R:如何拟合时间序列模型，例如"Y(t)＝αX+βY(t-1)"? [英] R: How to fit a time series model such as "Y(t) = αX + βY(t-1)"?

问题描述

如何逐步将此模型拟合到R中?我的范围是对t + 1进行预测.

How do I fit this model in R, step by step? My scope is to make a forecast for t+1.

• Y(t)<-1900年至2000年.
• X<-分数从0到100.
• Y(t-1)<-Y的1阶滞后值.

谢谢.

推荐答案

您的模型是带有协变量 x 的 y 的AR(1)时间序列.我们可以只使用R base中的 arima0 (无缺失值)或 arima (允许缺少值):

Your model is an AR(1) time series for y with covariate x. We can just use arima0 (no missing value) or arima (missing value allowed) from R base:

fit <- arima0(y, order = c(1, 0, 0), xreg = x)

让我们考虑一个小例子:

Let's consider a small example:

set.seed(0)
x <- runif(100)
## intercept: 0.1
## slope of `x`: 1.2
## AR(1) with coefficient 0.5
y <- 0.1 + 1.2 * x + arima.sim(list(ar = 0.5), n = 100, sd = 0.2)

fit <- arima0(y, order = c(1, 0, 0), xreg = x)

#Call:
#arima0(x = y, order = c(1, 0, 0), xreg = x)
#
#Coefficients:
#         ar1  intercept    xreg
#      0.4639     0.0645  1.2139
#s.e.  0.0879     0.0448  0.0590
#
#sigma^2 estimated as 0.03046:  log likelihood = 32.55,  aic = -57.11

请注意，估算值与我们的真实模型相符.

Note the estimate is consistent with our true model.

谢谢.我如何插入更多协变量(x1，x2等)，以防万一?

Thanks. How do I insert more covariates (x1,x2,etc.), just in case?

看看?arima0 (或?arima ):

xreg: Optionally, a vector or matrix of external regressors, which
      must have the same number of rows as ‘x’.

您可以通过 xreg 指定模型矩阵.假设在数据框 dat 中有回归变量 x1 ， x2 ， x3 ，则可以生成此模型矩阵通过:

You can specify a model matrix via xreg. Suppose you have regressors x1, x2, x3, in a data frame dat, you can generate this model matrix via:

X <- model.matrix(~ x1 + x2 + x3, dat)

然后

fit <- arima0(y, order = c(1, 0, 0), xreg = X)

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