Forecasting comparison between two nonlinear models: fuzzy regression versus SETAR

Abstract

In this article, we compare the forecasting performances of the Self-Exciting Threshold Autoregressive (SETAR) model and a fuzzy clustering regression model. The series used in this study are high-frequency financial data in the form of seven major stock prices in the US stock markets; the stock indices from seven world stock trading centres; the daily prices for two important commodities, gold and crude oil; and the daily exchange rate between the Canadian dollar and the US dollar. We find that the two models are not too different from each other in terms of the within-sample fit, but in terms of the forecasting performance, the fuzzy model gives better and stable forecasts.

Keywords:

• one-step-ahead forecast SETAR
• fuzzy set
• fuzzy regression

JEL Classification:

• C10
• C22
• C53
• G10

Acknowledgement

The author thanks Dr. David E.A. Giles for his helpful comments.

Notes

¹It may seem more appropriate to use both lagged series to partition the data into two clusters and cross-check the clustering result. In that case, we might end up with four clusters. However, we found that this refinement did not affect the clustering results.

²The gold price is the London afternoon fixed gold spot price, from 4 January 2000 to 22 April 2005. The crude oil price is the daily WTI Cushing Crude Oil Spot Price, from 6 January 1998 to 18 April 2005. The exchange rate is of the Canadian dollar to one US dollar, from 4 January 1971 to 8 April 2005.

³Partition figures are available upon request.

⁴The details are available from the author.

⁵Given the size of the sample for each series, we do not need to make a small-sample adjustment to the S-test.

⁶The number of cluster should also be optimized to gain a better fit. Feng and Giles (2009) had extended this discussion using a Bayesian approach.