Time Series 简明教程

Time Series - Modeling

Introduction

一个时间序列有如下 4 个组成部分：

A time series has 4 components as given below −

  1. Level − It is the mean value around which the series varies.

  2. Trend − It is the increasing or decreasing behavior of a variable with time.

  3. Seasonality − It is the cyclic behavior of time series.

  4. Noise − It is the error in the observations added due to environmental factors.

Time Series Modeling Techniques

为了捕捉这些成分，有许多流行的时间序列建模技术。本节对每种技术进行简要介绍，但我们将在即将到来的章节中详细讨论它们−

To capture these components, there are a number of popular time series modelling techniques. This section gives a brief introduction of each technique, however we will discuss about them in detail in the upcoming chapters −

Naïve Methods

这些是简单的估计技术，例如给定的预测值等于时间相关变量的前一个值的平均值，或前一个实际值。它们用于与复杂建模技术进行比较。

These are simple estimation techniques, such as the predicted value is given the value equal to mean of preceding values of the time dependent variable, or previous actual value. These are used for comparison with sophisticated modelling techniques.

Auto Regression

自回归将未来时期的值预测为前一个时期的值的函数。自回归的预测可能比朴素方法更适合数据，但它可能无法解释季节性。

Auto regression predicts the values of future time periods as a function of values at previous time periods. Predictions of auto regression may fit the data better than that of naïve methods, but it may not be able to account for seasonality.

ARIMA Model

自回归综合移动平均模型建模变量的值为前一个值和驻留时间序列前一个时间步长的残差误差的线性函数。但是，实际数据可能是非平稳的并且具有季节性，因此开发了 Seasonal-ARIMA 和 Fractional-ARIMA。ARIMA 在单变量时间序列上工作，为了处理多个变量引入了 VARIMA。

An auto-regressive integrated moving-average models the value of a variable as a linear function of previous values and residual errors at previous time steps of a stationary timeseries. However, the real world data may be non-stationary and have seasonality, thus Seasonal-ARIMA and Fractional-ARIMA were developed. ARIMA works on univariate time series, to handle multiple variables VARIMA was introduced.

Exponential Smoothing

它将变量的值建模为前一个值的指数加权线性函数。这个统计模型也可以处理趋势和季节性。

It models the value of a variable as an exponential weighted linear function of previous values. This statistical model can handle trend and seasonality as well.

LSTM

长短期记忆模型 (LSTM) 是一种循环神经网络，用于时间序列来解释长期依赖关系。它可以使用大量数据进行训练，以捕捉多变量时间序列中的趋势。

Long Short-Term Memory model (LSTM) is a recurrent neural network which is used for time series to account for long term dependencies. It can be trained with large amount of data to capture the trends in multi-variate time series.

所述建模技术用于时间序列回归。在接下来的章节中，让我们一个一个地探讨所有这些。

The said modelling techniques are used for time series regression. In the coming chapters, let us now explore all these one by one.