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Toggle## Pesaran-Timmermann test

The Pesaran-Timmermann test determines whether a forecast correctly predicts the change in direction of a time series. That is to say its directional precision.

## Description

For any time series ti having n elements, we first define

Now suppose we have a time series yi with n elements which is predicted by zi and define

Under the null hypothesis that z does not predict the direction of change in y (i.e. the sign of yi), we have the following test statistic

The Pesaran-Timmermann test is a one-tailed test in which the critical region (where the null hypothesis is rejected) is the upper tail of the standard normal distribution. So if

1 – NORM.S.DIST(PT, TRUE) < α

we can then reject the null hypothesis and assert with 1 – α confidence that the forecast accurately predicts the sign of yi.

Note that if the sign of all elements of yi (or zi) is the same, then the PT statistic will not be defined.

## Example

Use the Pesaran-Timmermann test to determine whether the predictions in column B of the figure accurately predict the direction of change for the data in column A.

The test proves that the forecast accurately predicts the direction of change in the data.