roll.win {desk}

Rolling Window Analysis of a Time Series

Description

Helps to (visually) detect whether a time series is stationary or non-stationary. A time series is a data-generating process with every observation - as a random variable - following a distribution. When expectational value, variance, and covariance (between different points in time) are constant, the time series is indicated as weekly dependent and seen as stationary. This desired property is a requirement to overcome the problem of spurious regression. Since there is no distribution but only one observation for each point in time, adjacent observations will be used as stand-in to calculate the indicators. Therefore, the chosen window should not be too large.

Usage

roll.win(x, window = 3, indicator = c("mean", "var", "cov"), tau = NULL)

Arguments

x

a vector, usually a time series.

window

the width of the window to calculate the indicator.

indicator

character string specifying type of indicator: expected value ("mean"), variance ("var") or covariance ("cov").

tau

number of lags to calculate the covariance. When not specified using "cov", the variance is calculated.

Value

a vector of the calculated indicators.

Note

Objects generated by roll.win() can be plotted using the regular plot() command.

Examples

## Plot the expected values with a window of width 5
exp.values <- roll.win(1:100, window = 5, indicator = "mean")
plot(exp.values)

## Spurious regression example
set.seed(123)
N <- 10^3
p.values <- rep(NA, N)

for (i in 1:N) {
  x <- 1:100 + rnorm(100) # time series with trend
  y <- 1:100 + rnorm(100) # time series with trend
  p.values[i] <- summary(ols(y ~ x))$coef[2,4]
}
sum(p.values < 0.05)/N    # share of significant results (100%)

for (i in 1:N) {
  x <- rnorm(100)         # time series without trend
  y <- 1:100 + rnorm(100) # time series with trend
  p.values[i] <- summary(ols(y ~ x))$coef[2,4]
}
sum(p.values < 0.05)/N    # share of significant results (~ 5%)