```
stepar(y, xreg = NULL, trend = c("linear", "quadratic", "constant"),
order = NULL, lead = 0, newx = NULL, output = TRUE, ...)
```

y

a numeric vector of response

xreg

a numeric vector or matrix of exogenous input variables. The default is

`NULL`

.trend

the type of trend with respective to time. The default is

`linear`

.order

the order to fit the AR model for residuals. The default is

`NULL`

.lead

the number of steps ahead for which prediction is required.
The default is

`0`

.newx

a matrix of new data of

`xreg`

for predictions. The default is
`NULL`

.output

a logical value indicating to print the results in R console. The default is

`NULL`

....

additional arguments for

`ar`

function.- A list with class "
`stepar`

" containing the following components: coef a estimated coefficient matrix including the t-test 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 `lead`

> 0.

`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.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)