On the Use of Yeo-Johnson Transformation in the Functional Multivariate Time Series

Box-Cox and Yeo-Johnson transformation models were utilized in this paper to use density function to improve multivariate time series forecasting. The K-Nearest Neighbor function is used in our model, with automatic bandwidth selection using a cross-validation approach and semi-metrics used to measure the proximity of functional data. Then, to decorrelate multivariate response variables, we use principal component analysis. The methodology was applied on two time series data examples with multiple responses. The first example includes three time series datasets of the monthly average of Humidity (H), Rainfall (R) and Temperature (T). The simulation studies are provided in the second example. Mean square errors of predicted values were calculated to show forecast efficiency. The results have proved that applying multivariate nonparametric time series transformed stationary datasets using the Yeo-Johnson model more efficient than applying the univariate nonparametric analysis to each response independently.