weakly stationary

简明释义

弱平稳

英英释义

例句

1.In time series analysis, we often check if the data is weakly stationary 弱平稳的 before applying certain statistical models.

在时间序列分析中，我们通常会检查数据是否是弱平稳的 weakly stationary，然后再应用某些统计模型。

2.To test for weakly stationary 弱平稳的 properties, one might use the Augmented Dickey-Fuller test.

为了检验弱平稳的 weakly stationary特性，可以使用增广的迪基-福勒检验。

3.A series is considered weakly stationary 弱平稳的 if its mean and variance do not change over time.

如果一个序列的均值和方差随时间不变，则该序列被认为是弱平稳的 weakly stationary。

4.Many econometric models assume that the underlying process is weakly stationary 弱平稳的 for valid inference.

许多计量经济模型假设基础过程是弱平稳的 weakly stationary，以便进行有效推断。

5.When performing regression analysis, it is important to ensure that the residuals are weakly stationary 弱平稳的.

在进行回归分析时，确保残差是弱平稳的 weakly stationary是很重要的。

作文

In the field of time series analysis, the concept of weakly stationary plays a crucial role in understanding the behavior of stochastic processes. A time series is said to be weakly stationary if its mean and variance are constant over time, and the covariance between any two time points depends only on the time lag between them, rather than the actual time at which the data was observed. This property allows researchers to make meaningful inferences about the underlying processes governing the data without being misled by trends or seasonal effects. To illustrate the importance of weakly stationary processes, consider the example of stock prices. Stock prices often exhibit random fluctuations; however, if we can assume that these prices are weakly stationary, we can apply various statistical techniques to model and predict future price movements. For instance, the Autoregressive Integrated Moving Average (ARIMA) model relies on the assumption of weakly stationary data to produce reliable forecasts. If the stock prices were not weakly stationary, the predictions made by such models could be significantly off the mark, leading to poor investment decisions. Furthermore, the concept of weakly stationary is essential when it comes to hypothesis testing in econometrics. Many statistical tests, such as the t-test or F-test, require the data to be weakly stationary to ensure valid results. If the data is non-stationary, it may lead to spurious correlations, where two unrelated variables appear to be related due to trends in the data. Therefore, before performing any analysis, researchers must first check for the weakly stationary condition. Techniques such as the Augmented Dickey-Fuller test or the Kwiatkowski-Phillips-Schmidt-Shin test can be employed to determine whether a time series meets the weakly stationary criteria. Moreover, recognizing the characteristics of weakly stationary processes can help in the identification of underlying patterns within the data. For example, if a time series exhibits constant mean and variance, it may indicate that the system is stable and predictable over time. On the other hand, if the time series shows signs of non-stationarity, such as trends or changing variances, it may suggest that external factors are influencing the data, warranting further investigation. In conclusion, the concept of weakly stationary is fundamental in the analysis of time series data. It provides a framework for understanding the stability and predictability of stochastic processes, allowing researchers to apply various statistical methods effectively. By ensuring that the data adheres to the weakly stationary condition, analysts can avoid pitfalls associated with non-stationary data, leading to more accurate insights and decisions. Therefore, mastering the concept of weakly stationary is essential for anyone engaged in time series analysis, whether in finance, economics, or any other field reliant on temporal data.

在时间序列分析领域，“weakly stationary”的概念在理解随机过程的行为中起着至关重要的作用。如果一个时间序列的均值和方差随时间保持不变，并且两个时间点之间的协方差仅依赖于它们之间的时间滞后，而不是实际观察数据的时间，则该时间序列被称为“weakly stationary”。这一特性使研究人员能够对支配数据的潜在过程进行有意义的推断，而不会被趋势或季节性效应误导。为了说明weakly stationary过程的重要性，考虑股票价格的例子。股票价格常常表现出随机波动；然而，如果我们可以假设这些价格是weakly stationary的，我们就可以应用各种统计技术来建模和预测未来的价格变动。例如，自回归积分滑动平均（ARIMA）模型依赖于weakly stationary数据的假设来产生可靠的预测。如果股票价格不是weakly stationary的，那么此类模型所做的预测可能会大相径庭，从而导致投资决策不佳。此外，weakly stationary的概念在计量经济学中的假设检验中也至关重要。许多统计检验，如t检验或F检验，都要求数据是weakly stationary的，以确保结果有效。如果数据是非平稳的，可能会导致虚假的相关性，即两个无关变量由于数据中的趋势而似乎相关。因此，在进行任何分析之前，研究人员必须首先检查weakly stationary条件。可以使用增强型迪基-福勒检验或Kwiatkowski-Phillips-Schmidt-Shin检验等技术来确定时间序列是否符合weakly stationary标准。此外，识别weakly stationary过程的特征可以帮助识别数据中的潜在模式。例如，如果一个时间序列表现出恒定的均值和方差，这可能表明系统在时间上是稳定和可预测的。另一方面，如果时间序列显示出非平稳的迹象，例如趋势或变化的方差，这可能表明外部因素正在影响数据，值得进一步调查。总之，weakly stationary的概念在时间序列数据分析中是基本的。它为理解随机过程的稳定性和可预测性提供了框架，使研究人员能够有效地应用各种统计方法。通过确保数据符合weakly stationary条件，分析师可以避免与非平稳数据相关的陷阱，从而获得更准确的见解和决策。因此，掌握weakly stationary的概念对于任何参与时间序列分析的人来说都是必不可少的，无论是在金融、经济学还是任何其他依赖时间数据的领域。