An Investigation into The Application of Function Fitting in Trend Analysis

Abstract

Trend information of discrete observations is an important input in science in data-driven environments. The following paper critically analyzes the usage value and risks of trend analysis with use of function fitting. To begin with, it classifies the five most popular fitting techniques, including linear, non-linear (polynomial), exponential, periodic, and power functions and it builds a method selection system ranging between easy and complicated. It then compares the effectiveness in various fitting schemes using stock prices, temperature changes, and drug pharmacokinetics as case studies to find the practical use of various fitting schemes in trend extraction, volatility smoothing and predictive accuracy enhancement. The results show that accuracy fitting depends on the synergies of the model complexity, data quality and domain knowledge and that overfitting and homoscedasticity and structure misidentification are important contributors to poor extrapolation reliability. The conclusion verifies that functional fitting is an important instrument that cannot be neglected in the trend analysis but its successful usage depends on correct perception of the peculiarities of the methods, strict control of the absence of data, and thorough combination with professional processes. The next efforts will involve machine learning and uncertainty quantification methods together in order to create a more robust and interpretable intelligent fitting algorithm, which can meet the needs of decision-making in high-dimensional complex data.