def __init__(self, P, RHO, ma_weights, T=None, epsilon=None):
# If not provided, epsilon is an array of N(0, 1).
if epsilon is None:
epsilon = normal(0, 1, (T,))
elif T is None:
raise ValueError("You must provide T or epsilon.")
self.epsilon = epsilon
# If not provided, T will be len(epsilon)
if T is None:
T = shape(epsilon)[0]
else:
assert T == shape(epsilon)[0], "T and shape(epsilon) are incoherent."
self.T = T
# Generating the ARMA process
Q = len(ma_weights)
X = array(typecode=Float32, shape=(T,))
for t in range(T):
X[t] = epsilon[t]
for k in range(1, min(t, Q)+1):
alpha_k = ma_weights[k-1] # offset by 1 since lists start at 0 in Python
X[t] += alpha_k * epsilon[t-k]
for p in range(1, min(t, P)+1):
X[t] += RHO**p * X[t-p]
self.x = X
self.p = P
self.q = Q
self.rho = RHO
self.ma_weights = ma_weights
def __init__(self, P, RHO, ma_weights, T=None, epsilon=None):
# If not provided, epsilon is an array of N(0, 1).
if epsilon is None:
epsilon = normal(0, 1, (T, ))
elif T is None:
raise ValueError("You must provide T or epsilon.")
self.epsilon = epsilon
# If not provided, T will be len(epsilon)
if T is None:
T = shape(epsilon)[0]
else:
assert T == shape(
epsilon)[0], "T and shape(epsilon) are incoherent."
self.T = T
# Generating the ARMA process
Q = len(ma_weights)
X = array(typecode=Float32, shape=(T, ))
for t in range(T):
X[t] = epsilon[t]
for k in range(1, min(t, Q) + 1):
alpha_k = ma_weights[
k - 1] # offset by 1 since lists start at 0 in Python
X[t] += alpha_k * epsilon[t - k]
for p in range(1, min(t, P) + 1):
X[t] += RHO**p * X[t - p]
self.x = X
self.p = P
self.q = Q
self.rho = RHO
self.ma_weights = ma_weights
def _test_ols_regression(T, K, alpha=0.0, scale=10.0, plot=False):
u = normal(0, 1, (T, ))
beta = range(1, K + 1)
X = scale * random((T, K))
Y = alpha + mmult(X, beta) + u
print "Beta:", beta
print
olsR = ols_regression(X, Y, False)
print "Beta OLS (no intercept):", olsR[1], "(%.3f)" % matrix_distance(
olsR[1], beta)
print
ols = ols_regression(X, Y, True)
print "Beta OLS (with intercept %s):" % ols[0], ols[
1], "(%.3f)" % matrix_distance(ols[1], beta)
print
if K == 1:
X = X.ravel()
scipy = stats.linregress(X, Y)
print "Beta SciPy (with intercept %s):" % scipy[1],
print scipy[0], "(%.3f)" % matrix_distance(array(scipy[0]), beta)
if plot:
import pylab
pylab.hold(True)
pylab.scatter(X, Y)
xlims = pylab.xlim()
pylab.plot([0, xlims[1]], [0, olsR[1][0] * xlims[1]],
label="No intercept")
intercept = ols[0][0]
line_end = intercept + ols[1][0] * xlims[1]
pylab.plot([0, xlims[1]], [intercept, line_end],
label="With intercept")
intercept = scipy[1]
line_end = intercept + scipy[0] * xlims[1]
pylab.plot([0, xlims[1]], [intercept, line_end], label="SciPy")
pylab.legend(loc=0)
pylab.show()
return X, Y, olsR, ols, scipy
def _test_ols_regression(T, K, alpha=0.0, scale=10.0, plot=False):
u = normal(0, 1, (T,))
beta = range(1, K+1)
X = scale * random((T, K))
Y = alpha + mmult(X, beta) + u
print "Beta:", beta
print
olsR = ols_regression(X, Y, False)
print "Beta OLS (no intercept):", olsR[1], "(%.3f)"%matrix_distance(olsR[1],beta)
print
ols = ols_regression(X, Y, True)
print "Beta OLS (with intercept %s):"%ols[0], ols[1], "(%.3f)"%matrix_distance(ols[1],beta)
print
if K==1:
X = X.ravel()
scipy = stats.linregress(X, Y)
print "Beta SciPy (with intercept %s):"%scipy[1],
print scipy[0], "(%.3f)"%matrix_distance(array(scipy[0]),beta)
if plot:
import pylab
pylab.hold(True)
pylab.scatter(X, Y)
xlims = pylab.xlim()
pylab.plot([0, xlims[1]], [0, olsR[1][0]*xlims[1]], label="No intercept")
intercept = ols[0][0]
line_end = intercept + ols[1][0]*xlims[1]
pylab.plot([0, xlims[1]], [intercept, line_end], label="With intercept")
intercept = scipy[1]
line_end = intercept + scipy[0]*xlims[1]
pylab.plot([0, xlims[1]], [intercept, line_end], label="SciPy")
pylab.legend(loc=0)
pylab.show()
return X, Y, olsR, ols, scipy
def __init__(self, T, n=1000):
self.T = T
self.n = n
self.n_inverse = 1.0/n
self.increments = normal(0, self.n_inverse, (n*T,))
self.discretization = cumsum(self.increments)
def __init__(self, T, n=1000):
self.T = T
self.n = n
self.n_inverse = 1.0 / n
self.increments = normal(0, self.n_inverse, (n * T, ))
self.discretization = cumsum(self.increments)
