神经网络和时间序列

神经网络可用于给时间序列变量生成预测。
R中的forecast包可用于实现有单层隐藏层的前馈神经网络，并以滞后输入值预测一元时间序列。

使用R中内置数据集Air Passengers
forecast::nnetar函数的用法和参数
获取帮助

library(forecast)
?nnetar

1.用法
nnetar(y, p, P=1, size, repeats=20, xreg=NULL, lambda=NULL, model=NULL,
    subset=NULL, scale.inputs=TRUE, x=y, ...)

2.参数
y    
A numeric vector or time series.  
数值向量或时间序列
p    
Embedding dimension for non-seasonal time series. Number of non-seasonal lags used as inputs. For non-seasonal time series, the default is the optimal number of lags (according to the AIC) for a linear AR(p) model. For seasonal time series, the same method is used but applied to seasonally adjusted data (from an stl decomposition).   
输入非季节性的滞后阶数
P    
Number of seasonal lags used as inputs.   
输入季节性的滞后阶数
size    
Number of nodes in the hidden layer. Default is half of the number of input nodes (including external regressors, if given) plus 1. 
隐藏层节点的个数
repeats 
Number of networks to fit with different random starting weights. These are then averaged when producing forecasts.
以不同随机权重拟合的网络个数
xreg    
Optionally, a vector or matrix of external regressors, which must have the same number of rows as y. Must be numeric.
用于拟合模型的外部回归
lambda  
Box-Cox transformation parameter.
称作box-cox转换参数

---

建立模型

## 查看下数据
str(AirPassengers)
# fit
fit <- nnetar(AirPassengers,p = 9,P = ,size = 10,repeats = 50,lambda = 0)
# plot
plot(forecast(fit,10))

一个基于神经网络的预测模型生成如下输出结果：

summary(fit)

结果如下：

         Length Class        Mode     
x         144    ts           numeric  
m           1    -none-       numeric  
p           1    -none-       numeric  
P           1    -none-       numeric  
scalex      2    -none-       list     
size        1    -none-       numeric  
lambda      1    -none-       numeric  
subset    144    -none-       numeric  
model      50    nnetarmodels list     
nnetargs    0    -none-       list     
fitted    144    ts           numeric  
residuals 144    ts           numeric  
lags       10    -none-       numeric  
series      1    -none-       character
method      1    -none-       character
call        6    -none-       call     

预测后续的10个区间，图形如下：

forecast(fit,10).png