prais (version 1.0.0)

prais_winsten: Prais-Winsten Estimator for AR(1) Serial Correlation

Description

The Prais-Winsten estimator takes into account AR(1) serial correlation of the errors in a linear regression model. The procedure recursively estimates the coefficients and the error autocorrelation of the specified model until sufficient convergence of the AR(1) coefficient is reached. All estimates are obtained by OLS.

Usage

prais_winsten(formula, max_iter = 50L, tol = 1e-06, twostep = FALSE, ...)
# S3 method for prais
print(x, digits = max(3L, getOption("digits") - 3L), ...)

Arguments

formula

an object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted.

max_iter

integer specifying the maximum number of allowed iterations. Default is 50.

tol

numeric specifying the maximum absolute difference between the estimator of rho in the current and the previous iteration that has to be attained to reach convergence. Default is 1e-6.

twostep

logical. If TRUE, the estimation will stop after the first iteration.

...

further arguments passed to or from other methods.

x

an object of class "prais", usually, a result of a call to prais_winsten.

digits

the number of significant digits to use when printing.

Value

a list of class "prais" containing the following components:

coefficients

a named vector of coefficients.

rho

the values of the AR(1) coefficient \(\rho\) from all iterations.

residuals

the residuals, that is the response minus the fitted values.

fitted.values

the fitted mean values.

rank

the numeric rank of the fitted linear model.

df.residual

the residual degrees of freedom.

call

the matched call.

model

the original model frame, i.e., before the Prais-Winsten transformation.

Methods (by generic)

• print:

References

Prais, S. J. and Winsten, C. B. (1954): Trend Estimators and Serial Correlation. Cowles Commission Discussion Paper, 383 (Chicago).

Wooldridge, J. M. (2013): Introductory Econometrics. A Modern Approach. 5th ed. Mason, OH: South-Western Cengage Learning Cengage.

Examples

# NOT RUN {
# Generate an artificial sample
set.seed(1234567)
n <- 100
x <- sample(20:40, n, replace = TRUE)
rho <- .5
u <- rnorm(n, 0, 5)
for (i in 2:n) {
  u[i] <- u[i] + rho * u[i - 1]
}
pw_sample <- data.frame("x" = x, "y" = 10 + 1.5 * x + u)

# Estimate
pw <- prais_winsten(y ~ x, data = pw_sample)
summary(pw)

# }