An autocorrelation coefficient is the numerical correlation between a time series and one of its lagged values.
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The formula
At lag (k), the coefficient is typically:
$$ \rho_k = \frac{\text{Cov}(y_t, y_{t-k})}{\text{Var}(y_t)} $$
for a covariance-stationary process. It tells you how strongly present and past values move together.
How economists use it
Autocorrelation coefficients help identify persistence, cycles, and model structure in time-series data. For example, a slowly declining autocorrelation pattern can suggest strong persistence, while sharp cutoffs can help distinguish different classes of models.
Practical interpretation
Values near 1 indicate strong positive serial dependence, values near 0 suggest weak dependence, and negative values indicate inverse movement across lags.
Related Terms
Knowledge Check
### What does the autocorrelation coefficient at lag 1 describe?
- [x] the relationship between a series and its immediately previous value
- [ ] the correlation between two unrelated variables
- [ ] the slope of a production function
- [ ] the average growth rate of the series
> **Explanation:** Lag 1 compares the series with its one-period lag.
### A coefficient close to 1 usually suggests:
- [x] strong positive persistence
- [ ] no time dependence
- [ ] perfect negative dependence
- [ ] zero variance
> **Explanation:** Large positive autocorrelation means adjacent values tend to move together strongly.
### Why are autocorrelation coefficients useful in model selection?
- [x] They help reveal the dependence pattern across lags
- [ ] They replace all hypothesis tests
- [ ] They guarantee stationarity
- [ ] They apply only to cross-sectional data
> **Explanation:** The pattern of autocorrelations helps economists diagnose and compare time-series models.