The Sama Circular Model on Real Life

Abstract

Mathematics is a universal language. The term "mathematics", is taken from the ancient Greek word; “mathema”; meaning it is the "subject of instruction”. It is the key to understanding all sciences. Mathematical modeling plays a vital role in real life. It converts a real-world problem into mathematical language and helps in decision-making. Mathematical models are classified in many ways. Some of them are, Static; Dynamic; Deterministic, and Stochastic models. A model is said to be “Static” when it does not have a time-dependent component. In contrast, dynamic models contain time-dependent components. Deterministic models are not associated with any randomness whilst the stochastic models do. Hence stochastic models or Statistical Models are more applicable in real life. The Statistical models can be broadly classified into two parts: univariate statistical models and multivariate statistical models. A univariate statistical model is an equation or set of equations explaining the behavior of a single random variable over time. The univariate statistical models are also known as Time Series models. Time series data comprises several components; Trend, Seasonal variations, cyclical variations, and irregular variations. These series follow irregular wave-like patterns. This type of data is common in the fields of, Meteorology, Agriculture, Finance, Economics, Education, Healthcare, and more. The Decomposition technique and the Auto-Regressive Integrated Moving Average (ARIMA)/Seasonal Auto-Regressive Integrated Moving Average (SARIMA) are the widely applied methods for forecasting such a series. Yet these techniques are unable to model the cyclical variation and they have some other weaknesses. According to the literature, modeling cyclical variation is highly important and crucial. Some researchers have attempted the Artificial Neural Network for this purpose, yet their success was doubtful. There were no Statistical techniques for the purpose. The Sama Circular Model (SCM) is a recently joined member of the family of forecasting techniques, developed on Newton’s law of Circular Motion, Fourier transformation, and Least Square Estimation. Indeed it is a frequency domain model. The SCM is capable of capturing all the components of a time series; Trend, Seasonal and Cyclical. It has been successful in various real-life applications and was superior to the other techniques.

Keywords: Stochastic Models, Time Series