Applies to: @RISK 6.x and Up, Industrial Edition

Time Series Correlation vs. Correlation of Regular Distributions in @RISK

You can correlate different time series in @RISK, but the correlation is often not visible in the displayed (output) numbers. This article explains why.

How @RISK Builds and Projects a Time Series

A time series is created by fitting a model to your real-world historical data. Most time-series models apply transformations—such as differencing or logarithms—before fitting.

Important points:

• @RISK fits transformed data, not the raw historical values.

• The underlying time series is stored and projected using this transformed data.

• Each projected period consists of:

  1. A formula term using previous transformed time-series values.

  2. A noise term (random error) generated during each iteration.

After these are calculated, @RISK reverses the transformation so the numbers shown in Excel look like the real-world data again.
Because of this, displayed values and underlying time-series values differ whenever transforms are used.

How Time Series Correlation Works

You can correlate time series using the Define Correlations window or the RiskCorrmat() function—similar to regular distributions.

However, correlation in time series works differently:

Correlation of Regular Distributions

• Correlation is applied to the full array of simulated values for each distribution across all iterations.

• The correlation structure is global and applies across the entire simulation.

Correlation of Time Series

• Correlation is applied inside each iteration, not across iterations.

• Only the noise terms of the time series are correlated.

• The formula portion of each time period cannot be correlated.

This means the correlation is embedded in the unseen noise terms, not visible in the final displayed values. Even without transforms, the displayed values include both formula and noise, so the correlation is diluted.

Result:
The correlation coefficients you see in the results will not match the correlation you defined.

Can I Correlate Successive Periods of a Single Time Series?

No.
@RISK does not allow correlation of noise terms within a single time series (i.e., period-to-period). Correlation can only be applied between separate time series.

What About Batch-Fit Correlated Time Series?

When you create correlated time series using the Batch Fit tool:

• @RISK produces a correlation matrix based on the historical data you supplied.

• You may edit this matrix—add/remove series, change coefficients, etc.

• Forward projections use these correlations the same way as other time-series correlations:

  • Correlations apply only to the noise terms during each iteration.

Again, these correlated noise terms are not shown directly.

Can I Define a Copula for Time Series?

No.
@RISK currently supports copulas only for regular input distributions, not for time-series array functions.