Attempt to uncover causal link between calorie intake and weight using CCM method as implemented in CauseMap Julia module.

CauseMap_cals-vs-weight.jl

using CauseMap

# specify parameter ranges to test over
E_vals     = 2:10  # range to test of system dimensionality
tau_s_vals = 1:1 # range for lag length for manifold reconstruction
tau_p_vals = 0:15  # range to test for time lag of causal effect

# weight and calorie intake data
weight = [69.0,68.7,68.1,68.3,67.6,68.0,68.2,66.7,67.7,67.1,67.1,67.3,67.0,67.5,66.0,66.6,67.0,66.7,66.7,66.4,66.4,66.2,65.8,66.2,65.8,65.6,65.5,65.4,66.4,65.0,65.4,65.2,64.9,64.4,64.6,65.0,64.6,64.4,64.5,63.9,63.6,63.7,64.0,64.0,63.7,63.8,63.4,63.7,64.0,63.7,64.2,64.1,63.8,63.8]
cals = [2207.0,1275.0,1069.0,1760.0,1498.0,2544.0,1116.0,1495.0,1224.0,1584.0,1381.0,1084.0,1723.0,1276.0,1356.0,1337.0,1674.0,1516.0,1499.0,1759.0,1221.0,1476.0,1212.0,2023.0,1528.0,1279.0,2130.0,1519.0,1954.0,1590.0,1769.0,1411.0,1337.0,1798.0,1756.0,899.0,1243.0,1411.0,1463.0,1284.0,2199.0,1611.0,1855.0,1498.0,1727.0,1517.0,1474.0,1876.0,1929.0,1518.0,1265.0,1641.0,1175.0,1387.0]

# run analysis
makeoptimizationplots(weight, cals,  
                                        E_vals, tau_s_vals, tau_p_vals, 
                                        "Weight", "Calories"; 
                                        nreps=10, left_E=2, left_tau_p=0,   # optional 
                                        right_E=7, right_tau_p=12, lagunit=.5, # optional
                                        unit="days", show_tau_s=false # optional
                                    )

Looks like CCM finds spurious causal links in random data.

using CauseMap

# specify parameter ranges to test over
E_vals     = 2:10  # range to test of system dimensionality
tau_s_vals = 1:1 # range for lag length for manifold reconstruction
tau_p_vals = 0:15  # range to test for time lag of causal effect

random1 = cumsum(randn(100))
random2 = cumsum(randn(100))

# run analysis
makeoptimizationplots(random1, random2,  
                                        E_vals, tau_s_vals, tau_p_vals, 
                                        "random1", "random2"; 
                                        nreps=10, left_E=2, left_tau_p=0,   # optional 
                                        right_E=7, right_tau_p=12, lagunit=.5, # optional
                                        unit="days", show_tau_s=false # optional
                                    )

Both series random1 and random2 are entirely random and independent, but the output suggests there are causal effects both ways.

I think this is not an implementation fault, but rather a shortcoming of the CCM method itself. Also posting it here for reference.