VoseThielU | Vose Software






Example model

Returns Thiel's inequality coefficient that compares observed with estimated time series values.

  • {Series1} - A series of observed time series values.

  • {Series2} - A series of estimated time series values.

Thiel's inequality coefficient, also known as Thiel's U, provides a measure of how well a time series of estimated values compares to a corresponding time series of observed values. The statistic measures the degree to which one time series ({Xi}, i = 1,2,3, ...n) differs from another ({Yi}, i = 1, 2, 3, ...n). Thiel's U is calculated as:

Thiel's inequality coefficient is useful for comparing different forecast methods: for example, whether a fancy forecast is in fact any better than a naïve forecast repeating the last observed value.

The closer the value of U is to zero, the better the forecast method. A value of 1 means the forecast is no better than a naïve guess.

Note that the formula is symmetric so switching Series1 and Series2 gives the same result.