Variogram
Topic of Dependence along a series, part of Time series
Variogram
| Type | Topic |
| Taught in | Dependence along a series |
| Part | Time series |
\operatorname{Var}(X_s-X_t) as a function of the times, equal to 2(\gamma_0-\gamma_{t-s}) for a weakly stationary process. It can exist when the covariance function does not, because a difference can be well behaved when the level is not.
In Dependence along a series
The variogram looks at the change rather than the level: \mathrm{Var}(X_s-X_t)=2(\gamma_0-\gamma_{t-s}) when the process is weakly stationary. People often care about how much tomorrow moves from today, not about the variance of today’s temperature in isolation. A variogram can exist when the covariance function does not, because the difference X_s-X_t can be well behaved when X_t itself is not.
Used in
See also
Weak stationarity · Covariance · Wold decomposition · Autoregression and moving averages · Stationarity of a time series · Random walk with drift · White noise · Gaussian process