Autocorrelation is the correlation between a time series and its own past values.
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Why it matters
If a series is autocorrelated, current observations contain information about future ones. That is common in macroeconomic, financial, and business data. Inflation, unemployment, and output often move gradually rather than jumping independently from one period to the next.
In econometrics
Autocorrelation matters for both modeling and inference. In a data-generating process it can be a real feature of economic behavior. In regression residuals it can signal misspecification and lead to misleading standard errors if ignored.
For lag (k), the autocorrelation is usually written:
$$
\rho_k = \frac{\gamma_k}{\gamma_0}
$$
where (\gamma_k) is autocovariance at lag (k) and (\gamma_0) is the variance.
Knowledge Check
### Autocorrelation measures:
- [x] how strongly a series is related to its own past values
- [ ] the correlation between two different countries only
- [ ] whether inflation is always positive
- [ ] the slope of a demand curve
> **Explanation:** The concept applies within a single series across time.
### Why can autocorrelation matter in regression residuals?
- [x] Because it can distort standard errors and suggest misspecification
- [ ] Because it guarantees unbiased estimates
- [ ] Because it removes the need for time-series models
- [ ] Because it means the data are cross-sectional
> **Explanation:** Serially correlated errors affect inference and can indicate omitted dynamics.
### A highly persistent macroeconomic series often shows:
- [x] positive autocorrelation
- [ ] no time dependence at all
- [ ] negative variance
- [ ] zero mean by definition
> **Explanation:** Persistence means current values tend to be related to recent past values.