def estimate_ar_coefficients(r, M):
'''
Runs Levinson-Durbin to compute the AR coefficients,
reflection coefficients, and prediction error powers up to M.
This function then uses a least squares fit to compute the
reflection coefficients from the AR coefficients and compares
the results.
'''
# Levinson Durbin:
_, ar_coeff, reflec_coeff, _, _ = stattools.levinson_durbin(r, M)
delta_0 = r.mean()*np.sum(ar_coeff)
print('\nLevinson Durbin Reflection coefficients:', -reflec_coeff)
print('Levinson-durbin delta:', delta_0)
# Least squares: (the actual regression is needed for the delta term)
y = np.transpose(np.array(r[M:], ndmin=2))
x = np.zeros([r.size-M, M])
x = np.insert(x, 0, 1, axis=1) # for the delta term (y-intercept)
for i in range(M, r.size):
for j in range(1, M+1):
x[i-M, j] = r[i-j]
beta = np.linalg.inv(np.transpose(x) @ x) @ np.transpose(x) @ y
ols_pacf = stattools.pacf_ols(r, M)
print('\nLeast Squares Reflection coefficients:', -1*ols_pacf)
print('Least Squares delta:', np.sum(beta[1:])*r.mean(), end='\n\n')
return np.sum((y - x @ beta)**2)/y.size
def test_ols_inefficient(self):
lag_len = 5
pacfols = pacf_ols(self.x, nlags=lag_len, efficient=False)
x = self.x.copy()
x -= x.mean()
n = x.shape[0]
lags = np.zeros((n - 5, 5))
lead = x[5:]
direct = np.empty(lag_len + 1)
direct[0] = 1.0
for i in range(lag_len):
lags[:, i] = x[5 - (i + 1):-(i + 1)]
direct[i + 1] = lstsq(lags[:, :(i + 1)], lead, rcond=None)[0][-1]
assert_allclose(pacfols, direct, atol=1e-8)
def test_ols_inefficient(self):
lag_len = 5
pacfols = pacf_ols(self.x, nlags=lag_len, efficient=False)
x = self.x.copy()
x -= x.mean()
n = x.shape[0]
lags = np.zeros((n - 5, 5))
lead = x[5:]
direct = np.empty(lag_len + 1)
direct[0] = 1.0
for i in range(lag_len):
lags[:, i] = x[5 - (i + 1):-(i + 1)]
direct[i + 1] = lstsq(lags[:, :(i + 1)], lead, rcond=None)[0][-1]
assert_allclose(pacfols, direct, atol=1e-8)
def plotACFandPACF(ts_log_diff):
lag_acf = acf(ts_log_diff, nlags=20)
lag_pacf = pacf_ols(ts_log_diff, nlags=20)
#Plot ACF:
plt.subplot(121)
plt.plot(lag_acf)
plt.axhline(y=0,linestyle='--',color='gray')
plt.axhline(y=-1.96/np.sqrt(len(ts_log_diff)),linestyle='--',color='gray')
plt.axhline(y=1.96/np.sqrt(len(ts_log_diff)),linestyle='--',color='gray')
plt.title('Autocorrelation Function')
#Plot PACF:
plt.subplot(122)
plt.plot(lag_pacf)
plt.axhline(y=0,linestyle='--',color='gray')
plt.axhline(y=-1.96/np.sqrt(len(ts_log_diff)),linestyle='--',color='gray')
plt.axhline(y=1.96/np.sqrt(len(ts_log_diff)),linestyle='--',color='gray')
plt.title('Partial Autocorrelation Function')
plt.tight_layout()
plt.show()
def test_pacf_ols():
pacfols = tsa.pacf_ols(x100, 20)
assert_array_almost_equal(mlpacf.pacf100.ravel(), pacfols, 8)
pacfols = tsa.pacf_ols(x1000, 20)
assert_array_almost_equal(mlpacf.pacf1000.ravel(), pacfols, 8)
clicksPerDay = clicksPerDay.set_index(newIndex) encountersPerDay = encountersPerDay.set_index(newIndex) #clicksPerDay.index.name = None #encountersPerDay.index.name = None clicksPerDay = pd.Series(data=clicksPerDay["count_clicks"], index=clicksPerDay.index) encountersPerDay = pd.Series(data=encountersPerDay["count_encounter"], index=encountersPerDay.index) clicksPerDay = clicksPerDay.fillna(method="ffill") encountersPerDay = encountersPerDay.fillna(method="ffill") ####################LJUNG-BOX#################### clicksPACF = stattools.pacf_ols(clicksPerDay, nlags=MAX_LAG) encountersPACF = stattools.pacf_ols(encountersPerDay, nlags=MAX_LAG) #my implementation results = _math.ljungBox(encountersPACF, len(encountersPerDay), MAX_LAG) lag, R, Q, p = zip(*results) print np.asarray(Q[1:]) print np.asarray(p[1:]) #statsmodels implementation results = diagnostic.acorr_ljungbox(encountersPerDay, lags=MAX_LAG) print results #my copy of the statsmodels implementation results = _math.ljungBox2(encountersPerDay, maxlag=MAX_LAG) print results
df1.head()
df2.head()
import warnings
warnings.filterwarnings('ignore') #to ignore the warnings which is unnecessary
df = pd.DataFrame({'a': [12, 5, 11, 12, 9]})
acf(df['a'])
pacf_yw(df['a'], nlags=4, method='mle')
pacf_yw(df['a'], nlags=4, method='unbiased')
pacf_ols(df['a'], nlags=4)
'''
Method in the above use different types of calculation corralation itself
'''
from pandas.plotting import lag_plot
lag_plot(df1['Thousands of Passengers'])
lag_plot(df2['Births'])
from statsmodels.graphics.tsaplots import plot_acf, plot_pacf
plot_acf(df1, lags=40)
plot_acf(df2, lags=40)
def test_pacf_ols():
pacfols = tsa.pacf_ols(x100, 20)
assert_array_almost_equal(mlpacf.pacf100.ravel(), pacfols, 8)
pacfols = tsa.pacf_ols(x1000, 20)
assert_array_almost_equal(mlpacf.pacf1000.ravel(), pacfols, 8)
def test_ols(self):
pacfols = pacf_ols(self.x, nlags=40)
assert_almost_equal(pacfols[1:], self.pacfols, DECIMAL_6)