用过去观察值来告知未来预测提供了强大的工具。无论是在商业预测还是气候建模中，掌握自回归序列的原则都可以增强我们做出基于数据的决策能力，提高我们的预测准确性。