I have developed an algorithm to loop through 15 variables and produce a simple OLS for each variable. Then the algorithm loops a further 11 times to produce the same 15 OLS regressions but the lag of the X variable increases by one each time. I select the independent variables with the highest r^2 and use the optimum lag for 3,4 or 5 variables
i.e.
Y_t+1 - Y_t = B ( X_t+k - X_t) + e
My dataset looks like this:
Regression = pd.DataFrame(np.random.randint(low=0, high=10, size=(100, 6)),
columns=['Y', 'X1', 'X2', 'X3', 'X4','X5'])
The OLS regression I have fitted so far uses the following code:
Y = Regression['Y']
X = Regression[['X1','X2','X3']]
Model = sm.OLS(Y,X).fit()
predictions = Model.predict(X)
Model.summary()
The issue is that with OLS, you can get negative coefficients (which I do). I'd appreciate the help in constraining this model with the following:
sum(B_i) = 1
B_i >= 0
This works nicely,
from scipy.optimize import minimize
# Define the Model
model = lambda b, X: b[0] * X[:,0] + b[1] * X[:,1] + b[2] * X[:,2]
# The objective Function to minimize (least-squares regression)
obj = lambda b, Y, X: np.sum(np.abs(Y-model(b, X))**2)
# Bounds: b[0], b[1], b[2] >= 0
bnds = [(0, None), (0, None), (0, None)]
# Constraint: b[0] + b[1] + b[2] - 1 = 0
cons = [{"type": "eq", "fun": lambda b: b[0]+b[1]+b[2] - 1}]
# Initial guess for b[1], b[2], b[3]:
xinit = np.array([0, 0, 1])
res = minimize(obj, args=(Y, X), x0=xinit, bounds=bnds, constraints=cons)
print(f"b1={res.x[0]}, b2={res.x[1]}, b3={res.x[2]}")
#Save the coefficients for further analysis on goodness of fit
beta1 = res.x[0]
beta2 = res.x[1]
beta3 = res.x[2]