Mathematical Validation of Trend Functions Under Deterministic Linear Growth: A Comparative Study

This study examines Fidelity Bank asset values across three trend observation periods. Firstly, mathematical formulations of the problem were developed to establish the share-price rate of change for three different trend functions, namely Linear, Quadratic and Cubic, each of which has a distinct impact on the modelled share prices of Fidelity Bank. We analyze column-wise trends, and evaluate row-wise descriptive statistics and trend functions using error metrics. Results show that all assets follow a perfect linear trend where the second and third observations are exactly twice and thrice the first. Mean and standard deviation increase proportionally across assets, with constant relative risk. Also, a two-way ANOVA based on Snedecor’s F-distribution is applied. Results reveal statistically significant differences in both trend-function and asset effects, with perfect linear scaling. The linear trend function fits perfectly with zero error. In addition, Quantile-Quantile (Q-Q) plots were used to compare the three trend-generated price series, confirming that they are exactly proportional by construction. The proposed framework offers a useful methodological benchmark for comparing trend-fitting approaches prior to their application to empirical, stochastically varying share-price data.