def decorator(model, params, nobs, burn=500, initial_value=None, x=None, initial_value_vol=None, data_only=False):
k_x = 0
if x is not None:
x = np.asarray(x)
k_x = x.shape[1]
if x.shape[0] != nobs + burn:
raise ValueError('x must have nobs + burn rows')
# added model._lags is not None for LS models
lags = model._lags if model._lags is not None else np.zeros((0, 0), int)
mc = int(model.constant) + lags.shape[1] + k_x
vc = model.volatility.num_params
dc = model.distribution.num_params
num_params = mc + vc + dc
params = ensure1d(params, 'params', series=False)
if params.shape[0] != num_params:
raise ValueError(f'params has the wrong number of elements. Expected {num_params}, got {params.shape[0]}. '
f'Perhaps you forgot to add the exogenous variables?')
dist_params = [] if dc == 0 else params[-dc:]
vol_params = params[mc:mc + vc]
simulator = model.distribution.simulate(dist_params)
sim_data = model.volatility.simulate(vol_params,
nobs + burn,
simulator,
burn,
initial_value_vol)
errors = sim_data[0]
vol = np.sqrt(sim_data[1])
max_lag = np.max(lags) if lags.size else 0
if initial_value is None:
initial_value = 0.0
elif not np.isscalar(initial_value):
initial_value = ensure1d(initial_value, 'initial_value')
if initial_value.shape[0] != max_lag:
raise ValueError('initial_value has the wrong shape')
y = np.zeros(nobs + burn)
y[:max_lag] = initial_value
simulate_harx(y, nobs + burn, k_x, max_lag, model.constant, x, errors, params, lags.T.astype(np.int64))
if data_only:
return y[burn:]
df = dict(data=y[burn:], volatility=vol[burn:], errors=errors[burn:])
df = pd.DataFrame(df)
return df
def simulate(
self, parameters: Union[int, float, Sequence[Union[float, int]], ArrayLike1D]
) -> Callable[[Union[int, Tuple[int, ...]]], NDArray]:
parameters = ensure1d(parameters, "parameters", False)
if parameters[0] <= 2.0:
raise ValueError("The shape parameter must be larger than 2")
self._parameters = parameters
return self._simulator
def decorator(model, params, nobs, reps, burn=500, initial_value=None, x=None, initial_value_vol=None):
k_x = 0
if x is not None:
x = np.asarray(x)
k_x = x.shape[1]
if x.shape[0] != nobs + burn:
raise ValueError('x must have nobs + burn rows')
# added model._lags is not None for LS models
lags = model._lags if model._lags is not None else np.zeros((0, 0), int)
mc = int(model.constant) + lags.shape[1] + k_x
vc = model.volatility.num_params
dc = model.distribution.num_params
num_params = mc + vc + dc
params = ensure1d(params, 'params', series=False)
if params.shape[0] != num_params:
raise ValueError(f'params has the wrong number of elements. Expected {num_params}, got {params.shape[0]}. '
f'Perhaps you forgot to add the exogenous variables?')
dist_params = [] if dc == 0 else params[-dc:]
vol_params = params[mc:mc + vc]
simulator = model.distribution.simulate(dist_params)
errors = model.volatility.simulate_mc(vol_params, nobs + burn, reps, simulator, burn, initial_value_vol)
max_lag = np.max(lags) if lags.size else 0
if initial_value is None:
initial_value = 0
elif np.isscalar(initial_value):
initial_value = np.repeat(initial_value, max_lag)
elif not np.isscalar(initial_value):
initial_value = ensure1d(initial_value, 'initial_value')
if initial_value.shape[0] != max_lag:
raise ValueError('initial_value has the wrong shape')
y = np.zeros((nobs + burn, reps), np.float64) # y is modified in place
y[:max_lag, :reps] = initial_value
return simulate_harx_mc(y, nobs + burn, reps, k_x, max_lag, model.constant, x, errors, params,
lags.T.astype(np.int64))[burn:]
def _cross_section(y: ArrayLike1D, x: ArrayLike2D,
trend: str) -> RegressionResults:
if trend not in ("n", "c", "ct", "ctt"):
raise ValueError('trend must be one of "n", "c", "ct" or "ctt"')
y = ensure1d(y, "y", True)
x = ensure2d(x, "x")
if not isinstance(x, pd.DataFrame):
cols = [f"x{i}" for i in range(1, x.shape[1] + 1)]
x = pd.DataFrame(x, columns=cols, index=y.index)
x = add_trend(x, trend)
res = OLS(y, x).fit()
return res
def __init__(
self,
x: ArrayLike,
bandwidth: Optional[float] = None,
df_adjust: int = 0,
center: bool = True,
weights: Optional[ArrayLike] = None,
force_int: bool = False,
):
self._x_orig = ensure2d(x, "x")
self._x = np.asarray(self._x_orig)
self._center = center
if self._center:
self._x = self._x - self._x.mean(0)
if bandwidth is not None and (not np.isscalar(bandwidth) or bandwidth < 0):
raise ValueError("bandwidth must be a non-negative scalar.")
self._bandwidth = bandwidth
self._auto_bandwidth = bandwidth is None
if not np.isscalar(df_adjust) or df_adjust < 0:
raise ValueError("df_adjust must be a non-negative integer.")
self._df_adjust = int(df_adjust)
self._df = self._x.shape[0] - self._df_adjust
if self._df <= 0:
raise ValueError(
"Degrees of freedom is <= 0 after adjusting the sample "
"size of x using df_adjust. df_adjust must be less than"
f" {self._x.shape[0]}"
)
if weights is None:
xw = self._x_weights = np.ones((self._x.shape[1], 1))
else:
xw = ensure1d(np.asarray(weights), "weights")
xw = self._x_weights = xw[:, None]
if (
xw.shape[0] != self._x.shape[1]
or xw.shape[1] != 1
or np.any(xw < 0)
or np.all(xw == 0)
):
raise ValueError(
f"weights must be a 1 by {self._x.shape[1]} (x.shape[1]) "
f"array with non-negative values where at least one value is "
"strictly greater than 0."
)
self._force_int = force_int
def simulate(
self,
parameters: Union[Sequence[Union[int, float]], ArrayLike1D],
nobs: int,
rng: RNGType,
burn: int = 500,
initial_value: Optional[float] = None) -> Tuple[NDArray, NDArray]:
parameters = ensure1d(parameters, "parameters", False)
errors = rng(nobs + burn)
if initial_value is None:
scale = np.ones_like(parameters)
persistence = np.sum(parameters[1:] * scale[1:])
if (1.0 - persistence) > 0:
initial_value = parameters[0] / (1.0 - persistence)
else:
from warnings import warn
warn(initial_value_warning, InitialValueWarning)
initial_value = parameters[0]
sigma2 = np.zeros(nobs + burn)
data = np.zeros(nobs + burn)
max_lag = 1
sigma2[:max_lag] = initial_value
data[:max_lag] = np.sqrt(sigma2[:max_lag]) * errors[:max_lag]
omega = parameters[0]
alpha = parameters[1]
beta = parameters[2]
theta = parameters[3]
sigma2[max_lag] = omega
data[max_lag] = errors[max_lag] * np.sqrt(sigma2[max_lag])
for t in range(max_lag + 1, nobs + burn):
loc = t - 1
sigma2[t] = \
omega + \
alpha * (data[loc] - theta * np.sqrt(sigma2[loc])) ** 2.0 + \
beta * sigma2[loc]
data[t] = errors[t] * np.sqrt(sigma2[t])
return data[burn:], sigma2[burn:]
def __init__(self, y, lags, trend, valid_trends):
self._y = ensure1d(y, 'y')
self._delta_y = diff(y)
self._nobs = self._y.shape[0]
self._lags = None
self.lags = lags
self._valid_trends = valid_trends
self._trend = ''
self.trend = trend
self._stat = None
self._critical_values = None
self._pvalue = None
self.trend = trend
self._null_hypothesis = 'The process contains a unit root.'
self._alternative_hypothesis = 'The process is weakly stationary.'
self._test_name = None
self._title = None
self._summary_text = None
def __init__(self, y, lags, trend, valid_trends):
self._y = ensure1d(y, 'y')
self._delta_y = diff(y)
self._nobs = self._y.shape[0]
self._lags = None
self.lags = lags
self._valid_trends = valid_trends
self._trend = ''
self.trend = trend
self._stat = None
self._critical_values = None
self._pvalue = None
self.trend = trend
self._null_hypothesis = 'The process contains a unit root.'
self._alternative_hypothesis = 'The process is weakly stationary.'
self._test_name = None
self._title = None
self._summary_text = None
def _check_constraints(
self, parameters: Optional[Union[Sequence[float],
ArrayLike1D]]) -> NDArray:
bounds = self.bounds(empty(0))
if parameters is not None:
params = ensure1d(parameters, "parameters", False)
nparams = len(params)
else:
nparams = 0
if nparams != len(bounds):
raise ValueError("parameters must have {0} elements".format(
len(bounds)))
if len(bounds) == 0:
return empty(0)
for p, n, b in zip(params, self.name, bounds):
if not (b[0] <= p <= b[1]):
raise ValueError("{0} does not satisfy the bounds requirement "
"of ({1}, {2})".format(n, *b))
return params
def _check_cointegrating_regression(
y: ArrayLike1D,
x: ArrayLike2D,
trend: str,
supported_trends: Tuple[str, ...] = ("n", "c", "ct", "ctt"),
) -> CointegrationSetup:
y = ensure1d(y, "y", True)
x = ensure2d(x, "x")
if y.shape[0] != x.shape[0]:
raise ValueError(
f"The number of observations in y and x differ. y has "
f"{y.shape[0]} observtations, and x has {x.shape[0]}.")
if not isinstance(x, pd.DataFrame):
cols = [f"x{i}" for i in range(1, x.shape[1] + 1)]
x_df = pd.DataFrame(x, columns=cols, index=y.index)
else:
x_df = x
trend = trend.lower()
if trend.lower() not in supported_trends:
trends = ",".join([f'"{st}"' for st in supported_trends])
raise ValueError(f"Unknown trend. Must be one of {{{trends}}}")
return CointegrationSetup(y, x_df, trend)
def test_ensure1d(self):
out = ensure1d(1.0, 'y')
assert_equal(out, np.array([1.0]))
out = ensure1d(np.arange(5.0), 'y')
assert_equal(out, np.arange(5.0))
out = ensure1d(np.arange(5.0)[:, None], 'y')
assert_equal(out, np.arange(5.0))
in_array = np.reshape(np.arange(16.0), (4, 4))
with pytest.raises(ValueError):
ensure1d(in_array, 'y')
y = Series(np.arange(5.0))
ys = ensure1d(y, 'y')
assert isinstance(ys, np.ndarray)
ys = ensure1d(y, 'y', True)
assert isinstance(ys, Series)
y = DataFrame(y)
ys = ensure1d(y, 'y')
assert isinstance(ys, np.ndarray)
ys = ensure1d(y, 'y', True)
assert isinstance(ys, Series)
y.columns = [1]
ys = ensure1d(y, 'y', True)
assert isinstance(ys, Series)
assert ys.name == '1'
y = Series(np.arange(5.0), name='series')
ys = ensure1d(y, 'y')
assert isinstance(ys, np.ndarray)
ys = ensure1d(y, 'y', True)
assert isinstance(ys, Series)
y = DataFrame(y)
ys = ensure1d(y, 'y')
assert isinstance(ys, np.ndarray)
ys = ensure1d(y, 'y', True)
assert isinstance(ys, Series)
ys.name = 1
ys = ensure1d(ys, None, True)
assert isinstance(ys, Series)
assert ys.name == '1'
y = DataFrame(np.reshape(np.arange(10), (5, 2)))
with pytest.raises(ValueError):
ensure1d(y, 'y')
def simulate(
self,
params: Union[Sequence[float], ArrayLike1D],
nobs: int,
burn: int = 500,
initial_value: Optional[Union[float, NDArray]] = None,
x: Optional[ArrayLike] = None,
initial_value_vol: Optional[Union[float, NDArray]] = None,
) -> DataFrame:
"""
Simulated data from a zero mean model
Parameters
----------
params : {ndarray, DataFrame}
Parameters to use when simulating the model. Parameter order is
[volatility distribution]. There are no mean parameters.
nobs : int
Length of series to simulate
burn : int, optional
Number of values to simulate to initialize the model and remove
dependence on initial values.
initial_value : None
This value is not used.
x : None
This value is not used.
initial_value_vol : {ndarray, float}, optional
An array or scalar to use when initializing the volatility process.
Returns
-------
simulated_data : DataFrame
DataFrame with columns data containing the simulated values,
volatility, containing the conditional volatility and errors
containing the errors used in the simulation
Examples
--------
Basic data simulation with no mean and constant volatility
>>> from arch.univariate import ZeroMean
>>> import numpy as np
>>> zm = ZeroMean()
>>> params = np.array([1.0])
>>> sim_data = zm.simulate(params, 1000)
Simulating data with a non-trivial volatility process
>>> from arch.univariate import GARCH
>>> zm.volatility = GARCH(p=1, o=1, q=1)
>>> sim_data = zm.simulate([0.05, 0.1, 0.1, 0.8], 300)
"""
params = ensure1d(params, "params", False)
if initial_value is not None or x is not None:
raise ValueError("Both initial value and x must be none when "
"simulating a constant mean process.")
_, vp, dp = self._parse_parameters(params)
sim_values = self.volatility.simulate(vp, nobs + burn,
self.distribution.simulate(dp),
burn, initial_value_vol)
errors = sim_values[0]
y = errors
vol = np.sqrt(sim_values[1])
df = dict(data=y[burn:], volatility=vol[burn:], errors=errors[burn:])
df = DataFrame(df)
return df
def simulate(
self,
params: Sequence[float],
nobs: int,
burn: int = 500,
initial_value: Optional[Union[float, NDArray]] = None,
x: Optional[ArrayLike] = None,
initial_value_vol: Optional[Union[float, NDArray]] = None,
) -> DataFrame:
"""
Simulates data from a linear regression, AR or HAR models
Parameters
----------
params : ndarray
Parameters to use when simulating the model. Parameter order is
[mean volatility distribution] where the parameters of the mean
model are ordered [constant lag[0] lag[1] ... lag[p] ex[0] ...
ex[k-1]] where lag[j] indicates the coefficient on the jth lag in
the model and ex[j] is the coefficient on the jth exogenous
variable.
nobs : int
Length of series to simulate
burn : int, optional
Number of values to simulate to initialize the model and remove
dependence on initial values.
initial_value : {ndarray, float}, optional
Either a scalar value or `max(lags)` array set of initial values to
use when initializing the model. If omitted, 0.0 is used.
x : {ndarray, DataFrame}, optional
nobs + burn by k array of exogenous variables to include in the
simulation.
initial_value_vol : {ndarray, float}, optional
An array or scalar to use when initializing the volatility process.
Returns
-------
simulated_data : DataFrame
DataFrame with columns data containing the simulated values,
volatility, containing the conditional volatility and errors
containing the errors used in the simulation
Examples
--------
>>> import numpy as np
>>> from arch.univariate import HARX, GARCH
>>> harx = HARX(lags=[1, 5, 22])
>>> harx.volatility = GARCH()
>>> harx_params = np.array([1, 0.2, 0.3, 0.4])
>>> garch_params = np.array([0.01, 0.07, 0.92])
>>> params = np.concatenate((harx_params, garch_params))
>>> sim_data = harx.simulate(params, 1000)
Simulating models with exogenous regressors requires the regressors
to have nobs plus burn data points
>>> nobs = 100
>>> burn = 200
>>> x = np.random.randn(nobs + burn, 2)
>>> x_params = np.array([1.0, 2.0])
>>> params = np.concatenate((harx_params, x_params, garch_params))
>>> sim_data = harx.simulate(params, nobs=nobs, burn=burn, x=x)
"""
k_x = 0
if x is not None:
k_x = x.shape[1]
if x.shape[0] != nobs + burn:
raise ValueError("x must have nobs + burn rows")
assert self._lags is not None
mc = int(self.constant) + self._lags.shape[1] + k_x
vc = self.volatility.num_params
dc = self.distribution.num_params
num_params = mc + vc + dc
params = ensure1d(params, "params", series=False)
if params.shape[0] != num_params:
raise ValueError("params has the wrong number of elements. "
"Expected " + str(num_params) + ", got " +
str(params.shape[0]))
dist_params = [] if dc == 0 else params[-dc:]
vol_params = params[mc:mc + vc]
simulator = self.distribution.simulate(dist_params)
sim_data = self.volatility.simulate(vol_params, nobs + burn, simulator,
burn, initial_value_vol)
errors = sim_data[0]
vol = np.sqrt(sim_data[1])
max_lag = np.max(self._lags)
y = np.zeros(nobs + burn)
if initial_value is None:
initial_value = 0.0
elif not np.isscalar(initial_value):
initial_value = ensure1d(initial_value, "initial_value")
if initial_value.shape[0] != max_lag:
raise ValueError("initial_value has the wrong shape")
y[:max_lag] = initial_value
for t in range(max_lag, nobs + burn):
ind = 0
if self.constant:
y[t] = params[ind]
ind += 1
for lag in self._lags.T:
y[t] += params[ind] * y[t - lag[1]:t - lag[0]].mean()
ind += 1
for i in range(k_x):
y[t] += params[ind] * x[t, i]
y[t] += errors[t]
df = dict(data=y[burn:], volatility=vol[burn:], errors=errors[burn:])
df = DataFrame(df)
return df
def test_ensure1d(self):
out = ensure1d(1.0, 'y')
assert_equal(out, np.array([1.0]))
out = ensure1d(np.arange(5.0), 'y')
assert_equal(out, np.arange(5.0))
out = ensure1d(np.arange(5.0)[:, None], 'y')
assert_equal(out, np.arange(5.0))
in_array = np.reshape(np.arange(16.0), (4, 4))
assert_raises(ValueError, ensure1d, in_array, 'y')
y = Series(np.arange(5.0))
ys = ensure1d(y, 'y')
assert_true(isinstance(ys, np.ndarray))
ys = ensure1d(y, 'y', True)
assert_true(isinstance(ys, Series))
y = DataFrame(y)
ys = ensure1d(y, 'y')
assert_true(isinstance(ys, np.ndarray))
ys = ensure1d(y, 'y', True)
assert_true(isinstance(ys, Series))
y = Series(np.arange(5.0), name='series')
ys = ensure1d(y, 'y')
assert_true(isinstance(ys, np.ndarray))
ys = ensure1d(y, 'y', True)
assert_true(isinstance(ys, Series))
y = DataFrame(y)
ys = ensure1d(y, 'y')
assert_true(isinstance(ys, np.ndarray))
ys = ensure1d(y, 'y', True)
assert_true(isinstance(ys, Series))
y = DataFrame(np.reshape(np.arange(10), (5, 2)))
assert_raises(ValueError, ensure1d, y, 'y')
def simulate(self, params, nobs, burn=500, initial_value=None, x=None,
initial_value_vol=None):
"""
Simulates data from a linear regression, AR or HAR models
Parameters
----------
params : array
Parameters to use when simulating the model. Parameter order is
[mean volatility distribution] where the parameters of the mean
model are ordered [constant lag[0] lag[1] ... lag[p] ex[0] ...
ex[k-1]] where lag[j] indicates the coefficient on the jth lag in
the model and ex[j] is the coefficient on the jth exogenous
variable.
nobs : int
Length of series to simulate
burn : int, optional
Number of values to simulate to initialize the model and remove
dependence on initial values.
initial_value : array or float, optional
Either a scalar value or `max(lags)` array set of initial values to
use when initializing the model. If omitted, 0.0 is used.
x : array, optional
nobs + burn by k array of exogenous variables to include in the
simulation.
initial_value_vol : array or float, optional
An array or scalar to use when initializing the volatility process.
Returns
-------
simulated_data : DataFrame
DataFrame with columns data containing the simulated values,
volatility, containing the conditional volatility and errors
containing the errors used in the simulation
Examples
--------
>>> import numpy as np
>>> from arch.univariate import HARX, GARCH
>>> harx = HARX(lags=[1, 5, 22])
>>> harx.volatility = GARCH()
>>> harx_params = np.array([1, 0.2, 0.3, 0.4])
>>> garch_params = np.array([0.01, 0.07, 0.92])
>>> params = np.concatenate((harx_params, garch_params))
>>> sim_data = harx.simulate(params, 1000)
Simulating models with exogenous regressors requires the regressors
to have nobs plus burn data points
>>> nobs = 100
>>> burn = 200
>>> x = np.random.randn(nobs + burn, 2)
>>> x_params = np.array([1.0, 2.0])
>>> params = np.concatenate((harx_params, x_params, garch_params))
>>> sim_data = harx.simulate(params, nobs=nobs, burn=burn, x=x)
"""
k_x = 0
if x is not None:
k_x = x.shape[1]
if x.shape[0] != nobs + burn:
raise ValueError('x must have nobs + burn rows')
mc = int(self.constant) + self._lags.shape[1] + k_x
vc = self.volatility.num_params
dc = self.distribution.num_params
num_params = mc + vc + dc
params = ensure1d(params, 'params', series=False)
if params.shape[0] != num_params:
raise ValueError('params has the wrong number of elements. '
'Expected ' + str(num_params) +
', got ' + str(params.shape[0]))
dist_params = [] if dc == 0 else params[-dc:]
vol_params = params[mc:mc + vc]
simulator = self.distribution.simulate(dist_params)
sim_data = self.volatility.simulate(vol_params,
nobs + burn,
simulator,
burn,
initial_value_vol)
errors = sim_data[0]
vol = np.sqrt(sim_data[1])
max_lag = np.max(self._lags)
y = zeros(nobs + burn)
if initial_value is None:
initial_value = 0.0
elif not isscalar(initial_value):
initial_value = ensure1d(initial_value, 'initial_value')
if initial_value.shape[0] != max_lag:
raise ValueError('initial_value has the wrong shape')
y[:max_lag] = initial_value
for t in range(max_lag, nobs + burn):
ind = 0
if self.constant:
y[t] = params[ind]
ind += 1
for lag in self._lags.T:
y[t] += params[ind] * y[t - lag[1]:t - lag[0]].mean()
ind += 1
for i in range(k_x):
y[t] += params[ind] * x[t, i]
y[t] += errors[t]
df = dict(data=y[burn:], volatility=vol[burn:], errors=errors[burn:])
df = DataFrame(df)
return df
def test_ensure1d(self):
out = ensure1d(1.0, 'y')
assert_equal(out, np.array([1.0]))
out = ensure1d(np.arange(5.0), 'y')
assert_equal(out, np.arange(5.0))
out = ensure1d(np.arange(5.0)[:, None], 'y')
assert_equal(out, np.arange(5.0))
in_array = np.reshape(np.arange(16.0), (4, 4))
with pytest.raises(ValueError):
ensure1d(in_array, 'y')
y = Series(np.arange(5.0))
ys = ensure1d(y, 'y')
assert isinstance(ys, np.ndarray)
ys = ensure1d(y, 'y', True)
assert isinstance(ys, Series)
y = DataFrame(y)
ys = ensure1d(y, 'y')
assert isinstance(ys, np.ndarray)
ys = ensure1d(y, 'y', True)
assert isinstance(ys, Series)
y.columns = [1]
ys = ensure1d(y, 'y', True)
assert isinstance(ys, Series)
assert ys.name == '1'
y = Series(np.arange(5.0), name='series')
ys = ensure1d(y, 'y')
assert isinstance(ys, np.ndarray)
ys = ensure1d(y, 'y', True)
assert isinstance(ys, Series)
y = DataFrame(y)
ys = ensure1d(y, 'y')
assert isinstance(ys, np.ndarray)
ys = ensure1d(y, 'y', True)
assert isinstance(ys, Series)
ys.name = 1
ys = ensure1d(ys, None, True)
assert isinstance(ys, Series)
assert ys.name == '1'
y = DataFrame(np.reshape(np.arange(10), (5, 2)))
with pytest.raises(ValueError):
ensure1d(y, 'y')