白噪音（WN）模型

R 的時間序列分析

David S. Matteson

Associate Professor at Cornell University

白噪音

White Noise（WN）是平穩過程中最簡單的例子。

「弱白」噪音過程具備：

白噪音的時間序列圖：

這也是白噪音的時間序列圖嗎？

# Simulate n = 50 observations from the WN model
WN_1 <- arima.sim(model = list(order = c(0, 0, 0)), n = 50)
head(WN_1)

-0.005052984  0.042669765  3.261154066  
 2.486431235  0.283119322  1.543525773

ts.plot(WN_1)

# Simulate from the WN model with mean = 4, sd = 2
WN_2 <- arima.sim(model = list(order = c(0, 0, 0)), 
                  n = 50, mean = 4, sd = 2)

ts.plot(WN_2)

# Fit the WN model with 
# arima()
arima(WN_2, 
      order = c(0, 0, 0))

Coefficients:
      intercept
         4.0739
s.e.     0.2698
sigma^2 estimated as 3.639

# Calculate the sample 
# mean and sample variance
# of WN
mean(WN_2)

4.0739

var(WN_2)

3.713

R 的時間序列分析