Improvement of the Nonparametric Estimation of Functional Stationary Time Series Using Yeo-Johnson Transformation with Application to Temperature Curves

Abstract

In this article, Box-Cox and Yeo-Johnson transformation models are applied to two time series datasets of monthly temperature averages to improve the forecast ability. An application algorithm was proposed to transform the positive original responses using the first model and the stationary responses using the second model to improve the nonparametric estimation of the functional time series. The Box-Cox model contributed to improving the results of the nonparametric estimation of the original data, but the results become somewhat confusing after attempting to make the transformed response variable stationary in the mean, while the functional time series predictions were more accurate using the transformed stationary datasets using the Yeo-Johnson model.

A New Approach of Power Transformations in Functional Non-Parametric Temperature Time Series

“…Where K is a kernel function and, h (depending on n) are a positive real bandwidth and dX , X i ðÞ denotes any semi-metric index of proximity between the observed curves based on the functional principal components [5,6,21]. Many authors have proposed a number of methods for measuring the proximity such as, the method of FPCA in which, dX , X i ðÞ is measuring by the square root of the quantity [4,[21][22][23][24][25]).…”

“…Step 3: Transform the original response variable Z according the Finney [11] PT model, Ψ Z ðÞ ¼ Z λ when λ 6 ¼ 0 and BCT model Eq. ( 1) to get the explanatory functional matrices Ψ λ X ðÞ ¼Ψ λ z ðÞ ½ nxτ (for more about the matrices file organizing in the R program, see [5,21]".…”

“…The PT models indicated in the proposed application algorithm have been applied to two examples of nonstationary time series of monthly temperature averages [21]. The first has a size of 200 observations of Nineveh City in Iraq (TSN) for the period 1976 to 2000 (Figure 1a).…”

Develop a Nonlinear Regression Model Using Box-Cox Transformation with Application

“…For a more comprehensive understanding of the array of criteria for optimal power parameter selection, refer to [14] and [15]. The third criterion involves selecting the highest pvalue from the Shapiro-Wilk test for the errors' normality resulting from the estimated nonlinear regression model of the original data vector, as specified by Eq.…”

On the Use of the Power Transformation Models to Improve the Temperature Time Series

“…The first is to perform the transformation before fitting the model [6]. While the second is a complicated procedure because the process of estimating the power parameter is conducted in conjunction with the estimation of the model parameters and the other fitting processes of the model [9,10,11]. This complexity in the second approach results from the fact that the autocorrelation structure of the transformed time series and its variations, is not independent of the selection of the power parameter [12].…”