In the Polynomial Global Approach to Time Series Analysis, the most costly (computationally speaking) step is the finding of the fitting polynomial. Here we present two routines that improve the forecasting. In the first, an algorithm that greatly improves this situation is introduced and implemented. The heart of this procedure is implemented on the specific routine which performs a mapping with great efficiency. In comparison with the similar procedure of the TimeS package developed by Carli et al. (2014), an enormous gain in efficiency and an increasing in accuracy are obtained. Another development in this work is the establishment of a level of confidence in global prediction with a statistical test for evaluating if the minimization performed is suitable or not. The other program presented in this article applies the Shapiro-Wilk test for checking the normality of the distribution of errors and calculates the expected deviation. The development is employed in observed and simulated time series to illustrate the performance obtained. Program summary Program title: LinMapTS Catalogue identifier: AFAJ_v1_0 Program summary URL: http://cpc.cs.qub.ac.ukisummaries/AFAJ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 9850 No. of bytes in distributed program, including test data, etc.: 223921 Distribution format: tar.gz Programming language: Maple 16. Computer: Any capable of running Maple. Operating system: Any capable of running Maple. Tested on Windows ME, Windows XP, Windows 7. RAM: 128 MB bytes Classification: 4.3, 4.9, 5. Nature of problem: Time series analysis and improving forecast capability. Solution method: The basis of the solution method is the result published in [1]. Restrictions: Global variables X [i] are used in the generated map; If more than 2000 vectors are, employed in the global mapping the normality test is not applicable. Unusual features: When many polynomial coefficients are calculated (e.g., 55) their values can be different in distinct computers. These discrepancies do not affect significantly the accuracy in forecasting. Running time: A few seconds are required for the usual applications. (C) 2016 Elsevier B.V. All rights reserved.