Decomposition of Japanese Yen Interest Rate Data through Local Regression

Seven di erent Japanese Yen interest rates recorded on a daily basis for the period from 1986 to 1992 are simultaneously analyzed. By introducing a new concept of \short term trend", we decompose each interest rate series into three components, \long term trend", \short term trend" and \irregular" by a two step lowess smoothing procedure. Furthermore, a multivariate autoregressive model (MAR) is tted to the seven irregular series. The decomposition and the model tting were quite satisfactory, and each component and the residuals of the MAR model are statistically well behaved. Thus it enables us to understand well various aspects of interest rate series from those trends, the MAR(2) coe cients, and its residuals. The result is compared with the decomposition through sabl and the advantages of our procedure will be discussed in relations to other parametric model tting like ARCH or GARCH. Based on the decomposition we can have better daily prediction and more stable long term forecasting.