This article presents a naw approach to study the dynamics of human body balance by way of analyzing two-channel time series record of weights for left and right sides of a standing human. The purpose of the study is to know the mechanism which is maintaining the body balance. Since the raw data suffer from the contamination with low frequency trend components, the mutual relationships of the left and right side weights time series is analyzed using a multivariate nonstationary time series model. With this model: 1) the detrending process can be executed in one stage without pre-manufacturing of the data, and 2) the cyclical component around the trend is assumed to be generated by a vector autoregressive model. The model is fitted by using Kalman filter algorithms to calculate the likelihood of the model and a numerical optimization procedure to maximize the likelihood. The Akaike Information Criterion AIC is used to select the best fit model. The estimated relationship of left and right side sway suggests the impotrance of the feedback for maintaining the body balance. The results clearly show superiority of the present approach over the conventional ones. Our approach is useful from the practical point of view, since it provides a new way of measuring the degree of partial paralytic.
Growth curve models for the analysis of longitudinal data often involve many parameters, which may be the cause of loss of efficiency in the inference or poor interpretation of the results of analysis. This paper proposes to introduce a family of linear structures into the fixed location parameters and the variance-covariance parameters in growth curve models. This leads to the models with fewer unknown paremeters, resulting in increased efficiency and easier interpetation in analysis. A noniterative algorithm is also provided for estimating unknown parameters in the model.