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When work on this project began, the author was a research Fellow at the European University Institute in Florence. The work has benefited from comments by Mike Artis, Wenda Zhang, Fabio Canova, and Denise Osborn. Thanks are also due to Hans lessen for providing the data.
where yt, xt
Imposing a common variance across the regimes makes the differences between the means more pronounced. However, these models do not provide sensible forecasts and are not discussed in this paper.
This is equal to 1/(1 − p11) = 6.2.
This may be due to accounting practises in the contruction of these two series.
These results are available upon request from the author.
Although the vector-switching model does not seem to improve overall the forecasting ability for the coincident cycles it significantly reduces the cost of forecasting in terms of computer time. For the post-sample forecasts the univariate-Markov switching model required 106,42,86 and 125 replications for convergence for IIP, Employment, Income and Sales. When the vector-switching model is used convergence is achieved after only 38 replications. Thus, estimating the parameters in this way leads to a quicker estimation and some improvement in the forecasting ability for two out of the four series.
We have also experimented with a model that restricts the variance to be common across the two regimes. Although the model produces turning points very close to the NBER reference cycle it fails when it comes to forecast the series. The deterioration in the forecasting performance in this case in dramatic.