def setup_class(cls):
nobs = 500
ar = [1, -0.5, 0.1]
ma = [1, 0.7]
dist = lambda n: np.random.standard_t(3, size=n)
np.random.seed(8659567)
x = arma_generate_sample(ar, ma, nobs, sigma=1, distrvs=dist,
burnin=500)
mod = Arma(x)
order = (2, 1)
cls.res_ls = mod.fit(order=order)
cls.res = mod.fit_mle(order=order,
start_params=np.r_[cls.res_ls[0], 1],
method='nm', disp=False)
cls.res1_table = np.array(
[[ 0.4339072 , -0.08402653, 0.73292344, 1.61661128],
[ 0.05854268, 0.05562941, 0.04034178, 0.0511207 ],
[ 7.4118102 , -1.51046975, 18.16785075, 31.62341666],
[ 0. , 0.1309236 , 0. , 0. ],
[ 0.06713617, 0.05469138, 0.03785006, 0.1071093 ],
[ 0.05504093, 0.0574849 , 0.04350945, 0.02510928]])
cls.res1_conf_int = np.array([[ 0.31916567, 0.54864874],
[-0.19305817, 0.0250051 ],
[ 0.65385501, 0.81199188],
[ 1.51641655, 1.71680602]])
cls.ls_params = np.array([ 0.43393123, -0.08402678, 0.73293058])
cls.ls_bse = np.array([ 0.0377741 , 0.03567847, 0.02744488])
def mcarma22(niter=10, nsample=1000, ar=None, ma=None, sig=0.5):
'''run Monte Carlo for ARMA(2,2)
DGP parameters currently hard coded
also sample size `nsample`
was not a self contained function, used instances from outer scope
now corrected
'''
#nsample = 1000
#ar = [1.0, 0, 0]
if ar is None:
ar = [1.0, -0.55, -0.1]
#ma = [1.0, 0, 0]
if ma is None:
ma = [1.0, 0.3, 0.2]
results = []
results_bse = []
for _ in range(niter):
y2 = arma_generate_sample(ar,ma,nsample+1000, sig)[-nsample:]
y2 -= y2.mean()
arest2 = Arma(y2)
rhohat2a, cov_x2a, infodict, mesg, ier = arest2.fit((2,2))
results.append(rhohat2a)
err2a = arest2.geterrors(rhohat2a)
sige2a = np.sqrt(np.dot(err2a,err2a)/nsample)
#print('sige2a', sige2a,
#print('cov_x2a.shape', cov_x2a.shape
#results_bse.append(sige2a * np.sqrt(np.diag(cov_x2a)))
if cov_x2a is not None:
results_bse.append(sige2a * np.sqrt(np.diag(cov_x2a)))
else:
results_bse.append(np.nan + np.zeros_like(rhohat2a))
return np.r_[ar[1:], ma[1:]], np.array(results), np.array(results_bse)
def SimulatePC1(p=50): m = np.zeros((nyears,p)) for j in range(p): b = arma_generate_sample(ar, ma, nyears) m[:,j] = b - np.mean(b[500:600]) u,s,v = svd(m,full_matrices=False) return(u[:,0])
def setup_class(cls):
nobs = 500
ar = [1, -0.5, 0.1]
ma = [1, 0.7]
dist = lambda n: np.random.standard_t(3, size=n)
np.random.seed(8659567)
x = arma_generate_sample(ar, ma, nobs, sigma=1, distrvs=dist,
burnin=500)
mod = TArma(x)
order = (2, 1)
cls.res_ls = mod.fit(order=order)
cls.res = mod.fit_mle(order=order,
start_params=np.r_[cls.res_ls[0], 5, 1],
method='nm', disp=False)
cls.res1_table = np.array(
[[ 0.46157133, -0.07694534, 0.70051876, 2.88693312, 0.97283396],
[ 0.04957594, 0.04345499, 0.03492473, 0.40854823, 0.05568439],
[ 9.31038915, -1.7706905 , 20.05795605, 7.06632146, 17.47049812],
[ 0. , 0.07661218, 0. , 0. , 0. ],
[ 0.05487968, 0.04213054, 0.03102404, 0.37860956, 0.05228474],
[ 0.04649728, 0.04569133, 0.03990779, 0.44315449, 0.05996759]])
cls.res1_conf_int = np.array([[ 0.36440426, 0.55873839],
[-0.16211556, 0.00822488],
[ 0.63206754, 0.76896998],
[ 2.08619331, 3.68767294],
[ 0.86369457, 1.08197335]])
cls.ls_params = np.array([ 0.43393123, -0.08402678, 0.73293058])
cls.ls_bse = np.array([ 0.0377741 , 0.03567847, 0.02744488])
def test_arma_generate_sample(dist, ar, ma):
# Test that this generates a true ARMA process
# (amounts to just a test that scipy.signal.lfilter does what we want)
T = 100
np.random.seed(1234)
eta = dist(T)
# rep1: from module function
np.random.seed(1234)
rep1 = arma_generate_sample(ar, ma, T, distrvs=dist)
# rep2: "manually" create the ARMA process
ar_params = -1 * np.array(ar[1:])
ma_params = np.array(ma[1:])
rep2 = _manual_arma_generate_sample(ar_params, ma_params, eta)
assert_array_almost_equal(rep1, rep2, 13)
def test_arma_order_select_ic():
# smoke test, assumes info-criteria are right
from statsmodels.tsa.arima_process import arma_generate_sample
arparams = np.array([.75, -.25])
maparams = np.array([.65, .35])
arparams = np.r_[1, -arparams]
maparam = np.r_[1, maparams]
nobs = 250
np.random.seed(2014)
y = arma_generate_sample(arparams, maparams, nobs)
res = arma_order_select_ic(y, ic=['aic', 'bic'], trend='nc')
# regression tests in case we change algorithm to minic in sas
aic_x = np.array([[ np.nan, 552.7342255 , 484.29687843],
[ 562.10924262, 485.5197969 , 480.32858497],
[ 507.04581344, 482.91065829, 481.91926034],
[ 484.03995962, 482.14868032, 483.86378955],
[ 481.8849479 , 483.8377379 , 485.83756612]])
bic_x = np.array([[ np.nan, 559.77714733, 494.86126118],
[ 569.15216446, 496.08417966, 494.41442864],
[ 517.61019619, 496.99650196, 499.52656493],
[ 498.12580329, 499.75598491, 504.99255506],
[ 499.49225249, 504.96650341, 510.48779255]])
aic = DataFrame(aic_x, index=lrange(5), columns=lrange(3))
bic = DataFrame(bic_x, index=lrange(5), columns=lrange(3))
assert_almost_equal(res.aic.values, aic.values, 5)
assert_almost_equal(res.bic.values, bic.values, 5)
assert_equal(res.aic_min_order, (1, 2))
assert_equal(res.bic_min_order, (1, 2))
assert_(res.aic.index.equals(aic.index))
assert_(res.aic.columns.equals(aic.columns))
assert_(res.bic.index.equals(bic.index))
assert_(res.bic.columns.equals(bic.columns))
index = pd.date_range('2000-1-1', freq='M', periods=len(y))
y_series = pd.Series(y, index=index)
res_pd = arma_order_select_ic(y_series, max_ar=2, max_ma=1,
ic=['aic', 'bic'], trend='nc')
assert_almost_equal(res_pd.aic.values, aic.values[:3, :2], 5)
assert_almost_equal(res_pd.bic.values, bic.values[:3, :2], 5)
assert_equal(res_pd.aic_min_order, (2, 1))
assert_equal(res_pd.bic_min_order, (1, 1))
res = arma_order_select_ic(y, ic='aic', trend='nc')
assert_almost_equal(res.aic.values, aic.values, 5)
assert_(res.aic.index.equals(aic.index))
assert_(res.aic.columns.equals(aic.columns))
assert_equal(res.aic_min_order, (1, 2))
def test(db):
np.random.seed(12345)
arparams = np.array([.75, -.25])
maparams = np.array([.65, .35])
arparams = np.r_[1, -arparams]
maparam = np.r_[1, maparams]
nobs = 250
y = arma_generate_sample(arparams, maparams, nobs)
dates = sm.tsa.datetools.dates_from_range('1980m1', length=nobs)
y = pandas.Series(y, index=dates)
arma_mod = sm.tsa.ARMA(y, order=(2, 2))
arma_res = arma_mod.fit(trend='nc', disp=-1)
print(arma_res.summary())
def test_arma_generate_sample():
# Test that this generates a true ARMA process
# (amounts to just a test that scipy.signal.lfilter does what we want)
T = 100;
dists = [np.random.randn]
for dist in dists:
np.random.seed(1234);
eta = dist(T);
for ar in arlist:
for ma in malist:
# rep1: from module function
np.random.seed(1234);
rep1 = arma_generate_sample(ar, ma, T, distrvs=dist);
# rep2: "manually" create the ARMA process
ar_params = -1*np.array(ar[1:]);
ma_params = np.array(ma[1:]);
rep2 = _manual_arma_generate_sample(ar_params, ma_params, eta)
assert_array_almost_equal(rep1, rep2, 13);
def calibrate_arma(ar=3, ma=2, data=None):
# Fitting an ARMA model for the required data
arma = sm.tsa.ARMA(data, (ar, ma)).fit(disp=0)
# Capturing the ARMA params
params = arma.params
# Splitting the params into AR and MA params
arparams = np.r_[1, -np.array(
params[len(params) - (ar + ma):len(params) - ma])]
maparams = np.r_[1, np.array(params[len(params) - ma:])]
# Creating a callback function for generating new series
def gen(nsample):
# Same mean and standard deviation
return [normalvariate(np.average(arma.resid), np.std(
arma.resid)) for i in range(nsample)]
# Generating new time series with the same properties of data
return MinMaxScaler((min(data), max(data))).fit_transform(
arma_generate_sample(arparams, maparams, len(data), distrvs=gen))
def generate_kindofgarch(nobs, ar, ma, mu=1.):
'''simulate garch like process but not squared errors in arma
used for initial trial but produces nice graph
'''
#garm1, gmam1 = [0.4], [0.2]
#pqmax = 1
# res = np.zeros(nobs+pqmax)
# rvs = np.random.randn(nobs+pqmax,2)
# for t in range(pqmax,nobs+pqmax):
# res[i] =
#ar = [1.0, -0.99]
#ma = [1.0, 0.5]
#this has the wrong distribution, should be eps**2
#TODO: use new version tsa.arima.??? instead, has distr option
#arest = tsa.arima.ARIMA()
#arest = tsa.arima.ARIMA #try class method, ARIMA needs data in constructor
from statsmodels.tsa.arima_process import arma_generate_sample
h = arma_generate_sample(ar,ma,nobs,0.1)
#h = np.abs(h)
h = (mu+h)**2
h = np.exp(h)
err = np.sqrt(h)*np.random.randn(nobs)
return err, h
import numpy as np
import numdifftools as ndt
from statsmodels.sandbox import tsa
from statsmodels.tsa.arma_mle import Arma # local import
from statsmodels.tsa.arima_process import arma_generate_sample
examples = ['arma']
if 'arma' in examples:
print("\nExample 1")
print('----------')
ar = [1.0, -0.8]
ma = [1.0, 0.5]
y1 = arma_generate_sample(ar,ma,1000,0.1)
y1 -= y1.mean() #no mean correction/constant in estimation so far
arma1 = Arma(y1)
arma1.nar = 1
arma1.nma = 1
arma1res = arma1.fit_mle(order=(1,1), method='fmin')
print(arma1res.params)
#Warning need new instance otherwise results carry over
arma2 = Arma(y1)
arma2.nar = 1
arma2.nma = 1
res2 = arma2.fit(method='bfgs')
print(res2.params)
print(res2.model.hessian(res2.params))
"""
Autoregressive Moving Average (ARMA) Model
"""
import numpy as np
import statsmodels.api as sm
# Generate some data from an ARMA process
from statsmodels.tsa.arima_process import arma_generate_sample
np.random.seed(12345)
arparams = np.array([.75, -.25])
maparams = np.array([.65, .35])
# The conventions of the arma_generate function require that we specify a
# 1 for the zero-lag of the AR and MA parameters and that the AR parameters
# be negated.
ar = np.r_[1, -arparams]
ma = np.r_[1, maparams]
nobs = 250
y = arma_generate_sample(ar, ma, nobs)
# Now, optionally, we can add some dates information. For this example,
# we'll use a pandas time series.
import pandas
dates = sm.tsa.datetools.dates_from_range('1980m1', length=nobs)
y = pandas.TimeSeries(y, index=dates)
arma_mod = sm.tsa.ARMA(y, order=(2, 2))
arma_res = arma_mod.fit(trend='nc', disp=-1)
Author: Josef Perktold
"""
from __future__ import print_function
import numpy as np
from statsmodels.tsa.arima_process import arma_generate_sample, ArmaProcess
from statsmodels.miscmodels.tmodel import TArma
from statsmodels.tsa.arima_model import ARMA
nobs = 500
ar = [1, -0.6, -0.1]
ma = [1, 0.7]
dist = lambda n: np.random.standard_t(3, size=n)
np.random.seed(8659567)
x = arma_generate_sample(ar, ma, nobs, sigma=1, distrvs=dist,
burnin=500)
mod = TArma(x)
order = (2, 1)
res = mod.fit(order=order)
res2 = mod.fit_mle(order=order, start_params=np.r_[res[0], 5, 1], method='nm')
print(res[0])
proc = ArmaProcess.from_coeffs(res[0][:order[0]], res[0][:order[1]])
print(ar, ma)
proc.nobs = nobs
# TODO: bug nobs is None, not needed ?, used in ArmaProcess.__repr__
print(proc.ar, proc.ma)
print(proc.ar_roots(), proc.ma_roots())
#
# Generate data
#
print 'Generating data...'
# generate labels
labels = np.array([1] * nq + [0] * nq + [1] * nq + [0] * nq)
# generate static features
static = np.vstack((np.random.normal(5.0, 1.0, (nq, nfeatures)),
np.random.normal(0.0, 1.0, (nq, nfeatures)),
np.random.normal(0.0, 1.0, (nq, nfeatures)),
np.random.normal(0.0, 1.0, (nq, nfeatures))))
# generate dynamic features
dynamic_q1 = np.vstack([ap.arma_generate_sample(arparams_pos, maparams_pos, seqlen) for i in range(nq * nseqfeatures)]).reshape(nq, nseqfeatures, seqlen)
dynamic_q2 = np.vstack([ap.arma_generate_sample(arparams_pos, maparams_pos, seqlen) for i in range(nq * nseqfeatures)]).reshape(nq, nseqfeatures, seqlen)
dynamic_q3 = np.vstack([ap.arma_generate_sample(arparams_neg, maparams_neg, seqlen) for i in range(nq * nseqfeatures)]).reshape(nq, nseqfeatures, seqlen)
dynamic_q4 = np.vstack([ap.arma_generate_sample(arparams_pos, maparams_pos, seqlen) for i in range(nq * nseqfeatures)]).reshape(nq, nseqfeatures, seqlen)
dynamic = np.vstack((dynamic_q1, dynamic_q2, dynamic_q3, dynamic_q4))
#
# Split the dataset into training and test sets
#
print 'Splitting train and test...'
# pick samples for training and for testing
train_idx = np.random.choice(range(0, nsamples), size=np.round(nsamples * 0.7, 0), replace=False)
test_idx = list(set(range(0, nsamples)) - set(train_idx))
_attrs = {}
_wrap_attrs = wrap.union_dicts(tsbase.TimeSeriesResultsWrapper._wrap_attrs, _attrs)
_methods = {}
_wrap_methods = wrap.union_dicts(tsbase.TimeSeriesResultsWrapper._wrap_methods, _methods)
wrap.populate_wrapper(ARMAResultsWrapper, ARMAResults)
if __name__ == "__main__":
import numpy as np
import statsmodels.api as sm
# simulate arma process
from statsmodels.tsa.arima_process import arma_generate_sample
y = arma_generate_sample([1.0, -0.75], [1.0, 0.25], nsample=1000)
arma = ARMA(y)
res = arma.fit(trend="nc", order=(1, 1))
np.random.seed(12345)
y_arma22 = arma_generate_sample([1.0, -0.85, 0.35], [1, 0.25, -0.9], nsample=1000)
arma22 = ARMA(y_arma22)
res22 = arma22.fit(trend="nc", order=(2, 2))
# test CSS
arma22_css = ARMA(y_arma22)
res22css = arma22_css.fit(trend="nc", order=(2, 2), method="css")
data = sm.datasets.sunspots.load()
ar = ARMA(data.endog)
resar = ar.fit(trend="nc", order=(9, 0))
try:
import scikits.talkbox.spectral.basic as stbs
except ImportError:
hastalkbox = False
ar = [1., -0.7] #[1,0,0,0,0,0,0,-0.7]
ma = [1., 0.3]
ar = np.convolve([1.] + [0] * 50 + [-0.6], ar)
ar = np.convolve([1., -0.5] + [0] * 49 + [-0.3], ar)
n_startup = 1000
nobs = 1000
# throwing away samples at beginning makes sample more "stationary"
xo = arma_generate_sample(ar, ma, n_startup + nobs)
x = xo[n_startup:]
plt.figure()
plt.plot(x)
rescale = 0
w, h = signal.freqz(ma, ar)
sd = np.abs(h)**2 / np.sqrt(2 * np.pi)
if np.sum(np.isnan(h)) > 0:
# this happens with unit root or seasonal unit root'
print('Warning: nan in frequency response h')
h[np.isnan(h)] = 1.
rescale = 0
import numpy as np
import matplotlib.pyplot as plt
from statsmodels.tsa.arima_model import ARIMA
from statsmodels.tsa.arima_process import arma_generate_sample
np.random.seed(12345)
arparams = np.array([0.6])
maparams = np.array([0.3])
ar = np.r_[0.6, -arparams] # add zero-lag and negate
y = arma_generate_sample(ar, 500)
plt.plot(y)
plt.show()
model = ARIMA(y, (1, 0, 1)).fit(trend='nc', disp=0)
plt.plot(model.fittedvalues)
plt.show()
print('NP')
# # # fit model
# model = ARIMA(series, order=(5,1,0))
# model.
# model_fit = model.fit(disp=0)
# #
#
'''
N=1000
x=np.zeros(N)
z=np.random.randn(N)
beta1=0.5
for i in np.arange(1,N,1):
x[i] = z[i] + beta1*z[i-1]
plt.plot(x);
plt.show()
'''
AR (2) process example
'''
tsaplots.plot_acf(x, lags=10, title='correlogram - AR(2)');
plt.show()
'''
ARMA(p,q) process example
'''
ar=[1, -0.9, 0.08]
ma=[1, 0.5, 0.9]
samps=arma_generate_sample(ar, ma, 5000)
plt.plot(samps);
tsaplots.plot_acf(samps, lags=40);
tsaplots.plot_pacf(samps, lags=40);
plt.show()
from statsmodels.tsa.arima_process import arma_generate_sample
# parameter settings
lags = 30 # lag value
n = 1000
alphas = np.array([0.])
# add zero-lag and negate alphas
ar = np.r_[1, -alphas]
ma1 = np.r_[1, np.array([0.5, 0.4])]
ma2 = np.r_[1, np.array([-0.5, 0.4])]
ma3 = np.r_[1, np.array([-0.5, -0.4])]
ma4 = np.r_[1, np.array([0.5, -0.4])]
f, axarr = plt.subplots(2, 2, figsize=(11, 6))
simulated_data_1 = arma_generate_sample(ar=ar, ma=ma1, nsample=n)
plot_pacf(simulated_data_1,
lags=lags,
ax=axarr[0, 0],
title='Sample ACF Plot with ' + r'$\beta_1$=' + str(ma1[1]) +
' and ' + r'$\beta_2$=' + str(ma1[2]))
axarr[0, 0].set_xlabel('lags')
simulated_data_2 = arma_generate_sample(ar=ar, ma=ma2, nsample=n)
plot_pacf(simulated_data_2,
lags=lags,
ax=axarr[0, 1],
title='Sample ACF Plot with ' + r'$\beta_1$=' + str(ma2[1]) +
' and ' + r'$\beta_2$=' + str(ma2[2]))
axarr[0, 1].set_xlabel('lags')
simulated_data_3 = arma_generate_sample(ar=ar, ma=ma3, nsample=n)
plot_pacf(simulated_data_3,
'''generates some ARMA random samples and saves to python module file
'''
import numpy as np
from statsmodels.sandbox import tsa
from statsmodels.tsa.arima_process import arma_generate_sample
from .maketests_mlabwrap import HoldIt
if __name__ == '__main__':
filen = 'savedrvs_tmp.py'
np.set_printoptions(precision=14, linewidth=100)
# check arma to return same as random.normal
np.random.seed(10000)
xo = arma_generate_sample([1], [1], nsample=100)
xo2 = np.round(xo * 1000).astype(int)
np.random.seed(10000)
rvs = np.random.normal(size=100)
rvs2 = np.round(xo * 1000).astype(int)
assert (xo2 == rvs2).all()
nsample = 1000
data = HoldIt('rvsdata')
np.random.seed(10000)
xo = arma_generate_sample([1, -0.8, 0.5], [1], nsample=nsample)
data.xar2 = np.round(xo * 1000).astype(int)
np.random.seed(10000)
xo = np.random.normal(size=nsample)
data.xnormal = np.round(xo * 1000).astype(int)
import numpy as np
from statsmodels.tsa.arima_process import arma_generate_sample
from statsmodels.iolib import savetxt
np.random.seed(12345)
# no constant
y_arma11 = arma_generate_sample([1., -.75],[1., .35], nsample=250)
y_arma14 = arma_generate_sample([1., -.75],[1., .35, -.75, .1, .35],
nsample=250)
y_arma41 = arma_generate_sample([1., -.75, .25, .25, -.75], [1., .35],
nsample=250)
y_arma22 = arma_generate_sample([1., -.75, .45],[1., .35, -.9], nsample=250)
y_arma50 = arma_generate_sample([1., -.75, .35, -.3, -.2, .1], [1.],
nsample=250)
y_arma02 = arma_generate_sample([1.], [1., .35, -.75], nsample=250)
# constant
constant = 4.5
y_arma11c = arma_generate_sample([1., -.75],[1., .35], nsample=250) + constant
y_arma14c = arma_generate_sample([1., -.75],[1., .35, -.75, .1, .35],
nsample=250) + constant
y_arma41c = arma_generate_sample([1., -.75, .25, .25, -.75], [1., .35],
nsample=250) + constant
y_arma22c = arma_generate_sample([1., -.75, .45],[1., .35, -.9], nsample=250) + \
constant
y_arma50c = arma_generate_sample([1., -.75, .35, -.3, -.2, .1], [1.],
""" import numpy as np import matplotlib.pyplot as plt from statsmodels.tsa.arima_process import arma_generate_sample, ArmaProcess from statsmodels.miscmodels.tmodel import TArma from statsmodels.tsa.arima_model import ARMA from statsmodels.tsa.arma_mle import Arma nobs = 500 ar = [1, -0.6, -0.1] ma = [1, 0.7] dist = lambda n: np.random.standard_t(3, size=n) np.random.seed(8659567) x = arma_generate_sample(ar, ma, nobs, scale=1, distrvs=dist, burnin=500) mod = TArma(x) order = (2, 1) res = mod.fit(order=order) res2 = mod.fit_mle(order=order, start_params=np.r_[res[0], 5, 1], method='nm') print(res[0]) proc = ArmaProcess.from_coeffs(res[0][:order[0]], res[0][:order[1]]) print(ar, ma) proc.nobs = nobs # TODO: bug nobs is None, not needed ?, used in ArmaProcess.__repr__ print(proc.ar, proc.ma) print(proc.ar_roots(), proc.ma_roots())
'''
from __future__ import print_function
import numpy as np
import statsmodels.api as sm
from statsmodels.tsa.arima_process import arma_generate_sample
from statsmodels.tsa.arma_mle import Arma as Arma
from statsmodels.tsa.arima_process import ARIMA as ARIMA_old
from statsmodels.sandbox.tsa.garch import Arma as Armamle_old
from statsmodels.tsa.arima import ARMA as ARMA_kf
print("\nExample 1")
ar = [1.0, -0.6, 0.1]
ma = [1.0, 0.5, 0.3]
nobs = 1000
y22 = arma_generate_sample(ar, ma, nobs + 1000, 0.5)[-nobs:]
y22 -= y22.mean()
start_params = [0.1, 0.1, 0.1, 0.1]
start_params_lhs = [-0.1, -0.1, 0.1, 0.1]
print('truelhs', np.r_[ar[1:], ma[1:]])
###bug in current version, fixed in Skipper and 1 more
###arr[1:q,:] = params[p+k:p+k+q] # p to p+q short params are MA coeffs
###ValueError: array dimensions are not compatible for copy
##arma22 = ARMA_kf(y22, constant=False, order=(2,2))
##res = arma22.fit(start_params=start_params)
##print res.params
print('\nARIMA new')
arest2 = Arma(y22)
# If we test the differenced series, that is the growth rate of moneystock, with a
# Null hypothesis of Random Walk with drift, then we can strongly reject the hypothesis
# that the growth rate has a unit root (p-value 0.0002)
#--------------------------------------------------------------------------------
# To choose the number of lagged terms, p and q, for ARIMA(p,d,q) processes, use the
# Box-Jenkins methodology to look at the pattern in the autocorrelation (acf) and
# partial autocorrelation (pacf) functions.
# scikits.statsmodels.tsa.arima_process contains a class that provides several properties
# of ARMA processes and a random process generator. This allows easy comparison of the
# theoretical properties of an ARMA process with their empirical counterparts.
# For exmaple, define the lag coefficients for an ARMA(2,2) process, generate a random
# process and compare the observed and theoretical pacf:
ar = np.r_[1., -0.5, -0.2]
ma = np.r_[1., 0.2, -0.2]
np.random.seed(123)
x = ap.arma_generate_sample(ar, ma, 20000, burnin=1000)
print "observed pacf: {0}".format(sm.tsa.pacf(x, 5))
theo_ap = ap.ArmaProcess(ar, ma)
print " theo pacf: {0}\n".format(theo_ap.pacf(6))
# We can see that observed and theoretical pacf are very close in a large generated
# sample like this.
#--------------------------------------------------------------------------------
# We can use Statsmodels Autoregressive Moving Average (ARMA) time-series models to
# simulate a series:
ar_coef = [1, .75, -.25]
ma_coef = [1, -.5]
nobs = 100
y = ap.arma_generate_sample(ar_coef, ma_coef, nobs)
y += 4 # add in a constant
# Estimate an ARMA model of the series
return 0
else:
return 1
def getP(acf, alpha):
if (max(acf) < alpha):
return 0
index = np.where(acf > alpha)
return min(index) - 1
def getQ(vals):
index = 0
for val in vals:
if 0 >= val[0] and 0 <= val[1]:
return index - 1
index += 1
return 0
ar = [1, 0.8, 0.5, 0.6, 0.4]
ma = [1]
sampleAR = ts.arma_generate_sample(ar, ma, 1000)
boxJenkinsAlgo(sampleAR)
ar = [1]
ma = [1, -0.8, -0.5, -0.6, -0.4]
sampleMA = ts.arma_generate_sample(ar, ma, 1000)
boxJenkinsAlgo(sampleMA)
reslst = modc.fit(order=(1, 1))
print(reslst[0])
rescmt = modct.fit_mle(order=(1, 1),
start_params=[-0.4, 0.4, 10, 1.],
maxiter=500,
maxfun=500)
print(rescmt.params)
mkf = ARMA(x)
##rkf = mkf.fit((1,1))
##rkf.params
rkf = mkf.fit((1, 1), trend='nc')
print(rkf.params)
np.random.seed(12345)
y_arma22 = arma_generate_sample([1., -.85, .35, -0.1], [1, .25, -.7],
nsample=1000)
##arma22 = ARMA(y_arma22)
##res22 = arma22.fit(trend = 'nc', order=(2,2))
##print 'kf ',res22.params
##res22css = arma22.fit(method='css',trend = 'nc', order=(2,2))
##print 'css', res22css.params
mod22 = Arma(y_arma22)
resls22 = mod22.fit(order=(2, 2))
print('ls ', resls22[0])
resmle22 = mod22.fit_mle(order=(2, 2), maxfun=2000)
print('mle', resmle22.params)
f = mod22.forecast()
f3 = mod22.forecast3(start=900)[-20:]
print(y_arma22[-10:])
fevd.plot()
print(res.test_whiteness())
print(res.test_causality('m1', 'realgdp'))
print(res.test_normality())
#Example TSA ARMA
# Generate some data from an ARMA process
arparams = np.array([.75, -.25])
maparams = np.array([.65, .35])
# The conventions of the arma_generate function require that we specify a
# 1 for the zero-lag of the AR and MA parameters and that the AR parameters
# be negated.
arparams = np.r_[1, -arparams]
maparam = np.r_[1, maparams]
nobs = 250
y = arma_generate_sample(arparams, maparams, nobs)
plt.figure()
plt.plot(y)
# Now, optionally, we can add some dates information. For this example,
# we'll use a pandas time series.
dates = sm.tsa.datetools.dates_from_range('1980m1', length=nobs)
y = Series(y, index=dates)
arma_mod = sm.tsa.ARMA(y, order=(2, 2), freq='M')
arma_res = arma_mod.fit(trend='nc', disp=-1)
print(arma_res.params)
plt.show()
from statsmodels.graphics.tsaplots import plot_acf
plot_acf(x, lags=10)
plt.show()
########## ARMA example
from statsmodels.tsa.arima_process import arma_generate_sample
import statsmodels as sm
np.random.seed(100)
alpha1 = -0.5
#alpha2 = -0.5
ma1 = 1.1
ma2 = 0.5
ar = [1, alpha1]
ma = [1, ma1, ma2]
y = arma_generate_sample(ar, ma, 10000)
plt.plot(
arma_generate_sample(ar, ma, 100),
color='k',
linewidth='1',
label=
'ARMA process $\u03C6_1$ = %2.1f, $\u03B8_1$ = %2.1f, $\u03B8_2$ = %2.1f' %
(-alpha1, ma1, ma2))
plt.legend()
plt.show()
########## ARIMA Model Fit
from pmdarima.arima import auto_arima
model = auto_arima(
y,
seasonality=False,
import numdifftools as ndt
import statsmodels.api as sm
from statsmodels.sandbox import tsa
from statsmodels.tsa.arma_mle import Arma # local import
from statsmodels.tsa.arima_process import arma_generate_sample
examples = ['arma']
if 'arma' in examples:
print "\nExample 1"
print '----------'
ar = [1.0, -0.8]
ma = [1.0, 0.5]
y1 = arma_generate_sample(ar,ma,1000,0.1)
y1 -= y1.mean() #no mean correction/constant in estimation so far
arma1 = Arma(y1)
arma1.nar = 1
arma1.nma = 1
arma1res = arma1.fit_mle(order=(1,1), method='fmin')
print arma1res.params
#Warning need new instance otherwise results carry over
arma2 = Arma(y1)
arma2.nar = 1
arma2.nma = 1
res2 = arma2.fit(method='bfgs')
print res2.params
print res2.model.hessian(res2.params)
result = adfuller(city_stationary['city_population'])
# Plot the differenced time series
fig, ax = plt.subplots()
city_stationary.plot(ax=ax)
plt.show()
# Print the test statistic and the p-value
print('ADF Statistic:', result[0])
print('p-value:', result[1])
amazon_diff = amazon.diff().dropna()
result_diff = adfuller(amazon_diff['close'])
print(result_diff)
amazon_log = np.log((amazon/amazon.shift(1)).dropna())
result_log = adfuller(amazon_log['close'])
print(result_log)
#Generating ARMA data
from statsmodels.tsa.arima_process import arma_generate_sample
np.random.seed(3)
# Set coefficients
ar_coefs = [1, 0.2]
ma_coefs = [1, 0.3, 0.4]
# Generate data
y = arma_generate_sample(ar_coefs, ma_coefs, nsample=100, sigma=0.5, )
plt.plot(y)
plt.ylabel(r'$y_t$')
plt.xlabel(r'$t$')
plt.show()
B_i.append(B_i_i)
V = C0.copy()
U = C0.copy()
for j in range(i):
V -= np.dot(A_i[j], self.C[j+1, :, :].T)
U -= np.dot(B_i[j], self.C[j+1, :, :])
A = A_i.copy()
B = B_i.copy()
return A
if __name__ == '__main__':
k, d, r, seed = 2, 1, 0.05, 123
T1, T2 = 5, 7
cf = ChangeFinder(k, d, r, T1, T2, seed)
#X1 = multivariate_normal([0.0, 0.0], [[1.0, 0.0], [0.0, 1.0]]).rvs(10000)
#X2 = multivariate_normal([1.0, 1.0], [[1.0, 0.8], [0.8, 1.0]]).rvs(1000)
#X = np.vstack((X1, X2))
#X = np.vstack((X1))
X = arma_generate_sample([1.0, -0.6, 0.5], [1.0, 0.0, 0.0], 100000)
X = X.reshape(-1, 1)
for i in range(X.shape[0]):
cf.update(X[i, :])
df = pd.DataFrame(index=index, columns=columns)
df = df.fillna(0) # With 0s rather than NaNs
print(df.head())
# In[4]:
# Simulation of ARMA processes
for i in np.arange(0,len(df.columns)):
arparams = np.array([1, random.uniform(-0.99,0.99), random.uniform(-0.99,0.99)])
maparams = np.array([1, random.uniform(-0.99,0.99), random.uniform(-0.99,0.99)])
df.iloc[:,i] = arma_generate_sample(arparams, maparams, nsample)
print(df.head())
# In[5]:
# Plots
df.plot(subplots=True, figsize=(30,20))
# ## VAR
# In[6]:
# Generate data
#
print 'Generating data...'
# generate labels
labels = np.array([1] * nq + [0] * nq + [1] * nq + [0] * nq)
# generate static features
static = np.vstack((np.random.normal(5.0, 1.0, (nq, nfeatures)),
np.random.normal(0.0, 1.0, (nq, nfeatures)),
np.random.normal(0.0, 1.0, (nq, nfeatures)),
np.random.normal(0.0, 1.0, (nq, nfeatures))))
# generate dynamic features
dynamic_q1 = np.vstack([
ap.arma_generate_sample(arparams_pos, maparams_pos, seqlen)
for i in range(nq * nseqfeatures)
]).reshape(nq, nseqfeatures, seqlen)
dynamic_q2 = np.vstack([
ap.arma_generate_sample(arparams_pos, maparams_pos, seqlen)
for i in range(nq * nseqfeatures)
]).reshape(nq, nseqfeatures, seqlen)
dynamic_q3 = np.vstack([
ap.arma_generate_sample(arparams_neg, maparams_neg, seqlen)
for i in range(nq * nseqfeatures)
]).reshape(nq, nseqfeatures, seqlen)
dynamic_q4 = np.vstack([
ap.arma_generate_sample(arparams_pos, maparams_pos, seqlen)
for i in range(nq * nseqfeatures)
]).reshape(nq, nseqfeatures, seqlen)
dynamic = np.vstack((dynamic_q1, dynamic_q2, dynamic_q3, dynamic_q4))
#Example TSA ARMA
import numpy as np
import statsmodels.api as sm
# Generate some data from an ARMA process
from statsmodels.tsa.arima_process import arma_generate_sample
arparams = np.array([.75, -.25])
maparams = np.array([.65, .35])
# The conventions of the arma_generate function require that we specify a
# 1 for the zero-lag of the AR and MA parameters and that the AR parameters
# be negated.
arparams = np.r_[1, -arparams]
maparam = np.r_[1, maparams]
nobs = 250
y = arma_generate_sample(arparams, maparams, nobs)
plt.figure()
plt.plot(y)
#Now, optionally, we can add some dates information. For this example,
# we'll use a pandas time series.
dates = sm.tsa.datetools.dates_from_range('1980m1', length=nobs)
y = Series(y, index=dates)
arma_mod = sm.tsa.ARMA(y, freq='M')
#arma_res = arma_mod.fit(order=(2,2), trend='nc', disp=-1) #fails
#old pandas 0.4.0: AttributeError: 'TimeSeries' object has no attribute 'name'
#arma_res.params
plt.show()
_attrs = {}
_wrap_attrs = wrap.union_dicts(tsbase.TimeSeriesResultsWrapper._wrap_attrs,
_attrs)
_methods = {}
_wrap_methods = wrap.union_dicts(
tsbase.TimeSeriesResultsWrapper._wrap_methods,
_methods)
wrap.populate_wrapper(ARMAResultsWrapper, ARMAResults)
if __name__ == "__main__":
import numpy as np
import statsmodels.api as sm
# simulate arma process
from statsmodels.tsa.arima_process import arma_generate_sample
y = arma_generate_sample([1., -.75],[1.,.25], nsample=1000)
arma = ARMA(y)
res = arma.fit(trend='nc', order=(1,1))
np.random.seed(12345)
y_arma22 = arma_generate_sample([1.,-.85,.35],[1,.25,-.9], nsample=1000)
arma22 = ARMA(y_arma22)
res22 = arma22.fit(trend = 'nc', order=(2,2))
# test CSS
arma22_css = ARMA(y_arma22)
res22css = arma22_css.fit(trend='nc', order=(2,2), method='css')
data = sm.datasets.sunspots.load()
ar = ARMA(data.endog)
##number of point of the time series
nsample = 1024
## Simulate a simple sinusoidal function
x1 = np.linspace(0, 100, nsample)
y=np.sin(x1) + 13826"""
import statsmodels.api as sm
from statsmodels.tsa.arima_process import arma_generate_sample
np.random.seed(12345)
arparams = np.array([0.9, -0.9])
maparams = np.array([-0.5, 1])
ar = np.r_[1, -arparams]
ma = np.r_[1, maparams]
y = pd.DataFrame(arma_generate_sample(arparams, maparams, 499) + 13825.680000,
columns=["AUD/USD"])
fxfwd = pd.concat([fxfwd, y])
#plt.plot(fxfwd)
# Splitting the Dataset
train = fxfwd[:int(0.8 * (len(fxfwd)))]
valid = fxfwd[int(0.8 * (len(fxfwd))):]
# split a univariate sequence into samples
def split_sequence(sequence, n_steps):
X, y = list(), list()
for i in range(len(sequence)):
try:
import scikits.talkbox.spectral.basic as stbs
except ImportError:
hastalkbox = False
ar = [1., -0.7]#[1,0,0,0,0,0,0,-0.7]
ma = [1., 0.3]
ar = np.convolve([1.]+[0]*50 +[-0.6], ar)
ar = np.convolve([1., -0.5]+[0]*49 +[-0.3], ar)
n_startup = 1000
nobs = 1000
# throwing away samples at beginning makes sample more "stationary"
xo = arma_generate_sample(ar,ma,n_startup+nobs)
x = xo[n_startup:]
plt.figure()
plt.plot(x)
rescale = 0
w, h = signal.freqz(ma, ar)
sd = np.abs(h)**2/np.sqrt(2*np.pi)
if np.sum(np.isnan(h)) > 0:
# this happens with unit root or seasonal unit root'
print('Warning: nan in frequency response h')
h[np.isnan(h)] = 1.
x = 1+np.arange(12)
for blocksize in [2,2,3,3,4,4,5,5,5]:
print(blocksize, block_shuffle(x, blocksize))
# tests of discretise
print('\ntests of discretise')
x = 1+np.arange(12)
np.random.shuffle(x)
print('x:', x)
for k in [1,2,3,4,12]:
print(k, discretise(x, k))
# tests of discretise + entropy_rate
# print('\ntests of discretise + entropy_rate')
# x = np.random.randint(0,2**8,size=100000).astype(np.uint32)
# xb = bytearray(x)
# print('x[:4]: ',x[:4],'xb[:4]: ',xb[:4],'list(xb)[:4]',list(xb)[:4])
# for method in ['lzma','bz2']:
# print(method,'undiscretised',entropy_rate(bytearray(x)))
# for discretisation_level in [2**j for j in [1,2,3,5,8,17]]:
# xd = discretise(x,discretisation_level)
# print(method,'discretised',discretisation_level,
# entropy_rate(bytearray(xd), method=method))
# tests of dependogram
print('\ntests of dependogram')
x = arma_generate_sample([1,.5],[1],nsample=10000).astype(np.float64)
xb = bytearray(x)
print('x[:5]',x[:5])
# print(dependogram(x, blocksizes=[1,2,3,100], nshuffles=100, nbins=4, plot=True))
# dependogram(x, nshuffles=100, nbins=8, plot=True)
# dependogram(x, nshuffles=100, nbins=6, plot=True)
dependogram(x, nshuffles=100, nbins=2, plot=False, method='lzma')
dependogram(x, nshuffles=100, nbins=2, plot=True, method='bz2')
print(reslst[0])
rescmt = modct.fit_mle(order=(1,1), start_params=[-0.4,0.4, 10, 1.],maxiter=500,
maxfun=500)
print(rescmt.params)
from statsmodels.tsa.arima_model import ARMA
mkf = ARMA(x)
##rkf = mkf.fit((1,1))
##rkf.params
rkf = mkf.fit((1,1), trend='nc')
print(rkf.params)
from statsmodels.tsa.arima_process import arma_generate_sample
np.random.seed(12345)
y_arma22 = arma_generate_sample([1.,-.85,.35, -0.1],[1,.25,-.7], nsample=1000)
##arma22 = ARMA(y_arma22)
##res22 = arma22.fit(trend = 'nc', order=(2,2))
##print 'kf ',res22.params
##res22css = arma22.fit(method='css',trend = 'nc', order=(2,2))
##print 'css', res22css.params
mod22 = Arma(y_arma22)
resls22 = mod22.fit(order=(2,2))
print('ls ', resls22[0])
resmle22 = mod22.fit_mle(order=(2,2), maxfun=2000)
print('mle', resmle22.params)
f = mod22.forecast()
f3 = mod22.forecast3(start=900)[-20:]
print(y_arma22[-10:])
def ar1_sim(y, p, t=None):
''' Produce p realizations of an AR(1) process of length n with lag-1 autocorrelation g calculated from `y` and (if provided) `t`
Parameters
----------
y : array
a time series; NaNs not allowed
p : int
column dimension (number of surrogates)
t : array
the time axis of the series
Returns
-------
ysim : array
n by p matrix of simulated AR(1) vector
See Also
--------
pyleoclim.utils.tsmodel.ar1_model : Simulates a (possibly irregularly-sampled) AR(1) process with given decay constant tau, à la REDFIT.
pyleoclim.utils.tsmodel.ar1_fit : Returns the lag-1 autocorrelation from AR(1) fit OR persistence from tauest.
pyleoclim.utils.tsmodel.ar1_fit_evenly : Returns the lag-1 autocorrelation from AR(1) fit assuming even temporal spacing.
pyleoclim.utils.tsmodel.tau_estimation : Estimates the temporal decay scale of an (un)evenly spaced time series.
'''
n = np.size(y)
ysim = np.empty(shape=(n, p)) # declare array
sig = np.std(y)
if is_evenly_spaced(t):
g = ar1_fit_evenly(y)
# specify model parameters (statmodel want lag0 coefficent as unity)
ar = np.r_[1, -g] # AR model parameter
ma = np.r_[1, 0.0] # MA model parameters
sig_n = sig * np.sqrt(
1 - g**2
) # theoretical noise variance for the process to achieve the same variance as y
# simulate AR(1) model for each column
for i in np.arange(p):
#ysim[:, i] = sm.tsa.arma_generate_sample(ar=ar, ma=ma, nsample=n, burnin=50, sigma=sig_n) # old statsmodels syntax
#ysim[:, i] = sm.tsa.ArmaProcess(ar, ma).generate_sample(nsample=n, scale=sig_n, burnin=50) # statsmodels v0.11.1-?
ysim[:, i] = arma_generate_sample(ar,
ma,
nsample=n,
scale=sig_n,
burnin=50) # statsmodels v0.12+
else:
# tau_est = ar1_fit(y, t=t, detrend=detrend, params=params)
tau_est = tau_estimation(y, t)
for i in np.arange(p):
# the output of ar1_model has unit variance,
# multiply by sig to be consistent with the original input timeseries
ysim[:, i] = ar1_model(t, tau_est, output_sigma=sig)
if p == 1:
ysim = ysim[:, 0]
return ysim
def generate_lstm_wins(nsamples, nfeatures, nseqfeatures, seqlen):
# size of 1/4th of a dataset
nq = nsamples / 4
# dynamical feature distribution parameters (for arma)
orders = [np.random.randint(1, 5, 4) for rep in range(nseqfeatures)]
arparams_pos = [np.hstack((1.0, np.random.uniform(-0.1, 0.1, ord[0]))) for ord in orders]
arparams_neg = [np.hstack((1.0, np.random.uniform(-0.1, 0.1, ord[1]))) for ord in orders]
maparams_pos = [np.hstack((1.0, np.random.uniform(-0.5, 0.5, ord[2]))) for ord in orders]
maparams_neg = [np.hstack((1.0, np.random.uniform(-0.5, 0.5, ord[3]))) for ord in orders]
#
# Generate data
#
print 'Generating data...'
# generate labels
labels = np.array([1] * nq + [0] * nq + [1] * nq + [0] * nq)
# generate distribution parameters for the static features
smean_pos = np.random.uniform(0, 2, nfeatures)
ssigm_pos = [1.0] * nfeatures
smean_neg = np.random.uniform(0, 2, nfeatures)
ssigm_neg = [1.0] * nfeatures
# generate static features
static_q1 = np.vstack([np.random.normal(smean_pos[f], ssigm_pos[f], nq) for f in range(nfeatures)])
static_q2 = np.vstack([np.random.normal(smean_neg[f], ssigm_neg[f], nq) for f in range(nfeatures)])
static_q3 = np.vstack([np.random.normal(smean_neg[f], ssigm_neg[f], nq) for f in range(nfeatures)])
static_q4 = np.vstack([np.random.normal(smean_neg[f], ssigm_neg[f], nq) for f in range(nfeatures)])
static = np.vstack((static_q1.T, static_q2.T, static_q3.T, static_q4.T))
# generate dynamic features
dynamic_q1 = np.vstack([ap.arma_generate_sample(arparams_pos[i % nseqfeatures], maparams_pos[i % nseqfeatures], seqlen)
for i in range(nq * nseqfeatures)]).reshape(nq, nseqfeatures, seqlen)
dynamic_q2 = np.vstack([ap.arma_generate_sample(arparams_pos[i % nseqfeatures], maparams_pos[i % nseqfeatures], seqlen)
for i in range(nq * nseqfeatures)]).reshape(nq, nseqfeatures, seqlen)
dynamic_q3 = np.vstack([ap.arma_generate_sample(arparams_neg[i % nseqfeatures], maparams_neg[i % nseqfeatures], seqlen)
for i in range(nq * nseqfeatures)]).reshape(nq, nseqfeatures, seqlen)
dynamic_q4 = np.vstack([ap.arma_generate_sample(arparams_pos[i % nseqfeatures], maparams_pos[i % nseqfeatures], seqlen)
for i in range(nq * nseqfeatures)]).reshape(nq, nseqfeatures, seqlen)
dynamic = np.vstack((dynamic_q1, dynamic_q2, dynamic_q3, dynamic_q4))
#
# Split the dataset into training and test sets
#
print 'Splitting train and test...'
# pick samples for training and for testing
train_idx = np.random.choice(range(0, nsamples), size=np.round(nsamples * 0.7, 0), replace=False)
test_idx = list(set(range(0, nsamples)) - set(train_idx))
train_static = static[train_idx, :]
train_dynamic = dynamic[train_idx, :, :]
test_static = static[test_idx, :]
test_dynamic = dynamic[test_idx, :, :]
train_labels = labels[train_idx]
test_labels = labels[test_idx]
return train_static, train_dynamic, test_static, test_dynamic, train_labels, test_labels
#1D Random walk
N=500 #number of observations
#Initialise
X=np.zeros((1,N), float)
epsilon=np.random.normal(loc=0.0, scale=1, size=(1,N))
X[0,0]=epsilon[0,0]
#Generate Random Walk
for i in range(N-1):
X[0,i+1]=X[0,i]+epsilon[0,i]
plt.plot(X[0,:])
#ARMA(2,2)
arparams = np.array([.75, -.25])
maparams = np.array([.65, .35])
arparams = np.r_[1, -arparams]#step is zero is unweighted
maparams = np.r_[1, maparams]#step is zero is unweighted
y = arma_generate_sample(arparams, maparams, 500)#mean zero variance 1
plt.plot(y)
#AR(1)
#Stable
X=np.zeros((1,N), float)
epsilon=np.random.normal(loc=0.0, scale=1, size=(1,N))
X[0,0]=epsilon[0,0]
for i in range(N-1):
X[0,i+1]=0.5*X[0,i]+epsilon[0,i]
plt.plot(X[0,:])
#Unstable
for i in range(N-1):
X[0,i+1]=2*X[0,i]+epsilon[0,i]
plt.plot(X[0,:])
#Estimate ACF and PACF
acf_X=acf(np.squeeze(X), nlags=10)
def GAP(self, method, measure, nrefs=250, maxClusters=10):
"""
Calculates optimal number of clusters using Gap Statistic from Tibshirani, Walther, Hastie
:param nrefs: number of sample reference datasets to create
:param maxClusters: Maximum number of clusters to test for
Returns: (k_opt, resultsdf)
"""
if method not in {
'k_medoids', 'hierarchical_single', 'hierarchical_complete',
'hierarchical_ward'
}:
raise ValueError(
"method not from set {'k_medoids', 'hierarchical_complete', 'hierarchical_ward'}"
)
if measure not in {
'manhattan', 'euclidean', 'chebyshev', 'dtw', 'lcss', 'dft',
'dwt'
}:
raise ValueError(
"measure not from set 'manhattan', 'euclidean', 'chebyshev', 'dtw', 'lcss', 'dft', 'dwt'"
)
self.create_distance_matrix(measure)
dm = self.distances.dm
np.random.seed(123)
gaps = np.zeros((len(range(1, maxClusters)), ))
s_ks = np.zeros((len(range(1, maxClusters)), ))
resultsdf = pd.DataFrame({'clusterCount': [], 'gap': [], 's_k': []})
for gap_index, k in enumerate(range(1, maxClusters)):
# Holder for reference dispersion results
refDisps = np.zeros(nrefs)
# For n references, generate random sample and perform clutsering getting resulting dispersion of each loop
for i in range(nrefs):
# Create new random reference set
ts_matrix_random = []
for j in range(len(self.distances.ts_matrix)):
arparams = np.array([0.9, -0.5])
maparams = np.array([0.25, 0])
ar = np.r_[1, -arparams] # add zero-lag and negate
ma = np.r_[1, maparams] # add zero-lag
y = arma_generate_sample(ar, ma,
len(self.distances.ts_matrix[0]))
y_norm = [
100 * (float(l) - min(y)) / (max(y) - min(y))
for l in y
]
ts_matrix_random.append(y_norm)
self.distances.ts_matrix = np.array(ts_matrix_random)
self.create_distance_matrix(measure)
# Fit to it
if method == 'k_medoids':
refDisp = self.k_medoids(k)
elif method == 'hierarchical_single':
refDisp = self.hierarchical('single', k)
elif method == 'hierarchical_complete':
refDisp = self.hierarchical('complete', k)
elif method == 'hierarchical_ward':
refDisp = self.hierarchical('ward', k)
refDisps[i] = refDisp
# Fit cluster to original data and create dispersion
self.distances.ts_matrix = np.array(self.ts_matrix)
self.distances.dm = dm
if method == 'k_medoids':
origDisp = self.k_medoids(k)
elif method == 'hierarchical_single':
origDisp = self.hierarchical('single', k)
elif method == 'hierarchical_complete':
origDisp = self.hierarchical('complete', k)
elif method == 'hierarchical_ward':
origDisp = self.hierarchical('ward', k)
# Calculate gap statistic
gap = np.mean(np.log(refDisps)) - np.log(origDisp)
sd_k = np.std(np.log(refDisps))
s_k = sd_k * np.sqrt(1 + 1 / nrefs)
# Assign this loop's gap statistic to gaps
gaps[gap_index] = gap
s_ks[gap_index] = s_k
resultsdf = resultsdf.append(
{
'clusterCount': k,
'gap': gap,
's_k': s_k
}, ignore_index=True)
# if method == 'k_medoids':
if np.nonzero(
np.array(gaps[0:(maxClusters - 2)]) >= np.array(
(gaps[1:(maxClusters - 1)] -
s_ks[1:(maxClusters - 1)])))[0].tolist() and k > 1:
k_opt = np.nonzero(
np.array(gaps[0:(maxClusters - 2)]) >= np.array((gaps[1:(
maxClusters - 1)] - s_ks[1:(maxClusters - 1)])))[0][0] + 1
else:
k_opt = gaps.argmax() + 1
return (k_opt, resultsdf)
daily_samples=365
daily_sigma=np.sqrt(25.18)
amplitude_ar=np.r_[1, amplitude_model.fit(disp=0).arparams]
amplitude_ma=np.r_[1,amplitude_model.fit(disp=0).maparams]
amplitude_samples=365
amplitude_sigma=np.sqrt(28.86)
simulation=np.array([])
paths = 10
k=0
sampling = [[None]] * (paths + 1)
while(k<paths):
hourly_residual_simulation, sampling[k] = armaSampling.arma_generate_sample_and_noise(ar=hourly_ar, ma=hourly_ma, nsample=hourly_samples,sigma=hourly_sigma, write_sample=False)
# arma_generate_sample(ar=hourly_ar, ma=hourly_ma, nsample=hourly_samples,sigma=hourly_sigma)
daily_residual_simulation=arma_generate_sample(ar=daily_ar, ma=daily_ma, nsample=daily_samples,sigma=daily_sigma)
amplitude_residual_simulation=arma_generate_sample(ar=amplitude_ar, ma=amplitude_ma, nsample=amplitude_samples,sigma=amplitude_sigma)
i=0
path=np.zeros(365*24)
while (i<len(hourly_residual_simulation)):
path[i]=(hourly_explain[i]+hourly_residual_simulation[i])*(amplitude_explain[i//24]+amplitude_residual_simulation[i//24])+daily_residual_simulation[i//24]+daily_explain[i//24]
i=i+1
if(k==0):
simulation=path.copy()
else:
simulation=np.c_[simulation,path]
k=k+1
sampling = zip(*sampling)
pd.DataFrame(sampling).to_csv(os.getcwd() + '/simulation/sampling/normal_sampling' + str(paths) + 'paths.csv')
'''
from __future__ import print_function
import numpy as np
import statsmodels.api as sm
from statsmodels.tsa.arima_process import arma_generate_sample
from statsmodels.tsa.arma_mle import Arma as Arma
from statsmodels.tsa.arima_process import ARIMA as ARIMA_old
from statsmodels.sandbox.tsa.garch import Arma as Armamle_old
print("\nExample 1")
ar = [1.0, -0.6, 0.1]
ma = [1.0, 0.5, 0.3]
nobs = 1000
y22 = arma_generate_sample(ar, ma, nobs+1000, 0.5)[-nobs:]
y22 -= y22.mean()
start_params = [0.1, 0.1, 0.1, 0.1]
start_params_lhs = [-0.1, -0.1, 0.1, 0.1]
print('truelhs', np.r_[ar[1:], ma[1:]])
###bug in current version, fixed in Skipper and 1 more
###arr[1:q,:] = params[p+k:p+k+q] # p to p+q short params are MA coeffs
###ValueError: array dimensions are not compatible for copy
##from statsmodels.tsa.arima import ARMA as ARMA_kf
##arma22 = ARMA_kf(y22, constant=False, order=(2,2))
mainv, wasinvertible = invertibleroots(ma)
if not wasinvertible:
start_params = res.params.copy()
start_params[self.nar:self.nar + self.nma] = mainv[1:]
#need to add args kwds
res = self.fit(start_params=start_params)
return res
if __name__ == '__main__':
nobs = 50
ar = [1.0, -0.8, 0.1]
ma = [1.0, 0.1, 0.2]
#ma = [1]
np.random.seed(9875789)
y = arma_generate_sample(ar, ma, nobs, 2)
y -= y.mean() #I have not checked treatment of mean yet, so remove
mod = MLEGLS(y)
mod.nar, mod.nma = 2, 2 #needs to be added, no init method
mod.nobs = len(y)
res = mod.fit(start_params=[0.1, -0.8, 0.2, 0.1, 1.])
print('DGP', ar, ma)
print(res.params)
from statsmodels.regression import yule_walker
print(yule_walker(y, 2))
#resi = mod.fit_invertible(start_params=[0.1,0,0.2,0, 0.5])
#print(resi.params
arpoly, mapoly = getpoly(mod, res.params[:-1])
data = sunspots.load(as_pandas=False)
'''
import numpy as np
from statsmodels.tsa.arima_process import arma_generate_sample
from .maketests_mlabwrap import HoldIt
if __name__ == '__main__':
filen = 'savedrvs_tmp.py'
np.set_printoptions(precision=14, linewidth=100)
# check arma to return same as random.normal
np.random.seed(10000)
xo = arma_generate_sample([1], [1], nsample=100)
xo2 = np.round(xo*1000).astype(int)
np.random.seed(10000)
rvs = np.random.normal(size=100)
rvs2 = np.round(xo*1000).astype(int)
assert (xo2==rvs2).all()
nsample = 1000
data = HoldIt('rvsdata')
np.random.seed(10000)
xo = arma_generate_sample([1, -0.8, 0.5], [1], nsample=nsample)
data.xar2 = np.round(xo*1000).astype(int)
np.random.seed(10000)
xo = np.random.normal(size=nsample)
data.xnormal = np.round(xo*1000).astype(int)
使用 arima_process.arma_generate_sample() 产生 ARMA 样本
使用 ar_model.AR() 从样本构建 AR 模型
使用 ar_model.AR.select_order() 给 AR 模型定阶，定阶准则为 AIC 或 BIC
使用 stattools.acovf() 计算序列样本自协方差函数
利用样本自协方差函数，使用 armaME() 得到 AR 模型矩估计 (Yule-Walker 估计)
以上函数，除了 armaME()，均来自于第三方库 statsmodel.tsa
其使用方法请参考官方帮助文档，或在导入库后使用 help 命令查询
'''
print('\n*********************\n chapter6: 1.5\n*********************')
def dist(x):
'''从均匀分布 U(-4,4) 中产生随机数'''
return 8 * np.random.random_sample(x) - 4
ar, ma = (1, 0.9, 1.4, 0.7, 0.6), (1, )
series = arima_process.arma_generate_sample(ar, ma, 500, distrvs=dist)
ARmodel = ar_model.AR(series)
maxlag = 12
print('\n----order selection using AIC----\n')
print('upper bound of order: %d' % maxlag)
ARorder_aic = ARmodel.select_order(maxlag, 'aic', trend='nc')
print('order: %d' % ARorder_aic)
armaAcovf = stattools.acovf(series, nlag=ARorder_aic, fft=False)
armaYW = armaME(ARorder_aic, 0, armaAcovf)
print('----order selection using BIC----\n')
print('upper bound of order: %d' % maxlag)
ARorder_bic = ARmodel.select_order(maxlag, 'bic', trend='nc')
print('order: %d' % ARorder_bic)
armaAcovf = stattools.acovf(series, nlag=ARorder_bic, fft=False)
import matplotlib.mlab as mlab
from statsmodels.tsa.arima_process import arma_generate_sample, arma_impulse_response
from statsmodels.tsa.arima_process import arma_acovf, arma_acf, ARIMA
#from movstat import acf, acovf
#from statsmodels.sandbox.tsa import acf, acovf, pacf
from statsmodels.tsa.stattools import acf, acovf, pacf
ar = [1., -0.6]
#ar = [1., 0.]
ma = [1., 0.4]
#ma = [1., 0.4, 0.6]
#ma = [1., 0.]
mod = ''#'ma2'
x = arma_generate_sample(ar, ma, 5000)
x_acf = acf(x)[:10]
x_ir = arma_impulse_response(ar, ma)
#print x_acf[:10]
#print x_ir[:10]
#irc2 = np.correlate(x_ir,x_ir,'full')[len(x_ir)-1:]
#print irc2[:10]
#print irc2[:10]/irc2[0]
#print irc2[:10-1] / irc2[1:10]
#print x_acf[:10-1] / x_acf[1:10]
# detrend helper from matplotlib.mlab
def detrend(x, key=None):
if key is None or key=='constant':
return detrend_mean(x)
import matplotlib.mlab as mlab
from statsmodels.tsa.arima_process import arma_generate_sample, arma_impulse_response
from statsmodels.tsa.arima_process import arma_acovf, arma_acf, ARIMA
#from movstat import acf, acovf
#from statsmodels.sandbox.tsa import acf, acovf, pacf
from statsmodels.tsa.stattools import acf, acovf, pacf
ar = [1., -0.6]
#ar = [1., 0.]
ma = [1., 0.4]
#ma = [1., 0.4, 0.6]
#ma = [1., 0.]
mod = ''#'ma2'
x = arma_generate_sample(ar, ma, 5000)
x_acf = acf(x)[:10]
x_ir = arma_impulse_response(ar, ma)
#print x_acf[:10]
#print x_ir[:10]
#irc2 = np.correlate(x_ir,x_ir,'full')[len(x_ir)-1:]
#print irc2[:10]
#print irc2[:10]/irc2[0]
#print irc2[:10-1] / irc2[1:10]
#print x_acf[:10-1] / x_acf[1:10]
# detrend helper from matplotlib.mlab
def detrend(x, key=None):
if key is None or key=='constant':
return detrend_mean(x)
import numpy as np
from statsmodels.tsa.arima_process import arma_generate_sample
from statsmodels.iolib import savetxt
np.random.seed(12345)
# no constant
y_arma11 = arma_generate_sample([1., -.75],[1., .35], nsample=250)
y_arma14 = arma_generate_sample([1., -.75],[1., .35, -.75, .1, .35],
nsample=250)
y_arma41 = arma_generate_sample([1., -.75, .25, .25, -.75], [1., .35],
nsample=250)
y_arma22 = arma_generate_sample([1., -.75, .45],[1., .35, -.9], nsample=250)
y_arma50 = arma_generate_sample([1., -.75, .35, -.3, -.2, .1], [1.],
nsample=250)
y_arma02 = arma_generate_sample([1.], [1., .35, -.75], nsample=250)
# constant
constant = 4.5
y_arma11c = arma_generate_sample([1., -.75],[1., .35], nsample=250) + constant
y_arma14c = arma_generate_sample([1., -.75],[1., .35, -.75, .1, .35],
nsample=250) + constant
y_arma41c = arma_generate_sample([1., -.75, .25, .25, -.75], [1., .35],
nsample=250) + constant
y_arma22c = arma_generate_sample([1., -.75, .45],[1., .35, -.9], nsample=250) + \
constant
y_arma50c = arma_generate_sample([1., -.75, .35, -.3, -.2, .1], [1.],
import statsmodels.tsa.arima_process as ts
import statsmodels.api as sm
from statsmodels.tsa.stattools import adfuller
import matplotlib.pyplot as plt
ar = [1, 0.7, 0.6, .5, .4]
ma = [1]
n = 1000
sample = ts.arma_generate_sample(ar, ma, n)
fig = plt.figure(figsize=(12, 8))
ax = fig.add_subplot(311)
ax.plot(sample)
ax1 = fig.add_subplot(312)
fig = sm.graphics.tsa.plot_acf(sample, lags=40, ax=ax1)
ax2 = fig.add_subplot(313)
fig = sm.graphics.tsa.plot_pacf(sample, lags=40, ax=ax2)
plt.show()
result = adfuller(sample)
print('ADF Statistic: %f' % result[0])
print('p-value: %f' % result[1])
print('Critical Values:')
for key, value in result[4].items():
print('\t%s: %.3f' % (key, value))
ar = [1, 0, -1.5, 0, 0.5]
ma = [1]
sample = ts.arma_generate_sample(ar, ma, n)
fig = plt.figure(figsize=(12, 8))