Explaining the Graphics in the Blog Posts and Reports

The blog posts and Reports contain graphics, and here we explain the interpretation of these graphics using examples from a past analysis of iBit the iShares Bitcoin Trust. Reports have a validity span of 20 trading days from date of report barring unforeseen significant disruptions to the market/sector/industry which the ETF tracks. These disruptions could be economic, regulatory, political, military or natural disasters. In today’s financial ecosystem, all financial markets and all asset classes have an impact on each other.

Note on MetaLog Distributions

One of the unique characteristics of our models is the use of a recent innovation in Statistics- MetaLog Distributions.  Financial markets data are often complex, noisy, and exhibit characteristics such as multi-modality and skewness that are not well captured by traditional Normal (Gaussian) distributions.

The MetaLog Distribution is a flexible distribution that can model a wide range of data types, including those with skewness, heavy tails, and other irregularities. It is known for its ability to fit both bounded and unbounded data with varying degrees of smoothness and flexibility.

Unlike traditional distributions that require assumptions about shape parameters, the MetaLog Distribution adapts to the empirical data, making it highly versatile for various applications.

It should be noted that in the model, data is fitted to a Distribution after it has gone through the various stages that make it ideal for forecasts.  Techniques like standardization with Z-score, and ARIMA will make the Distribution look in shape quite like a Normal (Gaussian) Distribution. Here is the iBit data fitted to a MetaLog Distribution. 

Simulated 1-20 steps ahead forecast trend

This graphic shows the output from running 1000-trials Monte Carlo Simulation, being the final stage of our 43-stages model building. Our Monte Carlo Simulation uses state-of-the-art Sobol RQMC sampling method and the Mersenne Twister Random Number Generator, both of which are ideal for financial markets data.

 It is meant for you to visualize the probable next 20-steps [equivalent to 20 trading days] direction of the ETF. Here you can see that while the ETF is not yet in a downtrend, the rate of change of each step forecasted is slowing down (the length of the ups and downs of Blue line from forecast step 1 to forecast step 20.) Verdict: In your investing on this ETF, trading err on the cautious side.

Probability Density Function (PDF)

This is an example of the data being fitted to a MetaLog Distribution. Note that the Fitted shape (Red) is very different from a Normal Distribution.

The PDF shows you the Support and Resistance price levels at the 5th and 95th percentiles after the model has been Run through Monte Carlo Simulation. See Table above.

It means: There is less than a 5% chance that the price will move below 32.93 and there is less than 5% chance that the price will move above 38.17. Taken in conjunction with the cautious outlook from the simulated forecast trend above, the Support and Resistance levels give you the range within which you can trade. As stated above the validity of the model output is 20 trading days barring unforeseen disruptions to the financial ecosystem. To continue the forecast the model has to be fed with the latest data and updated.

Q-Q chart

Interpretation of Q-Q chart.

X-axis and Y-axis Explanation:

X-axis (Theoretical Quantiles): This axis represents the expected quantiles based on the MetaLog Distribution model that was used to fit the data. In simpler terms, it shows the values that the model predicts should occur at specific points in the dataset.

Y-axis (Sample Quantiles): This axis shows the actual observed quantiles from your data. These are the values that were actually recorded in the dataset at those specific points.

Location of Confidence Band Boundaries:

The confidence bands are the outermost curved lines seen in the chart, providing a range where most data points are expected to fall if the model fits well.

X-axis (Theoretical Quantiles): The confidence bands extend horizontally from approximately 31.00 to 41.00, covering the range of theoretical quantiles expected from the MetaLog Distribution.

Y-axis (Sample Quantiles): Vertically, the confidence bands span from around 30.00 to 40.00, corresponding to the observed sample quantiles in your data.

For instance, around the theoretical quantile value of 35 on the X-axis, the upper confidence band boundary is just above 36, and the lower boundary is just below 34 on the Y-axis. Similarly, at a theoretical quantile value of 38, the upper boundary is close to 39.5, and the lower boundary is just above 36.5 on the Y-axis. These boundaries help visualize the expected range of the observed data.

Goodness of Fit Conclusion:

The goodness of fit is assessed by how closely the data points follow the straight line and remain within the confidence bands.

In this Q-Q chart, the majority of the data points closely follow the straight line and are within the confidence bands, indicating that the MetaLog Distribution provides a good fit to the data. There are only slight deviations at the tails (extremes) of the distribution, which is common and often acceptable depending on the context.

This indicates that the model effectively captures the characteristics of the dataset, making it a good representation of the underlying distribution of the data.