Universal Forecasting Schemes-II

In this research investigation, the authors propose two novel schemes such as a Locally Linear Transformations-based Forecasting Scheme and a Classical Forecasting Scheme based on RCB Similarity and Dissimilarity Measures. In the former case of Forecasting Scheme, the Dynamical State Vector of concern is Inner Producted Dimension-Wise with its past time history State Vectors and the Transformations therein connecting this mapped State to its next time instant State are applied on the current State Vector component (Dimension-Wise) as a special kind of KBKN Model of Ensemble Average to predict its next State. A BNB model of recursive schema is used to make the prediction a zero-error prediction as well. Furthermore, its robustness is enhanced considering a three consecutive State Vectors for such mapping analysis-based prediction. In the latter case of forecasting, the RCB model of Similarity and Dissimilarity Measures is used to compute an intermediary One-Step Future Average, i.e., forecast based on the causal and anti-causal triangular decompositions of the given series, which is again distilled with a two elements Future Average based series built in a consecutive chain sense. The same procedure is again applied exhaustively on such consecutive distilled differences till the difference series is an all zeros series. Finally, the basic Future Average forecasts and the difference series forecasts are algebraically balanced to give the next term of the considered series of concern.