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.

The aim of this paper is to select an appropriate ARIMA model for the time series after transforming the original responses. Box-Cox and Yeo-Johnson power transformation models were used on the response variables of two time series datasets of average temperatures and then diagnosed and built the appropriate ARIMA models for each time-series. The authors treat the results of the model fitting as a package in an attempt to decide and choose the best model by diagnosing the effect of the data transformation on the response normality, significant of estimated model parameters, forecastability and the behavior of the residuals. The authors conclude that the Yeo-Johnson model was more flexible in smoothing the data and contributedto accessing a simple model with good forecastability.

In nonparametric analyses, many authors indicate that the kernel density functions work well when the variable is close to the Gaussian shape. This chapter interest is on the improvement the forecastability of the functional nonparametric time series by using a new approach of the parametric power transformation. The choice of the power parameter in this approach is based on minimizing the mean integrated square error of kernel estimation. Many authors have used this criterion in estimating density under the assumption that the original data follow a known probability distribution. In this chapter, the authors assumed that the original data were of unknown distribution and set the theoretical framework to derive a criterion for estimating the power parameter and proposed an application algorithm in two-time series of temperature monthly averages.

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Outliers are data points or observations that stand out significantly from the rest of the group in terms of size or frequency. They are also referred to as "abnormal data". Before fitting a forecasting model, outliers are often eliminated from the data set, or if not removed, the forecasting model is altered to account for the presence of outliers. The first scenario covered in the study is the detection of outliers when the parameters have been established. Second, where there are unidentified parameters. This article mentions a number of causes for outlier correction and detection in time series analysis and forecasting. For the objective of the study, a time series of the volume of water entering the Dohuk dam reservoir in Dohuk city was used. The study arrived at the following conclusions after conducting their research: first, whenever the critical value increased, the value of residual standard error (with outlier adjustment) increased. Second, the quantity of outlier values dropped each time the critical value was raised. Third, forecasts with outlier correction perform better than forecasts without outlier adjustment when outliers are present.