def get_sample_data(self, m=ModelType.ar, p=1, q=1, n=None, b=0):
Validator.validate_attribute(p, int, True)
Validator.validate_attribute(q, int, True)
if n is None:
n = self.__n_samples
# the betas of the MA equal to 0 for an AR(p) model likewise
# the alphas of the AR equal to 0 for an MA(q) model
if m is SerialCorrelation.ModelType.ar:
alphas = self.get_alt_diminishing_random_list(size=p)
betas = np.array([0.]) # value of q does not matter in this case
elif m is SerialCorrelation.ModelType.ma:
alphas = np.array([0.]) # value of p does not matter in this case
betas = self.get_diminishing_random_list(size=q)
#betas = np.array([0.6, 0.4, 0.2])
elif m is SerialCorrelation.ModelType.arma:
alphas = self.get_alt_diminishing_random_list(size=p)
betas = self.get_diminishing_random_list(size=q)
#alphas = np.array([0.5, -0.25, 0.4])
#betas = np.array([0.5, -0.3])
# Python requires the zero-lag value as well which is 1
# also the alphas for the AR model must be negated
ar = np.r_[1, -alphas]
ma = np.r_[1, betas]
data = smt.arma_generate_sample(ar=ar, ma=ma, nsample=n, burnin=b)
return alphas, betas, data
def gen_ARMAsample(self,
alphas,
betas,
samples=1000,
burn=4000,
plot=False):
'''generate sample based on ARMA coefficients.
Arguments:
---------
alphas : 1D numpy array with MA coefficients
betas : 1D numpy array with MA coefficients
samples : number of samples
burn : burnin: no idea..
Return:
---------
y : ARMA sample'''
# 1D numpy arrays with coeff ready for filtering
alphas = np.r_[1, alphas]
betas = np.r_[1, betas]
y = smt.arma_generate_sample(ar=alphas,
ma=betas,
nsample=samples,
burnin=burn)
if plot:
plt.figure()
plt.title('ARMA sample: RA(%d) MA(%d)' % (len(alphas), len(betas)))
plt.plot(y, '-k', linewidth=0.7)
plt.tight_layout()
plt.show()
return y
def f5(self):
a = np.array([1, -.24, .13, .3, -.2, .3, -.3])
b = np.array([
1, 1.2, 1.2, 1.2, 1.2, 1.2, 1.2, 1.2, 1.2, 1.2, 1.2, 1.2, 1.2, 1.2,
1.2, .9
])
ar = np.r_[1, np.negative(a)]
ma = np.r_[b]
y = smt.arma_generate_sample(ar=ar,
ma=ma,
nsample=20001,
burnin=300,
sigma=0.02)
return y
def MA():
n = int(1000)
# set the AR(p) alphas equal to 0
alphas = np.array([0.])
betas = np.array([0.6])
# add zero-lag and negate alphas
ar = np.r_[1, -alphas]
ma = np.r_[1, betas]
ma1 = smt.arma_generate_sample(ar=ar, ma=ma, nsample=n)
_ = tsplot(ma1, lags=30)
max_lag = 30
mdl = smt.ARMA(ma1, order=(0, 1)).fit(maxlag=max_lag,
method='mle',
trend='nc')
print(mdl.summary())
def AR_p():
np.random.seed(1)
n_samples = int(1000)
a = 0.6
x = w = np.random.normal(size=n_samples)
for t in range(n_samples):
x[t] = a * x[t - 1] + w[t]
_ = tsplot(x, lags=30)
mdl = smt.AR(x).fit(maxlag=30, ic='aic', trend='nc')
est_order = smt.AR(x).select_order(maxlag=30, ic='aic', trend='nc')
true_order = 1
print('\nalpha estimate: {:3.5f} | best lag order = {}'.format(
mdl.params[0], est_order))
print('\ntrue alpha = {} | true order = {}'.format(a, true_order))
n = int(1000)
alphas = np.array([.666, -.333])
betas = np.array([0.])
# Python requires us to specify the zero-lag value which is 1
# Also note that the alphas for the AR model must be negated
# We also set the betas for the MA equal to 0 for an AR(p) model
# For more information see the examples at statsmodels.org
ar = np.r_[1, -alphas]
ma = np.r_[1, betas]
ar2 = smt.arma_generate_sample(ar=ar, ma=ma, nsample=n)
_ = tsplot(ar2, lags=30)
max_lag = 10
mdl = smt.AR(ar2).fit(maxlag=max_lag, ic='aic', trend='nc')
est_order = smt.AR(ar2).select_order(maxlag=max_lag, ic='aic', trend='nc')
true_order = 2
print('\ncoef estimate: {:3.4f} {:3.4f} | best lag order = {}'.format(
mdl.params[0], mdl.params[1], est_order))
print('\ntrue coefs = {} | true order = {}'.format([.666, -.333],
true_order))
def _generate_ARMA(self):
if self.seed is not None:
np.random.seed(self.seed)
ar = np.array(self.p)
ma = np.array(self.q)
ar = np.r_[1, -ar]
ma = np.r_[1, ma]
burn = int(self.datapoints / 10)
dataset = []
for i in range(self.n_series):
arma = smt.arma_generate_sample(ar=ar,
ma=ma,
nsample=self.datapoints,
burnin=burn)
dataset.append(arma)
return np.array(dataset)
# Plot graphs
xt.plot(ax=ax_xt)
ax_xt.set_title("Time Series")
plot_acf(xt, lags=50, ax=ax_acf)
plot_pacf(xt, lags=50, ax=ax_pacf)
plt.tight_layout()
return None
# Number of samples
n = 600
# Generate MA(1) dataset
ar = np.r_[1, -0]
ma = np.r_[1, 0.7]
ma1_data = smtsa.arma_generate_sample(ar=ar, ma=ma, nsample=n)
plotds(ma1_data)
# Generate MA(2) dataset
ar = np.r_[1, -0]
ma = np.r_[1, 0.6, 0.7]
ma2_data = smtsa.arma_generate_sample(ar=ar, ma=ma, nsample=n)
plotds(ma2_data)
# Generate MA(3) dataset
ar = np.r_[1, -0]
ma = np.r_[1, 0.6, 0.7, 0.5]
ma3_data = smtsa.arma_generate_sample(ar=ar, ma=ma, nsample=n)
plotds(ma3_data)
# Build MA(1) model
# In[19]: # Simulate an AR(2) process n = int(1000) alphas = np.array([.444, .333]) betas = np.array([0.]) # Python requires us to specify the zero-lag value which is 1 # Also note that the alphas for the AR model must be negated # We also set the betas for the MA equal to 0 for an AR(p) model # For more information see the examples at statsmodels.org ar = np.r_[1, -alphas] ma = np.r_[1, betas] ar2 = smt.arma_generate_sample(ar=ar, ma=ma, nsample=n) _ = tsplot(ar2, lags=12, title="AR(2) process") # ## AR(2) process -- has ACF tailing out and PACF cutting off at lag=2 # In[20]: # Simulate an MA(1) process n = int(1000) # set the AR(p) alphas equal to 0 alphas = np.array([0.]) betas = np.array([0.8]) # add zero-lag and negate alphas ar = np.r_[1, -alphas] ma = np.r_[1, betas] ma1 = smt.arma_generate_sample(ar=ar, ma=ma, nsample=n)
# Plot graphs
xt.plot(ax=ax_xt)
ax_xt.set_title('Time Series')
plot_acf(xt, lags=50, ax=ax_acf)
plot_pacf(xt, lags=50, ax=ax_pacf)
plt.tight_layout()
return None
# Number of samples
n = 600
# Generate AR(1) dataset
ar = np.r_[1, -0.6]
ma = np.r_[1, 0]
ar1_data = smtsa.arma_generate_sample(ar=ar, ma=ma, nsample=n)
plotds(ar1_data)
# Generate AR(2) dataset
ar = np.r_[1, 0.6, 0.7]
ma = np.r_[1, 0]
ar2_data = smtsa.arma_generate_sample(ar=ar, ma=ma, nsample=n)
plotds(ar2_data)
# Generate AR(3) dataset
ar = np.r_[1, 0.6, 0.7, 0.5]
ma = np.r_[1, 0]
ar3_data = smtsa.arma_generate_sample(ar=ar, ma=ma, nsample=n)
plotds(ar3_data)
# Build AR(1) model
plt.legend() plt.grid(True) plt.show() #%% np.random.seed(12345) arparams = np.array([.75, -.25]) maparams = np.array([.65, .35]) ar = np.r_[1, -arparams] # add zero-lag and negate ma = np.r_[1, maparams] # add zero-lag #%% Generate Samples num_samples = 250 y = smt.arma_generate_sample(ar, ma, nsample=num_samples) dates = pd.date_range(start='2020-01-01', freq="D", periods=num_samples) y = pd.Series(y, index=dates) set_size = len(y) train_size = int(len(y)*0.7) train_y = y.iloc[:train_size] test_y = y.iloc[train_size:] print(train_y, len(train_y)) #%% tsplot tsplot(train_y) #%% fit model model = smt.arima.ARIMA(train_y, order=(2, 0, 2), trend='n').fit() model.params
a = 0.6
x = w = np.random.normal(size=n_samples)
for t in range(n_samples):
x[t] = a*x[t-1] + w[t]
limit=12
_ = tsplot(x, lags=limit,title="AR(1)process")
#MA(2) simulated process
n = int(1000)
alphas = np.array([0.])
betas = np.array([0.6, 0.4])
ar = np.r_[1, -alphas]
ma = np.r_[1, betas]
ma3 = smt.arma_generate_sample(ar=ar, ma=ma, nsample=n)
_ = tsplot(ma3, lags=12,title="MA(2) process")
###--------------------------------------------------------------------
###ARIMA with prophet
from fbprophet import Prophet
#prophet reqiures a pandas df at the below config
# ( date column named as DS and the value column as Y)
ts=sales.groupby(["date_block_num"])["item_cnt_day"].sum()
ts.index=pd.date_range(start = '2013-01-01',end='2015-10-01', freq = 'MS')
ts=ts.reset_index()
# Plot graphs
xt.plot(ax=ax_xt)
ax_xt.set_title('Time Series')
plot_acf(xt, lags=50, ax=ax_acf)
plot_pacf(xt, lags=50, ax=ax_pacf)
plt.tight_layout()
return None
# Number of samples
n = 600
# Generate AR(1) dataset
ar = np.r_[1, 0.6]
ma = np.r_[1, 0.3]
ar1ma1_data = smtsa.arma_generate_sample(ar=ar, ma=ma, nsample=n)
plotds(ar1ma1_data )
# Impluse response curve
plt.plot(arima_process.arma_impulse_response(ar, ma, nobs=20))
plt.ylabel("Impact")
plt.xlabel("Lag")
# Build AR(1) model
ar1ma1 = smtsa.ARMA(ar1ma1_data.tolist(), order=(1, 1)).fit(
maxlag=30, method='mle', trend='nc')
ar1ma1.summary()
# Optimize ARMA parameters
def get_data(option, conditional=False):
if option == 1:
alphas = np.array([0.5, -0.25])
betas = np.array([0.5, -0.3])
ar = np.r_[1, -alphas]
ma = np.r_[1, betas]
n = int(100)
burn = int(n / 10) # number of samples to discard before fit
arma22 = smt.arma_generate_sample(ar=ar, ma=ma, nsample=n, burnin=burn)
samples = []
cond_arr = []
n_lists = 10000
for j in range(n_lists):
signals = []
cond_sig = []
signals.append(smt.arma_generate_sample(ar=ar, ma=ma, nsample=n, burnin=burn))
for i in range(0, n):
cond_sig.append([alphas,betas])
samples.append(np.array(signals).T)
cond_arr.append(np.array(cond_sig).T)
samples = np.array(samples)
scalar = MinMaxScaler(feature_range=(-1, 1))
samples = np.reshape(samples, newshape=(n_lists, n))
scalar.fit(samples)
samples = scalar.transform(samples)
samples = np.reshape(samples, newshape=[len(samples), n, 1])
if conditional == True:
return samples, cond_arr, scalar
else:
return samples, scalar
elif option == 2:
n_samples = int(100)
n = int(100)
b = 0.6
alphas = np.array([0.])
betas = np.array([0.6])
# add zero-lag and negate alphas
ar = np.r_[1, -alphas]
ma = np.r_[1, betas]
samples = []
cond_arr = []
n_lists = 10000
for j in range(n_lists):
# x = w = np.random.normal(size=n_samples)
signals = []
cond_sig = []
signals.append(smt.arma_generate_sample(ar=ar, ma=ma, nsample=n))
if conditional == True:
for i in range(0, n):
cond_sig.append(b)
samples.append(np.array(signals).T)
cond_arr.append(np.array(cond_sig).T)
samples = np.array(samples)
cond_arr = np.array(cond_arr)
scalar = MinMaxScaler(feature_range=(-1, 1))
samples = np.reshape(samples, newshape=(n_lists, n_samples))
scalar.fit(samples)
samples = scalar.transform(samples)
samples = np.reshape(samples, newshape=[len(samples), n_samples, 1])
if conditional == True:
return samples, cond_arr, scalar
else:
return samples, scalar
elif option == 3:
# autoregressive model
# dependent variable is regressed against one or more lagged values
samples = []
cond_arr = []
n_lists = 10000
n_samples = int(100)
a = 0.6
for j in range(n_lists):
x = w = np.random.normal(size=n_samples)
signals = []
cond_sig = []
for j in range(n_samples):
signals.append(a * x[j - 1] + w[j])
if conditional == True:
cond_sig.append(a)
samples.append(np.array(signals).T)
cond_arr.append(np.array(cond_sig).T)
samples = np.array(samples)
cond_arr = np.array(cond_arr)
scalar = MinMaxScaler(feature_range=(-1, 1))
scalar.fit(samples)
samples = scalar.transform(samples)
samples = np.reshape(samples, newshape=[len(samples), n_samples, 1])
if conditional == True:
return samples, cond_arr, scalar
else:
return samples, scalar
# Plot graphs
xt.plot(ax=ax_xt)
ax_xt.set_title('Time Series')
plot_acf(xt, lags=50, ax=ax_acf)
plot_pacf(xt, lags=50, ax=ax_pacf)
plt.tight_layout()
return None
# Number of samples
n = 600
# Generate AR(1) dataset
ar = np.r_[1, -0.6]
ma = np.r_[1, 0]
ar1_data = smtsa.arma_generate_sample(ar=ar, ma=ma, nsample=n)
plotds(ar1_data)
# Generate AR(2) dataset
ar = np.r_[1, 0.6, 0.7]
ma = np.r_[1, 0]
ar2_data = smtsa.arma_generate_sample(ar=ar, ma=ma, nsample=n)
plotds(ar2_data)
# Generate AR(3) dataset
ar = np.r_[1, 0.6, 0.7, 0.5]
ma = np.r_[1, 0]
ar3_data = smtsa.arma_generate_sample(ar=ar, ma=ma, nsample=n)
plotds(ar3_data)
