def unitroot_test(series):
# Basic statistic
plt.figure()
plt.plot(series)
plot_pacf(series)
# ADF test
# AIC & BIC from lags 12 to 1
print('$p$ & AIC & BIC \\\\')
max_lags = 12
for lags in (max_lags - i for i in range(max_lags)):
ar_model = AutoReg(series, lags, 'n')
res = ar_model.fit()
print(f'{lags} & {round(res.aic, 3)} & {round(res.bic, 3)} \\\\')
# Best lags by `ar_select_order`
sel = ar_select_order(series, max_lags, trend='n')
lags = sel.ar_lags[-1]
print(f'Lags selection: {sel.ar_lags}')
# Start ADF test
adf = ADF(series, lags)
print(adf.summary())
# PP test
pp_tau = PhillipsPerron(series, 3, test_type='tau') # q = 3
pp_rho = PhillipsPerron(series, 3, test_type='rho') # q = 3
print(pp_tau.summary())
print(pp_rho.summary())
def sample(self, lagged_values, lagged_times=None, **ignored):
""" Find Unique Values to see if outcomes are discrete or continuous """
uniques = np.unique(lagged_values)
if len(uniques) < 0.2 * len(
lagged_values
): #arbitrary cutoff of 20% to determine whether outcomes are continuous or quantized
v = [
s for s in (
np.random.choice(lagged_values, self.num_predictions))
] #randomly select from the lagged values and return as answer
else:
rev_values = lagged_values[::
-1] # our data are in reverse order, the AR model needs the opposite
""" Simple Autoregression """
ARmodel = ar_select_order(rev_values,
maxlag=int(0.1 * len(rev_values)))
model_fit = ARmodel.model.fit()
point_est = model_fit.predict(start=len(rev_values),
end=len(rev_values),
dynamic=False)
st_dev = np.std(rev_values)
#v = [s for s in (np.random.normal(point_est, st_dev, self.num_predictions))]
v = [
s for s in (np.linspace(start=point_est - 2 * st_dev,
stop=point_est + 2 * st_dev,
num=self.num_predictions))
] #spread the predictions out evenly
print(*v, sep=", ")
return v
def model(columna, n_periods):
mod = ar_select_order(columna.ravel(), maxlag=15, old_names=True)
AutoRegfit = AutoReg(columna, trend='c', lags=mod.ar_lags,
old_names=True).fit()
prediccion = AutoRegfit.predict(start=len(columna),
end=len(columna) + n_periods - 1,
dynamic=False)
return prediccion
def get_geweke_diags(chains, split=0.3, skip=0.5):
"""Function computes geweke statistic for markov chains"""
# Check dimensionality of chains
# If single chain add dimesion
n_dims = len(chains.shape)
if n_dims == 2:
chains = np.expand_dims(chains, axis=0)
# Compute split demarcations as integers to be used for indexing
n_floor = int(chains.shape[1] * (split + skip))
n_skip = int(chains.shape[1] * (skip))
# Initialize the vector in which we store z-scores
z_scores = np.zeros(chains.shape[0] * chains.shape[2])
# Main loop that computes statistics of interest
for i in range(chains.shape[0]):
for j in range(chains.shape[2]):
# Get Autoregression coefficients for each part of split of chain
sel_1 = ar_select_order(chains[i, n_skip:n_floor, j],
maxlag=10,
seasonal=False)
sel_2 = ar_select_order(chains[i, n_floor:, j],
maxlag=10,
seasonal=False)
res_1 = sel_1.model.fit()
res_2 = sel_2.model.fit()
# Compute the Autoregression corrected respective standard deviations
s_1 = res_1.sigma2 / np.square(1 - np.sum(res_1.params[1:]))
s_2 = res_2.sigma2 / np.square(1 - np.sum(res_2.params[1:]))
# Compute (absolute) z scores that form the basis of the test of whether or not to continue sampling
z_scores[i * chains.shape[2] + j] = np.abs(
(np.mean(chains[i, n_skip:n_floor, j]) -
np.mean(chains[i, n_floor:, j])) /
np.sqrt((1 / (n_floor - n_skip)) * s_1 +
(1 / (chains.shape[1] - n_floor)) * s_2))
# Continuation check: All absolute z scores below 2? If yes stop sampling
continue_ = int((np.sum(z_scores > 2)) > 0)
return continue_, z_scores
def ar_model(data):
from statsmodels.tsa.ar_model import AutoReg, ar_select_order
sel = ar_select_order(data["GMSLNA"],
20,
old_names=False,
seasonal=True,
period=12)
res = sel.model.fit()
return res
def test_ar_order_select():
# GH#2118
np.random.seed(12345)
y = arma_generate_sample([1, -0.75, 0.3], [1], 100)
ts = Series(y, index=date_range(start="1/1/1990", periods=100, freq="M"))
res = ar_select_order(ts, maxlag=12, ic="aic")
assert tuple(res.ar_lags) == (1, 2)
assert isinstance(res.aic, dict)
assert isinstance(res.bic, dict)
assert isinstance(res.hqic, dict)
assert isinstance(res.model, AutoReg)
assert not res.seasonal
assert res.trend == "c"
assert res.period is None
def test_ar_order_select():
# GH#2118
np.random.seed(12345)
y = sm.tsa.arma_generate_sample([1, -.75, .3], [1], 100)
ts = Series(y, index=date_range(start='1/1/1990', periods=100, freq='M'))
res = ar_select_order(ts, maxlag=12, ic='aic', old_names=False)
assert tuple(res.ar_lags) == (1, 2)
assert isinstance(res.aic, dict)
assert isinstance(res.bic, dict)
assert isinstance(res.hqic, dict)
assert isinstance(res.model, AutoReg)
assert not res.seasonal
assert res.trend == 'c'
assert res.period is None
def fit_ar(x):
n = len(x)
ar_selection = ar_select_order(x,
min(int(np.floor(n)),
int(np.floor(10 * np.log10(n)))),
ic='aic',
trend='n',
seasonal=False)
order = ar_selection.ar_lags[-1]
model_fit = ar_selection.model.fit()
return model_fit.params, model_fit.sigma2, order
def sample(self, lagged_values, lagged_times=None, **ignored):
""" Find Unique Values to see if outcomes are discrete or continuous """
rev_values = lagged_values[::
-1] # our data are in reverse order, the AR model needs the opposite
ARmodel = ar_select_order(rev_values,
maxlag=int(0.1 * len(rev_values)))
model_fit = ARmodel.model.fit()
point_est = model_fit.predict(start=len(rev_values),
end=len(rev_values),
dynamic=False)[0]
st_dev = np.std(rev_values)
ps = self.evenly_spaced_percentiles(self.num_predictions)
vs = [point_est + st_dev * self.norminv(p) for p in ps]
jiggle = 0.2 * abs(vs[114] - vs[113]) * np.random.rand()
v_jiggled = [v + jiggle for v in vs]
return v_jiggled
def rem_lags(csv_name):
'''
Analyzing the Remainder and save the df in a csv file.
Parameters
----------
train: pd.dataframe()
The dataframe with the data
Returns
---------
train: pd.dataframe()
The dataframe with all columns: .
csv-file in the folder
'''
train_re = pd.read_csv(csv_name, index_col=0, parse_dates=True)
plot_pacf(train_re['remainder'])
mod = ar_select_order(endog=train_re['remainder'], maxlag=10, old_names=False)
lags = mod.ar_lags
return train_re, lags
def fit_AR_p():
N, t, p, max_order = 200, 180, 1, 10
realisations = pd.Series(list(sample_random_walk(0, N)), range(N))
sel = ar_select_order(realisations[0:t], max_order)
res = sel.model.fit()
print(res.summary())
print("Std residuals: " + str(statistics.stdev(res.resid)))
f = plt.figure(1)
res.plot_diagnostics(fig=f, lags=30)
plt.tight_layout()
plt.savefig('/Users/gwren/Downloads/43_ar_1_fit_diagnostics.svg',
format='svg')
f.show()
f = plt.figure(1)
res.plot_predict(start=t, end=N)
plt.plot(realisations[0:N], label="realisations")
plt.legend(loc="upper left")
plt.grid(True)
plt.xlabel('Period ($t$)')
plt.savefig('/Users/gwren/Downloads/44_ar_1_fit_forecasts.svg',
format='svg')
f.show()
def train_gv_AR(params_gv, gv, max_lag, sel_crit):
"""
Derive AR parameters of global variability under the assumption that gv does not
depend on the scenario.
Parameters
----------
params_gv : dict
parameter dictionary containing keys which do not depend on applied method
- ["targ"] (variable, i.e., tas or tblend, str)
- ["esm"] (Earth System Model, str)
- ["method"] (applied method, i.e., AR, str)
- ["scenarios"] (emission scenarios used for training, list of strs)
gv : dict
nested global mean temperature variability (volcanic influence removed)
dictionary with keys
- [scen] (2d array (nr_runs, nr_ts) of globally-averaged temperature variability
time series)
max_lag: int
maximum number of lags considered during fitting
sel_crit: str
selection criterion for the AR process order, e.g., 'bic' or 'aic'
Returns
-------
params : dict
parameter dictionary containing original keys plus
- ["max_lag"] (maximum lag considered when finding suitable AR model, hardcoded
to 15 here, int)
- ["sel_crit"] (selection criterion applied to find suitable AR model, hardcoded
to Bayesian Information Criterion bic here, str)
- ["AR_int"] (intercept of the AR model, float)
- ["AR_coefs"] (coefficients of the AR model for the lags which are contained in
the selected AR model, list of floats)
- ["AR_order_sel"] (selected AR order, int)
- ["AR_std_innovs"] (standard deviation of the innovations of the selected AR
model, float)
Notes
-----
- Assumptions
- number of runs per scenario and the number of time steps in each scenario can
vary
- each scenario receives equal weight during training
"""
params_gv["max_lag"] = max_lag
params_gv["sel_crit"] = sel_crit
# select the AR Order
nr_scens = len(gv.keys())
AR_order_scens_tmp = np.zeros(nr_scens)
for scen_idx, scen in enumerate(gv.keys()):
nr_runs = gv[scen].shape[0]
AR_order_runs_tmp = np.zeros(nr_runs)
for run in np.arange(nr_runs):
run_ar_lags = ar_select_order(gv[scen][run],
maxlag=max_lag,
ic=sel_crit,
old_names=False).ar_lags
# if order > 0 is selected,add selected order to vector
if len(run_ar_lags) > 0:
AR_order_runs_tmp[run] = run_ar_lags[-1]
AR_order_scens_tmp[scen_idx] = np.percentile(AR_order_runs_tmp,
q=50,
interpolation="nearest")
# interpolation is not a good way to go here because it could lead to an AR
# order that wasn't chosen by run -> avoid it by just taking nearest
AR_order_sel = int(
np.percentile(AR_order_scens_tmp, q=50, interpolation="nearest"))
# determine the AR params for the selected AR order
params_gv["AR_int"] = 0
params_gv["AR_coefs"] = np.zeros(AR_order_sel)
params_gv["AR_order_sel"] = AR_order_sel
params_gv["AR_std_innovs"] = 0
for scen_idx, scen in enumerate(gv.keys()):
nr_runs = gv[scen].shape[0]
AR_order_runs_tmp = np.zeros(nr_runs)
AR_int_tmp = 0
AR_coefs_tmp = np.zeros(AR_order_sel)
AR_std_innovs_tmp = 0
for run in np.arange(nr_runs):
AR_model_tmp = AutoReg(gv[scen][run],
lags=AR_order_sel,
old_names=False).fit()
AR_int_tmp += AR_model_tmp.params[0] / nr_runs
AR_coefs_tmp += AR_model_tmp.params[1:] / nr_runs
AR_std_innovs_tmp += np.sqrt(AR_model_tmp.sigma2) / nr_runs
params_gv["AR_int"] += AR_int_tmp / nr_scens
params_gv["AR_coefs"] += AR_coefs_tmp / nr_scens
params_gv["AR_std_innovs"] += AR_std_innovs_tmp / nr_scens
# check if fitted AR process is stationary
# (highly unlikely this test will ever fail but better safe than sorry)
ar = np.r_[1, -params_gv["AR_coefs"]] # add zero-lag and negate
ma = np.r_[1] # add zero-lag
arma_process = sm.tsa.ArmaProcess(ar, ma)
if not arma_process.isstationary:
raise ValueError(
"The fitted AR process is not stationary. Another solution is needed."
)
return params_gv
# Right now an annual date series must be datetimes at the end of the
# year.
from datetime import datetime
dates = pd.date_range("1700-1-1", periods=len(data.endog), freq="A-DEC")
# ## Using Pandas
#
# Make a pandas TimeSeries or DataFrame
data.endog.index = dates
endog = data.endog
endog
# Instantiate the model
selection_res = ar_select_order(endog,
9,
old_names=False,
seasonal=True,
period=11)
pandas_ar_res = selection_res.model.fit()
# Out-of-sample prediction
pred = pandas_ar_res.predict(start="2005", end="2027")
print(pred)
fig = pandas_ar_res.plot_predict(start="2005", end="2027")
from statsmodels.tsa.ar_model import AutoReg, ar_select_order
from statsmodels.tsa.api import acf, pacf, graphics
pd.plotting.register_matplotlib_converters()
# Default figure size
sns.mpl.rc('figure', figsize=(16, 6))
# %%
ts = stats_df[['created_at',
'percentage_correct']].set_index('created_at').dropna()
temp = ts.asfreq('1H', method='pad')
# Scale by 100 to get percentages
fig, ax = plt.subplots()
ax = ts.plot(ax=ax)
plt.show()
# %%
mod = AutoReg(ts, 3, old_names=False)
res = mod.fit()
print(res.summary())
# %%
res = mod.fit(cov_type="HC0")
print(res.summary())
# %%
sel = ar_select_order(ts, 13, old_names=False)
sel.ar_lags
res = sel.model.fit()
print(res.summary())
# %%
fig = plt.figure(figsize=(16, 9))
fig = res.plot_diagnostics(fig=fig, lags=30)
plt.show()
def test_ar_select_order_smoke():
data = sunspots.load(as_pandas=True).data["SUNACTIVITY"]
ar_select_order(data, 4, glob=True, trend="n")
ar_select_order(data, 4, glob=False, trend="n")
ar_select_order(data, 4, seasonal=True, period=12)
ar_select_order(data, 4, seasonal=False)
ar_select_order(data, 4, glob=True)
ar_select_order(data, 4, glob=True, seasonal=True, period=12)
lh, rh, p = m.getPanda(twitterColumns, pollColumns)
h_agg, p_agg, p_var = m.aggregate(lh,
rh,
p,
splitPolls=False,
interpolate=True)
_, p_onl, p_tel = m.aggregate(lh, rh, p, splitPolls=True, interpolate=True)
kalmanData = m.getKalmanData(p_agg, h_agg)
all_data = kalmanData['remain_perc'].iloc[startTrain:]
remain_data = all_data.values
dates_train = all_data.index
# run experiment for lags
print("order to use", ar_select_order(remain_data, maxlag=13)._aic)
n_lag = 7
runs = 100
k = np.arange(4, 5)
res = np.zeros(shape=(len(k), n_lag - 1))
sorted = np.zeros(shape=(len(k), n_lag - 1))
for i, j in enumerate(k):
res[i] = experiment_lags(remain_data, n_lag, runs, j)
print("sum of results: " + str(np.sum(res, axis=0)))
optimal_lag = np.argmin(np.sum(res, axis=0)) + 1
print("optimal lag = " + str(optimal_lag))
optimal_lag = 1
runs = 3
# We can start with an AR(3). While this is not a good model for this # data, it demonstrates the basic use of the API. mod = AutoReg(housing, 3, old_names=False) res = mod.fit() print(res.summary()) # `AutoReg` supports the same covariance estimators as `OLS`. Below, we # use `cov_type="HC0"`, which is White's covariance estimator. While the # parameter estimates are the same, all of the quantities that depend on the # standard error change. res = mod.fit(cov_type="HC0") print(res.summary()) sel = ar_select_order(housing, 13, old_names=False) sel.ar_lags res = sel.model.fit() print(res.summary()) # `plot_predict` visualizes forecasts. Here we produce a large number of # forecasts which show the string seasonality captured by the model. fig = res.plot_predict(720, 840) # `plot_diagnositcs` indicates that the model captures the key features in # the data. fig = plt.figure(figsize=(16, 9)) fig = res.plot_diagnostics(fig=fig, lags=30)
def AutoRegression(df_input,
target_column,
time_column,
epochs_to_forecast=1,
epochs_to_test=1,
hyper_params_ar={}):
"""
This function performs regression using feature augmentation and then training XGB with Crossvalidation.
Parameters:
- df_input (pandas.DataFrame): Input Time Series.
- target_column (str): name of the column containing the target feature
- time_column (str): name of the column containing the pandas Timestamps
- frequency_data (str): string representing the time frequency of record, e.g. "h" (hours), "D" (days), "M" (months)
- epochs_to_forecast (int): number of steps for predicting future data
- epochs_to_test (int): number of steps corresponding to most recent records to test on
- hyper_params_ar: Parameters of AR model
Returns:
- df_output (pandas.DataFrame): Output DataFrame with forecast
"""
# create and evaluate an updated autoregressive model
# load dataset
input_series = df_input[:-(epochs_to_forecast+epochs_to_test)].set_index(time_column, 1)[target_column]
# split dataset
model = ar_select_order(input_series, **hyper_params_ar)
for hyp_param in ["maxlag","glob","ic"]:
if hyp_param in hyper_params_ar.keys():
del hyper_params_ar[hyp_param]
model = AutoReg(input_series, lags=model.ar_lags, **hyper_params_ar)
res = model.fit()
print(res.summary())
#start_idx = df_input[:-(epochs_to_forecast+epochs_to_test)][time_column].max()
start_idx = df_input[-(epochs_to_forecast+epochs_to_test):][time_column].min()
end_idx = df_input[-(epochs_to_forecast+epochs_to_test):][time_column].max()
# =============================================================================
# ### for statsmodels< 0.12.0
# #forecast_steps = model.predict(res.params, start=start_idx, end=end_idx, dynamic=True)
# forecast = df_input[target_column] * np.nan
# forecast[-(epochs_to_forecast+epochs_to_test):] = forecast_steps
# df_output = df_input.copy()
# df_output["forecast"] = forecast
# df_output["forecast_up"] = forecast * 1.1
# df_output["forecast_low"] = forecast * 0.9
# =============================================================================
### for statsmodels>= 0.12.0
forecast_steps = res.get_prediction(start=start_idx, end=end_idx)
forecast_steps_mean = forecast_steps.predicted_mean
forecast_steps_low = forecast_steps.conf_int()["lower"]
forecast_steps_up = forecast_steps.conf_int()["upper"]
forecast = df_input[target_column] * np.nan
forecast_low = df_input[target_column] * np.nan
forecast_up = df_input[target_column] * np.nan
forecast[-(epochs_to_forecast+epochs_to_test):] = forecast_steps_mean
forecast_low[-(epochs_to_forecast+epochs_to_test):] = forecast_steps_low
forecast_up[-(epochs_to_forecast+epochs_to_test):] = forecast_steps_up
df_output = df_input.copy()
df_output["forecast"] = forecast
df_output["forecast_low"] = forecast_low
df_output["forecast_up"] = forecast_up
return df_output
import matplotlib.pyplot as plt
import pandas as pd
import pandas_datareader as pdr
import seaborn as sns
from statsmodels.tsa.ar_model import AutoReg, ar_select_order
from statsmodels.tsa.api import acf, pacf, graphics
import numpy as np
data = pdr.get_data_fred('INDPRO', '1959-01-01', '2019-06-01')
ind_prod = data.INDPRO.pct_change(12).dropna().asfreq('MS')
_, ax = plt.subplots(figsize=(16, 9))
ind_prod.plot(ax=ax)
sel = ar_select_order(ind_prod, 13, 'bic', old_names=False)
res = sel.model.fit()
print(res.summary())
sel = ar_select_order(ind_prod, 13, 'bic', glob=True, old_names=False)
sel.ar_lags
res_glob = sel.model.fit()
print(res.summary())
ind_prod.shape
fig = res_glob.plot_predict(start=714, end=732)
res_ar5 = AutoReg(ind_prod, 5, old_names=False).fit()
predictions = pd.DataFrame({
"AR(5)":
res_ar5.predict(start=714, end=726),
"AR(13)":
### Plot sealevel ### plt.plot(data["year"],data["GMSLNA"]) plt.show() x = data["GMSLNA"] ### ACF and PACF ### graphics.plot_acf(x) graphics.plot_pacf(x) plt.show() ### AR ### sel = ar_select_order(x, 13, old_names=False, seasonal=True, period=37) sel.ar_lags res = sel.model.fit() ax = res.plot_predict(1000, 1100) ax = x.plot(fig=ax) plt.show() ### ARIMA RANDOM WALK ### mod1 = ARIMA(x, seasonal_order = (0,1,0, 37)) res1 = mod1.fit() predict = res1.get_forecast(100) predictions = predict.predicted_mean[-100:]
def train(
data: np.ndarray,
used_model: str = "autoreg",
p: int = 5,
d: int = 1,
q: int = 0,
cov_type="nonrobust",
method="cmle",
trend="nc",
solver="lbfgs",
maxlag=13,
# SARIMAX args
seasonal=(0, 0, 0, 0),
) -> Any:
"""Autoregressive model from statsmodels library. Only univariate data.
Args:
data (np.ndarray): Time series data.
used_model (str, optional): Used model. Defaults to "autoreg".
p (int, optional): Order of ARIMA model (1st - proportional). Check statsmodels docs for more. Defaults to 5.
d (int, optional): Order of ARIMA model. Defaults to 1.
q (int, optional): Order of ARIMA model. Defaults to 0.
cov_type: Parameters of model call or fit function of particular model. Check statsmodels docs for more.
Defaults to 'nonrobust'.
method: Parameters of model call or fit function of particular model. Check statsmodels docs for more.
Defaults to 'cmle'.
trend: Parameters of model call or fit function of particular model. Check statsmodels docs for more.
Defaults to 'nc'.
solver: Parameters of model call or fit function of particular model. Check statsmodels docs for more.
Defaults to 'lbfgs'.
maxlag: Parameters of model call or fit function of particular model. Check statsmodels docs for more.
Defaults to 13.
seasonal: Parameters of model call or fit function of particular model. Check statsmodels docs for more.
Defaults to (0, 0, 0, 0).
Returns:
statsmodels.model: Trained model.
"""
import statsmodels.tsa.api as sm
from statsmodels.tsa.statespace.sarimax import SARIMAX
from statsmodels.tsa.arima.model import ARIMA
from statsmodels.tsa import ar_model
used_model = used_model.lower()
if used_model == "ar":
model = sm.AR(data)
fitted_model = model.fit(method=method, trend=trend, solver=solver, disp=0)
elif used_model == "arima":
order = (p, d, q)
model = ARIMA(data, order=order)
fitted_model = model.fit()
elif used_model == "sarimax":
order = (p, d, q)
model = SARIMAX(data, order=order, seasonal_order=seasonal)
fitted_model = model.fit(method=method, trend=trend, solver=solver, disp=0)
elif used_model == "autoreg":
auto = ar_model.ar_select_order(data, maxlag=maxlag)
model = ar_model.AutoReg(
data,
lags=auto.ar_lags,
trend=auto.trend,
seasonal=auto.seasonal,
period=auto.period,
)
fitted_model = model.fit(cov_type=cov_type)
else:
raise ValueError(
f"Used model has to be one of ['ar', 'arima', 'sarimax', 'autoreg']. You configured: {used_model}"
)
setattr(fitted_model, "my_name", used_model)
setattr(fitted_model, "data_length", len(data))
return fitted_model
import numpy as np
import statsmodels.api as sm
import statsmodels.tsa.stattools as stattools
from statsmodels.tsa.ar_model import AutoReg, ar_select_order
from arch.univariate import ARX, GARCH
from arch import arch_model
data = pd.read_excel('hw6/NYSEReturns.38135430_第三章.xlsx')
rates = data['RATE'].dropna().to_numpy()
# Statistic description
plt.plot(rates)
sm.graphics.tsa.plot_acf(rates)
# ARCH effect
ar_res = ar_select_order(rates, 5).model.fit()
# Test of no serial correlation and homoskedasticity
print(ar_res.diagnostic_summary())
print(ar_res.summary())
plt.figure()
plt.plot(ar_res.resid)
# a = ar_res.resid
# a_res = ar_select_order(a, 5).model.fit()
# print(a_res.diagnostic_summary())
# Fit with GARCH(p, q)
ar = ARX(rates, lags=[1, 2]) # Mean model
ar.volatility = GARCH(p=1, q=1) # Volatility model
res = ar.fit()
res.plot()
def test_ar_select_order_smoke():
data = sm.datasets.sunspots.load(as_pandas=True).data['SUNACTIVITY']
ar_select_order(data, 4, glob=True, trend='n', old_names=False)
ar_select_order(data, 4, glob=False, trend='n', old_names=False)
ar_select_order(data, 4, seasonal=True, period=12, old_names=False)
ar_select_order(data, 4, seasonal=False, old_names=False)
ar_select_order(data, 4, glob=True, old_names=False)
ar_select_order(data,
4,
glob=True,
seasonal=True,
period=12,
old_names=False)
fig, axes = plt.subplots(1, 2, clear=True, figsize=(10, 5))
#df.plot(ax=axes[0], title="$\Delta$ log(GDPC1)")
plot_acf(df.values.squeeze(), lags=20, ax=axes[0])
plot_pacf(df, lags=20, ax=axes[1])
plt.tight_layout(pad=2)
plt.savefig(os.path.join(imgdir, 'acf.jpg'))
plt.show()
# Select AR lag order with BIC
from statsmodels.tsa.ar_model import AutoReg, ar_select_order
s = 'GDPC1' # real gdp, seasonally adjusted
df = alf(s, log=1, diff=1, start=19591201, freq='Q').loc[:20191231].dropna()
df.index = pd.DatetimeIndex(df.index.astype(str), freq='infer')
df_train = df[df.index <= '2017-12-31']
df_test = df[df.index > '2017-12-31']
lags = ar_select_order(df_train, maxlag=13, ic='bic', old_names=False).ar_lags
print('(BIC) lags= ', len(lags), ':', lags)
# AR and SARIMAX
## AR(p) is simplest time-model, can nest in SARIMAX(p,d,q,s) with
## moving average MA(q), integration order I(d), seasonality S(s), exogenous X
from statsmodels.tsa.statespace.sarimax import SARIMAX
adf = alf(s, log=1, freq='Q').loc[19591201:20171231]
adf.index = pd.DatetimeIndex(adf.index.astype(str), freq='infer')
arima = SARIMAX(adf, order=(2, 1, 0), trend='c').fit()
fig = arima.plot_diagnostics(figsize=(10, 6))
plt.tight_layout(pad=2)
plt.savefig(os.path.join(imgdir, 'ar.jpg'))
plt.show()
arima.summary()
import pandas as pd
import matplotlib.pyplot as plt
from math import sqrt, pi, acos
from statsmodels.tsa.ar_model import ar_select_order
from statsmodels.tsa.arima.model import ARIMA
from numpy.polynomial.polynomial import polyroots
# Load data
gnp = pd.read_csv('../data/dgnp82.txt', delimiter='\s+', header=None, names=['gnp'])
# create a time-series object
gnp = pd.DataFrame({"gnp": gnp['gnp'].to_list()}, index=pd.date_range(start='1947-05', freq='Q', periods=len(gnp)))
# plot
gnp.plot()
plt.show()
# Find the AR order
m1 = ar_select_order(gnp, maxlag=13, ic='aic')
print(f"AR order: {m1.ar_lags[-1]}")
m2 = ARIMA(gnp, order=(m1.ar_lags[-1], 0, 0))
res = m2.fit()
# Estimation
print(res.summary())
# ‘‘const’’ denotes the mean of the series.
# Therefore, the constant term is obtained below:
tmp = 1
for i in range(1, len(res.params) - 1):
tmp -= res.params[i]
const = res.params[0] * tmp
print(f"const: {const}")
# Residual standard error
print(f"Residual standard error: {sqrt(res.params[-1])}")
fig, ax = plt.subplots()
ax = housing.plot(ax=ax)
'''
We can start with an AR(3). While this is not a good model for this data, it demonstrates the basic use of the API.
'''
mod = AutoReg(housing, 3, old_names=False)
res = mod.fit()
#print(res.summary())
'''
AutoReg supports the same covariance estimators as OLS. Below, we use cov_type="HC0", which is White’s covariance estimator.
While the parameter estimates are the same, all of the quantities that depend on the standard error change.
'''
res = mod.fit(cov_type="HC0")
#print(res.summary())
sel = ar_select_order(housing, 13, old_names=False)
sel.ar_lags
res = sel.model.fit()
#print(res.summary())
#fig = res.plot_predict(720, 840)
# fig = plt.figure(figsize=(16,9))
# fig = res.plot_diagnostics(fig=fig, lags=30)
sel = ar_select_order(housing, 13, seasonal=True, old_names=False)
sel.ar_lags
res = sel.model.fit()
print(res.summary())
yoy_housing = data.HOUSTNSA.pct_change(12).resample("MS").last().dropna()
_, ax = plt.subplots()