Time-Varying Ordinary Least Squares

Source: R/tvOLS.R

tvOLS estimate time-varying coefficient of univariate linear models using the kernel smoothing OLS.

tvOLS(x, ...)

# S3 method for matrix
tvOLS(
  x,
  y,
  z = NULL,
  ez = NULL,
  bw,
  est = c("lc", "ll"),
  tkernel = c("Triweight", "Epa", "Gaussian"),
  singular.ok = TRUE,
  ...
)

# S3 method for tvlm
tvOLS(x, ...)

# S3 method for tvar
tvOLS(x, ...)

# S3 method for tvvar
tvOLS(x, ...)

Arguments

x

An object used to select a method.
...

Other arguments passed to specific methods.
y

A vector with dependent variable.
z

A vector with the variable over which coefficients are smooth over.
ez

(optional) A scalar or vector with the smoothing values. If values are included then the vector z is used.
bw

A numeric vector.
est

The nonparametric estimation method, one of "lc" (default) for linear constant or "ll" for local linear.
tkernel

A character, either "Triweight" (default), "Epa" or "Gaussian" kernel function.
singular.ok

Logical. If FALSE, a singular model is an error.

Value

tvOLS returns a list containing:

coefficients

A vector of length obs, number of observations time observations.

fitted

A vector of length obs with the fitted values from the estimation.

residuals

A vector of length obs with the residuals from the estimation.

See also

bw for bandwidth selection, tvLM and tvAR.

Examples

tau <- seq(1:500)/500
beta <- data.frame(beta1 = sin(2*pi*tau), beta2 = 2*tau)
X <- data.frame(X1 = rnorm(500), X2 = rchisq(500, df = 4))
error <- rt(500, df = 10)
y <- apply(X*beta, 1, sum) + error
coef.lm <- stats::lm(y~0+X1+X2, data = X)$coef
coef.tvlm <-  tvOLS(x = as.matrix(X), y = y, bw = 0.1)$coefficients
plot(tau, beta[, 1], type="l", main="", ylab = expression(beta[1]), xlab = expression(tau),
ylim = range(beta[,1], coef.tvlm[, 1]))

abline(h = coef.lm[1], col = 2)

lines(tau, coef.tvlm[, 1], col = 4)

legend("topright", c(expression(beta[1]), "lm", "tvlm"), col = c(1, 2, 4), bty="n", lty = 1)