Univariate forecasts

Univariate Projections

Ferra often produces univariate projections, mostly for monthly but also for quarterly econometric time series. Here, the term univariate refers to the fact that the projections are made in isolation, whereas multivariate projections are made using an interdependent model, the solution of one variable being determined by the solution of another, so that the model needs to be solved iteratively.

Univariate projections are prepared via a weighted combination of several time series type projection models, as described in this article. This method allows the expert preparing the projections to alter the combination of weights according to the most recent information available as well as to a degree of arbitrary, subjective judgement.

Such univariate projections provide good accuracy in the short term and are relatively easy to prepare. The small scale macro model that is used for longer term projections is calibrated to agree with the univariate models during the fisrt few out of sample points.

Because these models are mostly used for shorter term projections, they are also known as short term projection models and are also discussed here.

Below are some screenshots taken from the univariate projection process.

Weight allocation

Univariate model weight allocation

In this example a spreadsheet is used to edit the weights allocated to each of the various univariate models.

Projection table

Univariate model output table

This table shows the projection results. It displays actual projections and also calculate year on year and month on month growth rates.

Projection graph

Univariate model projection graph

This plot of the projection results, calculated to a year on year growth rate, shows not only the expected outcome, but also the asymetric confidence levels around the projection.

Interpretation

US economic growth rate projection

Note how economic growth falters and falls away from trend growth. If the upper band represents a highly favourable scenario, then a return to trend growth is possible, but not likely. Also note the V shaped recovery.

Accuracy

Univariate projection accuracy

The accuracy of all univariate models are noted and investigated over time. The accuracy has been very good and these models are also good at detecting turning points early.