Time Series

Lag One Autocorrelation Calculator

Measures linear association between adjacent observations one period apart. The worked condition keeps the method and source values visible for an independent check.

Time-series inputs

Supply the comparison values for the stated inputs

Separate values with commas, spaces, semicolons, or new lines.
Calculated result

Lag-one autocorrelation

Result
corr(y_t,y_(t−1))

    The design boundary when the sample changes

    Autocorrelation depends on ordering, trend, seasonality, and the chosen window; it is not independent evidence of causation. The page-specific quantity is lag-one autocorrelation.

    The unit of analysis, time order, sample boundary, and treatment of ties or missing values remain outside the answer unless they are entered. Keep those choices beside this time-series result. The chosen lag-one autocorrelation convention remains attached to the source record. Before reusing this result, write down the observed scale, model boundary, and convention behind the displayed value. That record separates a changed dataset from a changed definition and gives the next analyst a clear route back to the original calculation.

    A check on the stated parameter during an independent review

    Check scales and domains before evaluating lag one autocorrelation. Counts, probabilities, rates, windows, and squared units are not interchangeable merely because a field accepts a number.

    If one input changes, predict the direction of the result from the formula first. That catches reversed groups, invalid windows, and parameterization errors. The chosen lag-one autocorrelation convention remains attached to the source record. Before reusing this result, write down the observed scale, model boundary, and convention behind the displayed value. That record separates a changed dataset from a changed definition and gives the next analyst a clear route back to the original calculation.

    A compact route to the answer at the chosen parameters

    Recalculate one intermediate quantity from corr(y_t,y_(t−1)) and work back from the displayed answer. The source values should be enough for another analyst to reproduce lag one autocorrelation.

    Use a boundary case when possible: equal values, a probability near zero, a window of two, or a rate of zero. Expected limiting behavior is often more informative than another decimal place. The chosen lag-one autocorrelation convention remains attached to the source record.

    A note on convention before comparing methods

    The number answers one statistical question. It does not establish causation, model fit, representativeness, or a useful decision threshold by itself. The page-specific quantity is lag-one autocorrelation.

    Practical meaning depends on the measurement scale and consequences. State the comparison or benchmark before presenting lag one autocorrelation as evidence.

    The quantity this page defines when the result is reused

    Autocorrelation depends on ordering, trend, seasonality, and the chosen window; it is not independent evidence of causation. Outliers, dependence, extrapolation, seasonality, or a mismatched convention can change the appropriate method. The page-specific quantity is lag-one autocorrelation.

    Choose an alternative because the design or data require it, not because its result is more favorable. Preserve the selected convention in the report. The chosen lag-one autocorrelation convention remains attached to the source record.

    Where the method applies in the worked condition

    Save the entered values, units, formula version, exclusions, and unrounded output with lag one autocorrelation. A copied number without its condition is not reproducible.

    Round after downstream calculations are complete. Extra digits cannot repair a biased sample, unstable fit, or unsupported distributional assumption. The chosen lag-one autocorrelation convention remains attached to the source record.

    Questions about interpretation under the stated assumptions

    When software results differ, does this result prove a causal relationship?

    No. A robust summary or forecast arithmetic does not replace design, measurement, or substantive reasoning. The reported quantity here is lag-one autocorrelation.

    At the selected scale, what belongs in the saved record?

    Preserve the source data, formula convention, units, exclusions, and method version. The reported quantity here is lag-one autocorrelation.

    For the saved dataset, what should be checked before reusing this result?

    Keep the inputs, units, method name, exclusions, and unrounded output together. The reported quantity here is lag-one autocorrelation.

    At the stated exposure, why might another program return a different number?

    Parameterization, interpolation, tie rules, window placement, and rounding can differ. The reported quantity here is lag-one autocorrelation.