Autocovariance is the covariance between a time series and one of its own lagged values.
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The definition
For lag (k), the autocovariance is:
$$
\gamma_k = \text{Cov}(y_t, y_{t-k})
$$
In a covariance-stationary process, this depends only on the lag length (k), not on calendar time.
Why it matters
Autocovariance is the raw building block behind autocorrelation and many time-series models. It tells economists how strongly values separated by (k) periods move together before that dependence is normalized by the variance.
Interpretation
Large positive autocovariance means values tend to move together across the relevant lag. Negative autocovariance means high values are often followed by lower ones, or vice versa. Because the scale depends on the units of the data, economists often convert autocovariances into autocorrelations for easier comparison.
Knowledge Check
### Autocovariance measures:
- [x] how a series covaries with its own lagged values
- [ ] how two countries' GDP levels always differ
- [ ] only the mean of a series
- [ ] the slope of a demand curve
> **Explanation:** It is a within-series covariance concept across time lags.
### Why do economists often convert autocovariance into autocorrelation?
- [x] Because autocorrelation is normalized and easier to compare across series
- [ ] Because autocovariance is mathematically invalid
- [ ] Because variance never matters
- [ ] Because time-series models do not use covariance
> **Explanation:** Dividing by variance removes the scale effect.
### In a covariance-stationary series, autocovariance depends on:
- [x] lag length rather than calendar time
- [ ] the current date only
- [ ] whether inflation is high
- [ ] how many countries are in the sample
> **Explanation:** Stationarity means the dependence structure is stable over time.