QUANTITATIVE ANALYSIS OF GSIW: POLYNOMIAL MODELING AND EVIDENCE OF CYCLES IN A CONTRACTION SCENARIO

 Analyzing financial assets using traditional statistical tools often falls short of capturing the complexity of market movements. To understand the recent dynamics of GSIW, a mixed-methods approach was implemented, combining fundamental descriptive statistics with econometric polynomial curve modeling. The results offer a clear perspective on its structural trend and the behavior of its price cycles.

Looking at the distribution of historical data (based on a sample of periods), the first red flag comes from the disparity between the measures of central tendency: While the arithmetic mean stands at 586.33, the median plummets to 116.31. This marked difference, coupled with a positive skewness of 1.25, indicates that the asset has spent most of its time at low price levels, interrupted by sporadic and very high peaks at the beginning of the series (a high of 3100 versus a low of 6.7).

The standard deviation of 793.87 far exceeds the mean, reflecting an environment of extreme volatility. The coefficient of variation (CV) of 1.35 quantitatively confirms that the risk associated with the dispersion of this asset is remarkably high.

The negative Sharpe ratio (-0.00128) and a 5-year return of -97.60% confirm the severe correction and value destruction process that the asset has undergone in the medium term.

To isolate market "noise" and understand the underlying trajectory, three regression models are evaluated: linear, third-order polynomial, and sixth-order polynomial. The linear regression shows a clear negative slope. Although it explains almost two-thirds of the variability, it is a flat model that ignores the asset's structural reversals.

The third-order polynomials substantially improve the fit, capturing the curvature of the prolonged decline and the subsequent stabilization at the lower end of the sample. Sixth-order polynomials are undoubtedly the model with the greatest explanatory power. By modeling higher-order oscillations, this approach allows us to precisely identify mathematically the inflection points and cyclical phases that linear models completely omit.

The graphical analysis of the solution to the sixth-order equation reveals a highly interesting cyclical structure for strategy design:

Cycle 1 (peak-to-peak) lasted 367 periods, traveling from Peak 1 to Peak 2, after passing through a Low 1 at period 193.30. The first expansion phase (Peak-Valley) of this cycle lasted 231 days.

Cycle 2 (peak-to-peak) showed a significant time elongation, extending for 679 days to reach Peak 3 at period 1102.46.

In the current expansion phase, the model identifies a second expansion phase (Peak-Valley) of 379 periods after surpassing Low 2. The calculated inflection points act as critical transition zones where the asset's momentum changes concavity, offering key signals of market regime shifts. The medium term (30 to 360 days) shows negative values ​​due to the strong bearish bias of the entire series. However, for the quantitative investor, the true value lies in studying the polynomial waves.

GSIW is an asset that moves according to deep and mathematically well-defined cyclical patterns. Having consolidated an apparent bottom around Low 2, the key now is to monitor whether the modeled expansion phase manages to sustain itself or whether the strength of the main downtrend will force a new accumulation structure. In assets of this nature, algorithmic timing based on calculated turning points is superior to any Buy & Hold strategy.