Autocorrelação lag 1
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
About this calculator
Autocorrelation lag 1 evaluates the relationship between a time series and its immediate previous values. It calculates the covariance between original data (x_t) and its one-period lagged version (x_{t-1}), divided by the data variance. This metric is critical for identifying cyclic patterns or serial dependence in series such as sales, prices, or climate data.
The formula is cov(x_t, x_{t-1}) / var(x_t). Values near 1 indicate strong positive correlation (values follow a trend), while values near -1 suggest negative correlation (alternating values). A result close to 0 implies no autocorrelation. This tool is ideal for time series analyses in economics, environmental studies, or any context where temporal dependence is relevant.
Use this calculator when assessing sequential data for influence from prior periods. For example, to forecast demand based on historical patterns or detect seasonality in sales data. Ensure the series is stationary (no unaddressed trends or seasonality) before analysis.
Common precautions include avoiding superficial interpretations of high values, which might mask unobserved patterns. Complement results with partial autocorrelation function (PACF) plots for validation. Avoid use on series with missing data or non-stationarity without proper preprocessing.
Frequently asked questions
Is autocorrelation lag 1 the same as other types of autocorrelation?
No. Lag 1 refers specifically to correlation with the immediate previous period. Higher-lag autocorrelations (e.g., lag 2) analyze relationships with values delayed by more periods.
How does the calculator handle missing data?
It requires a continuous time series. Missing data must be addressed (e.g., interpolated) before calculation.
What does a value close to 0 in lag 1 autocorrelation indicate?
A value near 0 suggests no dependence between the current and immediate previous value, implying randomness in the series.
Should this tool be used on non-stationary series?
Not recommended. Non-stationary series may yield misleading results. Apply transformations (e.g., differencing) to make them stationary first.
When should I not trust the lag 1 autocorrelation result?
Avoid trusting it for series with strong unmodeled seasonality or significant outliers, which can distort the measure.