stepar {aTSA}

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 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.

Details

The stewise autoregressive model uses a two-stage 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 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.

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)