stepar {aTSA}  R Documentation 
Stepwise Autoregressive Model
Description
Fit a stepwise autoregressive model
Usage
stepar(y, xreg = NULL, trend = c("linear", "quadratic", "constant"),
order = NULL, lead = 0, newx = NULL, output = TRUE, ...)
Arguments
y 
a numeric vector of response 
xreg 
a numeric vector or matrix of exogenous input variables. The default is

trend 
the type of trend with respective to time. The default is 
order 
the order to fit the AR model for residuals. The default is 
lead 
the number of steps ahead for which prediction is required.
The default is 
newx 
a matrix of new data of 
output 
a logical value indicating to print the results in R console. The default is

... 
additional arguments for 
Details
The stewise autoregressive model uses a twostage procedure to fit time series.
The first stage is to fit a (constant
,linear
,quadratic
)
model with respective to time sequence:
t = (1:n)/n
, where n = length(y)
. If xreg
is supplied,
the fitted model is updated by
y = \mu + \beta*xreg + e[t]
for trend = "constant"
, and
y = \mu + \beta*xreg + \alpha*t + e[t]
for trend = "linear"
, and
y = \mu + \beta*xreg + \alpha[1]*t + \alpha[2]*t^2 + e[t]
for trend = "quadratic"
.
The second stage is to fit an autoregressive process to the residuals of the fitted
model obtained in the first stage, which is accomplished by using ar
function
in stats
package.
Value
A list with class "stepar
" containing the following components:
coef 
a estimated coefficient matrix including the ttest results. 
sigma 
the square root of the estimated variance of the random error. 
R.squared 
the R^2 for fitted model in the first stage. 
pred 
the predictions, only available for 
Note
If lead
> 0 and xreg
is supplied, newx
must also be
supplied in order to make a prediction. The newx
must be a matrix with
the same number of columns as xreg
and the number of rows being
equal to lead
. The predictions should be used with cautions.
Author(s)
Debin Qiu
Examples
x < 5*(1:100)/100
x < x + arima.sim(list(order = c(1,0,0),ar = 0.4),n = 100)
stepar(x)
stepar(x,order = 1)
# with xreg supplied
X < matrix(rnorm(200),100,2)
y < 0.1*X[,1] + 1.2*X[,2] + rnorm(100)
stepar(y,X)
# make a prediction with lead = 1; used with caution.
newdat1 < matrix(rnorm(2),nrow = 1)
fit1 < stepar(y,X,lead = 1,newx = newdat1,output = FALSE)
# make a prediction with lead = 2; used with caution.
newdat2 < matrix(rnorm(4),nrow = 2)
fit2 < stepar(y,X,lead = 2,newx = newdat2,output = FALSE)