Lab · A · Graph diffusion
The test results of the user's fabric model: lagged relationships, Granger causality, sparse VAR(1) and graph dynamics.
Edge count before and after cleaning
What it is: The number of significant edges the same lagged relationship test finds on raw return and on residual return.
What data feeds it: The leadLag result of the selected run. The total number of (leader, follower, lag) triples tested is also shown.
What it shows: On real data, 170 edges are found on raw return and 16 on residual return.
What can be concluded from it: The difference is spurious propagation created by the market factor. The fabric model is meaningful only if it is built on residual return.
Lagged relationship edges
What it is: Pairs in which one stock's movement today has a significant correlation with another stock's movement k days later; residual on the left, raw return on the right.
What data feeds it: L_k(i,j) = corr(ε_i[t], ε_j[t+k]), k = 1..5. p-value via Fisher z, then the false discovery rate is controlled at q = 0.05 with Benjamini–Hochberg.
What it shows: Leader, follower, lag, correlation and p-value; the 15 most significant edges.
What can be concluded from it: If the correlations are around 0.1, the relationship exists statistically but is economically weak. Pairs that make intuitive sense (such as banks in the same group) increase the credibility of the result.
Granger causality
What it is: A test of whether one stock's history carries information beyond another stock's own history.
What data feeds it: Only for pairs that pass the lagged relationship screen: the F test of the restricted and full VAR(p=3) models, followed by BH-FDR.
What it shows: Leader, follower, F statistic and p-value.
What can be concluded from it: If the table is empty, lagged causality in this data is not strong enough to pass the control; this is an honest and possible result.
Heat equation and wave equation
What it is: Fitting two physical dynamics on the graph to the data and comparing them out of sample.
What data feeds it: The heat equation (x(t+1) = x(t) − a·L·x(t)) and the damped wave equation on the Laplacian of the map graph; the coefficients are fitted by least squares on the first 70% of the data, and the error is measured on the last 30%.
What it shows: The out-of-sample mean squared error of the two models, the direction hit rate, the fitted coefficients, and which fits the data better.
What can be concluded from it: Heat predicts only spreading; the wave predicts overshoot and reversal. Which one wins gives an idea of whether movement in the market is "spreading" or "oscillating"; but if the hit rate of both models is close to 50%, neither is usable.
Sparse VAR(1) coefficient matrix
What it is: A heatmap of the matrix W linking each stock's residual return tomorrow to all stocks' residual returns today, and a model comparison.
What data feeds it: A separate LASSO for each target in the last walk-forward fold; candidate predictors are screened by lag-1 correlation, and λ is chosen by time-ordered block cross-validation. At most 60 stocks are shown for readability.
What it shows: The row is the affected stock, the column the affecting stock; blue is a positive, red a negative effect. Below it, the mean squared error of LASSO, ridge and OLS, and the number of non-zero coefficients per target.
What can be concluded from it: The matrix being largely empty shows that lagged propagation is sparse. If LASSO's error is not clearly lower than OLS's, the structure found cannot be distinguished from noise.
Strongest leaders
What it is: The list of the five stocks that most affect each stock.
What data feeds it: Ranking by the absolute value of the sparse VAR(1) coefficients.
What it shows: Each row has a ticker and at most five leader stocks that most affect its residual return tomorrow, ranked by the size of the coefficient.
What can be concluded from it: If no leader is found for any stock, LASSO has set all coefficients to zero and there is no lagged propagation signal in this data.
The investment information, comments and recommendations given here are not within the scope of investment advisory services. Investment advisory services are provided under an investment advisory agreement to be signed between a client and brokerage houses, portfolio management companies, or banks that do not accept deposits. The signals here are produced from historical data with statistical models, are shown the same to everyone and are not personalised; they may not suit your financial situation or your risk and return preferences. Therefore, making investment decisions based solely on the information given here may not produce results that meet your expectations.