Time Serise Analysis［Using R］

Posted 2022-11-06 ZJun310

Time Serise Analysis［Using R］

［近期需要用到时间序列分析，顺便整理下笔记以供日后参考］

时间序列分析基本流程

  时间序列分析在R中的实战分析

1. #### 导入数据

# Get Work Directory
getwd()
# Import Data From local File
Data <- read.csv('~/Documents/data.csv', fill = TRUE, header = TRUE)
# Use data which is incorporated in R
Data  <- AirPassengers
#Generate Data
t = ts(seq(1,30))
Date_List <- seq(from = as.Date('2016-9-1'),by=1,length.out = 30)
Data = data.frame(Date_List,t)

1. 可视化数据

   可视化时间序列数据的目的在于分析数据的趋势性、季节性以及它的随机表现

   plot(AirPassengers)
   abline(reg=lm(AirPassengers~time(AirPassengers)))

   

2. 平稳化时间序列

   时间序列的平稳性有3个基本的判别准则

   1. The mean of the series should not be a function of time rather should be a constant.

      

   2. The variance of the series should not a be a function of time. This property is known as homoscedasticity.

      

   3. The covariance of the i th term and the (i + m) th term should not be a function of time.

      

   
   # Dickey Fuller Test of Stationarity
   
   
   # AR or MA are not applicable on non-stationary series.
   
   install.packages('fUnitRoots')
   library(fUnitRoots)
   adfTest(AirPassengers)
   
   
   # Result
   
   Title:
   Augmented Dickey-Fuller Test
   
   Test Results:
    PARAMETER:
      Lag Order: 1
    STATISTIC:
      Dickey-Fuller: -0.3524
    P VALUE:
      0.5017 

   将时间序列平稳化的三个基本技巧

   1. Detrending

      Here, we simply remove the trend component from the time series. (If We Know the trend component)

   2. Differencing

   3. Seasonality

      Seasonality can easily be incorporated in the ARIMA model directly

   adfTest(diff(log(AirPassengers)))
   
   
   # Result
   
   Title:
   Augmented Dickey-Fuller Test
   
   Test Results:
    PARAMETER:
      Lag Order: 1
    STATISTIC:
      Dickey-Fuller: -8.8157
    P VALUE:
      0.01 

   ​

3. 依据ACF、PACF寻找合适的参数

   Once we have got the stationary time series, we must answer two primary questions:

   Q1. Is it an AR or MA process?

   Q2. What order of AR or MA process do we need to use?

   Simple Example:

   • AR : [x(t) = alpha * x(t – 1) + error (t)]
   • MA : [x(t) = beta * error(t-1) + error (t)]

   acf(diff(log(AirPassengers))) # FOR Parameters p (MA Model)

   

   pacf(diff(log(AirPassengers))) # FOR Parameters q (AR Model)

   

   Clearly, ACF plot cuts off after the first lag. Hence, we understood that value of p should be 0 as the ACF is the curve getting a cut off. While value of q should be 1 or 2. After a few iterations, we found that (0,1,1) as (p,d,q) comes out to be the combination with least AIC and BIC.

4. 建立ARIMA模型

   The value found in the previous section might be an approximate estimate and we need to explore more (p,d,q) combinations. The one with the lowest BIC and AIC should be our choice.

   fit <- arima(log(AirPassengers), c(0, 1, 1),seasonal = list(order = c(0, 1, 1), period = 12))
   
   # d choose 1 because diff's order is 1
   

5. 模型预测

   pred <- predict(fit, n.ahead = 10*12)
   ts.plot(AirPassengers,2.718^pred$pred, log = "y", lty = c(1,3))

   

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Reference :A Complete Tutorial on Time Series Modeling in R