Bootstrap estimate of Kullback-Leibler information for model selection

Estimation of Kullback-Leibler amount of information is a crucial part of deriving a statistical model selection procedure which is based on likelihood principle like AIC. To discriminate nested models, we have to estimate it up to the order of constant while the Kullback-Leibler information itself is of the order of the number of observations. A correction term employed in AIC is an example to ful ll this requirement but it is a simple minded bias correction to the log maximum likelihood. Therefore there is no assurance that such a bias correction yields a good estimate of Kullback-Leibler information. In this paper as an alternative, bootstrap type estimation is considered. We will rst show that both bootstrap estimates proposed by Efron (1983,1986,1993) and Cavanaugh and Shumway(1994) are at least asymptotically equivalent and there exist many other equivalent bootstrap estimates. We also show that all such methods are asymptotically equivalent to a non-bootstrap method, known as TIC (Takeuchi's Information Criterion) which is a generalization of AIC

DECOMPOSITION OF JAPANESE YEN INTEREST RATE DATA THROUGH LOCAL REGRESSION

Abstract. 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, andeachcomponent 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. 1

Decomposition of Japanese Yen Interest Rate Data Through Local Regression

Seven different 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 termtrend’, ‘short term trend’ and ‘irregular’. It is obtained by a two step lowess smoothing technique. After that, a multivariate autoregressive model (MAR) is fitted to the vector valued time series obtained by combining those seven irregular components. The decomposition and MAR model fitting were quite satisfactory. It enables us to understand well various aspects of interest rate series from the trends, the MAR (2) coefficients and its residuals. The result is compared with the decomposition through sabl and the advantages of our procedure will be demonstrated in relations to other parametric model fitting like ARCH or GARCH. Based on the decomposition we can have better daily prediction and more stable long term forecasting. Copyright Kluwer Academic Publishers 1997Decomposition of Times Series, Local Regression, Sabl, Short Term Trend, Smoothing, Yen Interest Rates,

Multiplicative Correlations

Correlation modeling, Factorization of variables, Neural science, Partial correlation, Reduction method,

High-dimensional data visualisation: The textile plot

The textile plot is a parallel coordinate plot in which the ordering, locations and scales of the axes are simultaneously chosen so that the connecting lines, each of which represents a case, are aligned as horizontally as possible. Plots of this type can accommodate numerical data as well as ordered or unordered categorical data, or a mixture of these different data types. Knots and parallel wefts are features of the textile plot which greatly aid the interpretation of the data. Several practical examples are presented which illustrate the potential usefulness of the textile plot as an aid to the interpretation of multivariate data.