from statsmodels.compat.python import lrange, lzip
from statsmodels.compat.numpy import recarray_select
import numpy as np
import numpy.lib.recfunctions as nprf
import pandas as pd
from pandas import DataFrame
from pandas.tseries import offsets
from pandas.tseries.frequencies import to_offset
from statsmodels.tools.validation import int_like, bool_like, string_like
from statsmodels.tools.sm_exceptions import ValueWarning
from statsmodels.tools.data import _is_using_pandas, _is_recarray
from statsmodels.tools.validation import array_like
[docs]def add_trend(x, trend="c", prepend=False, has_constant='skip'):
"""
Add a trend and/or constant to an array.
Parameters
----------
x : array_like
Original array of data.
trend : str {'n', 'c', 't', 'ct', 'ctt'}
The trend to add.
* 'n' add no trend.
* 'c' add constant only.
* 't' add trend only.
* 'ct' add constant and linear trend.
* 'ctt' add constant and linear and quadratic trend.
prepend : bool
If True, prepends the new data to the columns of X.
has_constant : str {'raise', 'add', 'skip'}
Controls what happens when trend is 'c' and a constant column already
exists in x. 'raise' will raise an error. 'add' will add a column of
1s. 'skip' will return the data without change. 'skip' is the default.
Returns
-------
array_like
The original data with the additional trend columns. If x is a
recarray or pandas Series or DataFrame, then the trend column names
are 'const', 'trend' and 'trend_squared'.
See Also
--------
statsmodels.tools.tools.add_constant
Add a constant column to an array.
Notes
-----
Returns columns as ['ctt','ct','c'] whenever applicable. There is currently
no checking for an existing trend.
"""
prepend = bool_like(prepend, 'prepend')
trend = string_like(trend, 'trend', options=('n', 'c', 't', 'ct', 'ctt'))
has_constant = string_like(has_constant, 'has_constant',
options=('raise', 'add', 'skip'))
# TODO: could be generalized for trend of aribitrary order
columns = ['const', 'trend', 'trend_squared']
if trend == 'n':
return x.copy()
elif trend == "c": # handles structured arrays
columns = columns[:1]
trendorder = 0
elif trend == "ct" or trend == "t":
columns = columns[:2]
if trend == "t":
columns = columns[1:2]
trendorder = 1
elif trend == "ctt":
trendorder = 2
is_recarray = _is_recarray(x)
is_pandas = _is_using_pandas(x, None) or is_recarray
if is_pandas or is_recarray:
if is_recarray:
# deprecated: remove recarray support after 0.12
import warnings
from statsmodels.tools.sm_exceptions import recarray_warning
warnings.warn(recarray_warning, FutureWarning)
descr = x.dtype.descr
x = pd.DataFrame.from_records(x)
elif isinstance(x, pd.Series):
x = pd.DataFrame(x)
else:
x = x.copy()
else:
x = np.asanyarray(x)
nobs = len(x)
trendarr = np.vander(np.arange(1, nobs + 1, dtype=np.float64), trendorder + 1)
# put in order ctt
trendarr = np.fliplr(trendarr)
if trend == "t":
trendarr = trendarr[:, 1]
if "c" in trend:
if is_pandas or is_recarray:
# Mixed type protection
def safe_is_const(s):
try:
return np.ptp(s) == 0.0 and np.any(s != 0.0)
except:
return False
col_const = x.apply(safe_is_const, 0)
else:
ptp0 = np.ptp(np.asanyarray(x), axis=0)
col_is_const = ptp0 == 0
nz_const = col_is_const & (x[0] != 0)
col_const = nz_const
if np.any(col_const):
if has_constant == 'raise':
if x.ndim == 1:
base_err = "x is constant."
else:
columns = np.arange(x.shape[1])[col_const]
if isinstance(x, pd.DataFrame):
columns = x.columns
const_cols = ", ".join([str(c) for c in columns])
base_err = (
"x contains one or more constant columns. Column(s) "
f"{const_cols} are constant."
)
msg = (
f"{base_err} Adding a constant with trend='{trend}' is not allowed."
)
raise ValueError(msg)
elif has_constant == 'skip':
columns = columns[1:]
trendarr = trendarr[:, 1:]
order = 1 if prepend else -1
if is_recarray or is_pandas:
trendarr = pd.DataFrame(trendarr, index=x.index, columns=columns)
x = [trendarr, x]
x = pd.concat(x[::order], 1)
else:
x = [trendarr, x]
x = np.column_stack(x[::order])
if is_recarray:
x = x.to_records(index=False)
new_descr = x.dtype.descr
extra_col = len(new_descr) - len(descr)
if prepend:
descr = new_descr[:extra_col] + descr
else:
descr = descr + new_descr[-extra_col:]
x = x.astype(np.dtype(descr))
return x
[docs]def add_lag(x, col=None, lags=1, drop=False, insert=True):
"""
Returns an array with lags included given an array.
Parameters
----------
x : array_like
An array or NumPy ndarray subclass. Can be either a 1d or 2d array with
observations in columns.
col : 'string', int, or None
If data is a structured array or a recarray, `col` can be a string
that is the name of the column containing the variable. Or `col` can
be an int of the zero-based column index. If it's a 1d array `col`
can be None.
lags : int
The number of lags desired.
drop : bool
Whether to keep the contemporaneous variable for the data.
insert : bool or int
If True, inserts the lagged values after `col`. If False, appends
the data. If int inserts the lags at int.
Returns
-------
array : ndarray
Array with lags
Examples
--------
>>> import statsmodels.api as sm
>>> data = sm.datasets.macrodata.load(as_pandas=False)
>>> data = data.data[['year','quarter','realgdp','cpi']]
>>> data = sm.tsa.add_lag(data, 'realgdp', lags=2)
Notes
-----
Trims the array both forward and backward, so that the array returned
so that the length of the returned array is len(`X`) - lags. The lags are
returned in increasing order, ie., t-1,t-2,...,t-lags
"""
lags = int_like(lags, 'lags')
drop = bool_like(drop, 'drop')
if x.dtype.names:
names = x.dtype.names
if not col and np.squeeze(x).ndim > 1:
raise IndexError("col is None and the input array is not 1d")
elif len(names) == 1:
col = names[0]
if isinstance(col, int):
col = x.dtype.names[col]
contemp = x[col]
# make names for lags
tmp_names = [col + '_'+'L(%i)' % i for i in range(1, lags+1)]
ndlags = lagmat(contemp, maxlag=lags, trim='Both')
# get index for return
if insert is True:
ins_idx = list(names).index(col) + 1
elif insert is False:
ins_idx = len(names) + 1
else: # insert is an int
if insert > len(names):
import warnings
warnings.warn("insert > number of variables, inserting at the"
" last position", ValueWarning)
ins_idx = insert
first_names = list(names[:ins_idx])
last_names = list(names[ins_idx:])
if drop:
if col in first_names:
first_names.pop(first_names.index(col))
else:
last_names.pop(last_names.index(col))
if first_names: # only do this if x is not "empty"
# Workaround to avoid NumPy FutureWarning
_x = recarray_select(x, first_names)
first_arr = nprf.append_fields(_x[lags:], tmp_names, ndlags.T,
usemask=False)
else:
first_arr = np.zeros(len(x)-lags, dtype=lzip(tmp_names,
(x[col].dtype,)*lags))
for i,name in enumerate(tmp_names):
first_arr[name] = ndlags[:,i]
if last_names:
return nprf.append_fields(first_arr, last_names,
[x[name][lags:] for name in last_names], usemask=False)
else: # lags for last variable
return first_arr
else: # we have an ndarray
if x.ndim == 1: # make 2d if 1d
x = x[:,None]
if col is None:
col = 0
# handle negative index
if col < 0:
col = x.shape[1] + col
contemp = x[:,col]
if insert is True:
ins_idx = col + 1
elif insert is False:
ins_idx = x.shape[1]
else:
if insert < 0: # handle negative index
insert = x.shape[1] + insert + 1
if insert > x.shape[1]:
insert = x.shape[1]
import warnings
warnings.warn("insert > number of variables, inserting at the"
" last position", ValueWarning)
ins_idx = insert
ndlags = lagmat(contemp, lags, trim='Both')
first_cols = lrange(ins_idx)
last_cols = lrange(ins_idx,x.shape[1])
if drop:
if col in first_cols:
first_cols.pop(first_cols.index(col))
else:
last_cols.pop(last_cols.index(col))
return np.column_stack((x[lags:,first_cols],ndlags,
x[lags:,last_cols]))
[docs]def detrend(x, order=1, axis=0):
"""
Detrend an array with a trend of given order along axis 0 or 1.
Parameters
----------
x : array_like, 1d or 2d
Data, if 2d, then each row or column is independently detrended with
the same trendorder, but independent trend estimates.
order : int
The polynomial order of the trend, zero is constant, one is
linear trend, two is quadratic trend.
axis : int
Axis can be either 0, observations by rows, or 1, observations by
columns.
Returns
-------
ndarray
The detrended series is the residual of the linear regression of the
data on the trend of given order.
"""
order = int_like(order, 'order')
axis = int_like(axis, 'axis')
if x.ndim == 2 and int(axis) == 1:
x = x.T
elif x.ndim > 2:
raise NotImplementedError('x.ndim > 2 is not implemented until it is needed')
nobs = x.shape[0]
if order == 0:
# Special case demean
resid = x - x.mean(axis=0)
else:
trends = np.vander(np.arange(float(nobs)), N=order + 1)
beta = np.linalg.pinv(trends).dot(x)
resid = x - np.dot(trends, beta)
if x.ndim == 2 and int(axis) == 1:
resid = resid.T
return resid
[docs]def lagmat(x, maxlag, trim='forward', original='ex', use_pandas=False):
"""
Create 2d array of lags.
Parameters
----------
x : array_like
Data; if 2d, observation in rows and variables in columns.
maxlag : int
All lags from zero to maxlag are included.
trim : {'forward', 'backward', 'both', 'none', None}
The trimming method to use.
* 'forward' : trim invalid observations in front.
* 'backward' : trim invalid initial observations.
* 'both' : trim invalid observations on both sides.
* 'none', None : no trimming of observations.
original : {'ex','sep','in'}
How the original is treated.
* 'ex' : drops the original array returning only the lagged values.
* 'in' : returns the original array and the lagged values as a single
array.
* 'sep' : returns a tuple (original array, lagged values). The original
array is truncated to have the same number of rows as
the returned lagmat.
use_pandas : bool
If true, returns a DataFrame when the input is a pandas
Series or DataFrame. If false, return numpy ndarrays.
Returns
-------
lagmat : ndarray
The array with lagged observations.
y : ndarray, optional
Only returned if original == 'sep'.
Notes
-----
When using a pandas DataFrame or Series with use_pandas=True, trim can only
be 'forward' or 'both' since it is not possible to consistently extend
index values.
Examples
--------
>>> from statsmodels.tsa.tsatools import lagmat
>>> import numpy as np
>>> X = np.arange(1,7).reshape(-1,2)
>>> lagmat(X, maxlag=2, trim="forward", original='in')
array([[ 1., 2., 0., 0., 0., 0.],
[ 3., 4., 1., 2., 0., 0.],
[ 5., 6., 3., 4., 1., 2.]])
>>> lagmat(X, maxlag=2, trim="backward", original='in')
array([[ 5., 6., 3., 4., 1., 2.],
[ 0., 0., 5., 6., 3., 4.],
[ 0., 0., 0., 0., 5., 6.]])
>>> lagmat(X, maxlag=2, trim="both", original='in')
array([[ 5., 6., 3., 4., 1., 2.]])
>>> lagmat(X, maxlag=2, trim="none", original='in')
array([[ 1., 2., 0., 0., 0., 0.],
[ 3., 4., 1., 2., 0., 0.],
[ 5., 6., 3., 4., 1., 2.],
[ 0., 0., 5., 6., 3., 4.],
[ 0., 0., 0., 0., 5., 6.]])
"""
maxlag = int_like(maxlag, 'maxlag')
use_pandas = bool_like(use_pandas, 'use_pandas')
trim = string_like(trim, 'trim', optional=True,
options=('forward', 'backward', 'both', 'none'))
original = string_like(original, 'original', options=('ex', 'sep', 'in'))
# TODO: allow list of lags additional to maxlag
orig = x
x = array_like(x, 'x', ndim=2, dtype=None)
is_pandas = _is_using_pandas(orig, None) and use_pandas
trim = 'none' if trim is None else trim
trim = trim.lower()
if is_pandas and trim in ('none', 'backward'):
raise ValueError("trim cannot be 'none' or 'forward' when used on "
"Series or DataFrames")
dropidx = 0
nobs, nvar = x.shape
if original in ['ex', 'sep']:
dropidx = nvar
if maxlag >= nobs:
raise ValueError("maxlag should be < nobs")
lm = np.zeros((nobs + maxlag, nvar * (maxlag + 1)))
for k in range(0, int(maxlag + 1)):
lm[maxlag - k:nobs + maxlag - k,
nvar * (maxlag - k):nvar * (maxlag - k + 1)] = x
if trim in ('none', 'forward'):
startobs = 0
elif trim in ('backward', 'both'):
startobs = maxlag
else:
raise ValueError('trim option not valid')
if trim in ('none', 'backward'):
stopobs = len(lm)
else:
stopobs = nobs
if is_pandas:
x = orig
x_columns = x.columns if isinstance(x, DataFrame) else [x.name]
columns = [str(col) for col in x_columns]
for lag in range(maxlag):
lag_str = str(lag + 1)
columns.extend([str(col) + '.L.' + lag_str for col in x_columns])
lm = DataFrame(lm[:stopobs], index=x.index, columns=columns)
lags = lm.iloc[startobs:]
if original in ('sep', 'ex'):
leads = lags[x_columns]
lags = lags.drop(x_columns, 1)
else:
lags = lm[startobs:stopobs, dropidx:]
if original == 'sep':
leads = lm[startobs:stopobs, :dropidx]
if original == 'sep':
return lags, leads
else:
return lags
[docs]def lagmat2ds(x, maxlag0, maxlagex=None, dropex=0, trim='forward',
use_pandas=False):
"""
Generate lagmatrix for 2d array, columns arranged by variables.
Parameters
----------
x : array_like
Data, 2d. Observations in rows and variables in columns.
maxlag0 : int
The first variable all lags from zero to maxlag are included.
maxlagex : {None, int}
The max lag for all other variables all lags from zero to maxlag are
included.
dropex : int
Exclude first dropex lags from other variables. For all variables,
except the first, lags from dropex to maxlagex are included.
trim : str
The trimming method to use.
* 'forward' : trim invalid observations in front.
* 'backward' : trim invalid initial observations.
* 'both' : trim invalid observations on both sides.
* 'none' : no trimming of observations.
use_pandas : bool
If true, returns a DataFrame when the input is a pandas
Series or DataFrame. If false, return numpy ndarrays.
Returns
-------
ndarray
The array with lagged observations, columns ordered by variable.
Notes
-----
Inefficient implementation for unequal lags, implemented for convenience.
"""
maxlag0 = int_like(maxlag0, 'maxlag0')
maxlagex = int_like(maxlagex, 'maxlagex', optional=True)
trim = string_like(trim, 'trim', optional=True,
options=('forward', 'backward', 'both', 'none'))
if maxlagex is None:
maxlagex = maxlag0
maxlag = max(maxlag0, maxlagex)
is_pandas = _is_using_pandas(x, None)
if x.ndim == 1:
if is_pandas:
x = pd.DataFrame(x)
else:
x = x[:, None]
elif x.ndim == 0 or x.ndim > 2:
raise ValueError('Only supports 1 and 2-dimensional data.')
nobs, nvar = x.shape
if is_pandas and use_pandas:
lags = lagmat(x.iloc[:, 0], maxlag, trim=trim,
original='in', use_pandas=True)
lagsli = [lags.iloc[:, :maxlag0 + 1]]
for k in range(1, nvar):
lags = lagmat(x.iloc[:, k], maxlag, trim=trim,
original='in', use_pandas=True)
lagsli.append(lags.iloc[:, dropex:maxlagex + 1])
return pd.concat(lagsli, axis=1)
elif is_pandas:
x = np.asanyarray(x)
lagsli = [lagmat(x[:, 0], maxlag, trim=trim, original='in')[:, :maxlag0 + 1]]
for k in range(1, nvar):
lagsli.append(lagmat(x[:, k], maxlag, trim=trim, original='in')[:, dropex:maxlagex + 1])
return np.column_stack(lagsli)
def vec(mat):
return mat.ravel('F')
def vech(mat):
# Gets Fortran-order
return mat.T.take(_triu_indices(len(mat)))
# tril/triu/diag, suitable for ndarray.take
def _tril_indices(n):
rows, cols = np.tril_indices(n)
return rows * n + cols
def _triu_indices(n):
rows, cols = np.triu_indices(n)
return rows * n + cols
def _diag_indices(n):
rows, cols = np.diag_indices(n)
return rows * n + cols
def unvec(v):
k = int(np.sqrt(len(v)))
assert(k * k == len(v))
return v.reshape((k, k), order='F')
def unvech(v):
# quadratic formula, correct fp error
rows = .5 * (-1 + np.sqrt(1 + 8 * len(v)))
rows = int(np.round(rows))
result = np.zeros((rows, rows))
result[np.triu_indices(rows)] = v
result = result + result.T
# divide diagonal elements by 2
result[np.diag_indices(rows)] /= 2
return result
def duplication_matrix(n):
"""
Create duplication matrix D_n which satisfies vec(S) = D_n vech(S) for
symmetric matrix S
Returns
-------
D_n : ndarray
"""
n = int_like(n, 'n')
tmp = np.eye(n * (n + 1) // 2)
return np.array([unvech(x).ravel() for x in tmp]).T
def elimination_matrix(n):
"""
Create the elimination matrix L_n which satisfies vech(M) = L_n vec(M) for
any matrix M
Parameters
----------
Returns
-------
"""
n = int_like(n, 'n')
vech_indices = vec(np.tril(np.ones((n, n))))
return np.eye(n * n)[vech_indices != 0]
def commutation_matrix(p, q):
"""
Create the commutation matrix K_{p,q} satisfying vec(A') = K_{p,q} vec(A)
Parameters
----------
p : int
q : int
Returns
-------
K : ndarray (pq x pq)
"""
p = int_like(p, 'p')
q = int_like(q, 'q')
K = np.eye(p * q)
indices = np.arange(p * q).reshape((p, q), order='F')
return K.take(indices.ravel(), axis=0)
def _ar_transparams(params):
"""
Transforms params to induce stationarity/invertability.
Parameters
----------
params : array_like
The AR coefficients
Reference
---------
Jones(1980)
"""
newparams = np.tanh(params/2)
tmp = np.tanh(params/2)
for j in range(1,len(params)):
a = newparams[j]
for kiter in range(j):
tmp[kiter] -= a * newparams[j-kiter-1]
newparams[:j] = tmp[:j]
return newparams
def _ar_invtransparams(params):
"""
Inverse of the Jones reparameterization
Parameters
----------
params : array_like
The transformed AR coefficients
"""
params = params.copy()
tmp = params.copy()
for j in range(len(params)-1,0,-1):
a = params[j]
for kiter in range(j):
tmp[kiter] = (params[kiter] + a * params[j-kiter-1])/\
(1-a**2)
params[:j] = tmp[:j]
invarcoefs = 2*np.arctanh(params)
return invarcoefs
def _ma_transparams(params):
"""
Transforms params to induce stationarity/invertability.
Parameters
----------
params : ndarray
The ma coeffecients of an (AR)MA model.
Reference
---------
Jones(1980)
"""
newparams = ((1-np.exp(-params))/(1+np.exp(-params))).copy()
tmp = ((1-np.exp(-params))/(1+np.exp(-params))).copy()
# levinson-durbin to get macf
for j in range(1,len(params)):
b = newparams[j]
for kiter in range(j):
tmp[kiter] += b * newparams[j-kiter-1]
newparams[:j] = tmp[:j]
return newparams
def _ma_invtransparams(macoefs):
"""
Inverse of the Jones reparameterization
Parameters
----------
params : ndarray
The transformed MA coefficients
"""
tmp = macoefs.copy()
for j in range(len(macoefs)-1,0,-1):
b = macoefs[j]
for kiter in range(j):
tmp[kiter] = (macoefs[kiter]-b *macoefs[j-kiter-1])/(1-b**2)
macoefs[:j] = tmp[:j]
invmacoefs = -np.log((1-macoefs)/(1+macoefs))
return invmacoefs
def unintegrate_levels(x, d):
"""
Returns the successive differences needed to unintegrate the series.
Parameters
----------
x : array_like
The original series
d : int
The number of differences of the differenced series.
Returns
-------
y : array_like
The increasing differences from 0 to d-1 of the first d elements
of x.
See Also
--------
unintegrate
"""
d = int_like(d, 'd')
x = x[:d]
return np.asarray([np.diff(x, d - i)[0] for i in range(d, 0, -1)])
def unintegrate(x, levels):
"""
After taking n-differences of a series, return the original series
Parameters
----------
x : array_like
The n-th differenced series
levels : list
A list of the first-value in each differenced series, for
[first-difference, second-difference, ..., n-th difference]
Returns
-------
y : array_like
The original series de-differenced
Examples
--------
>>> x = np.array([1, 3, 9., 19, 8.])
>>> levels = unintegrate_levels(x, 2)
>>> levels
array([ 1., 2.])
>>> unintegrate(np.diff(x, 2), levels)
array([ 1., 3., 9., 19., 8.])
"""
levels = list(levels)[:] # copy
if len(levels) > 1:
x0 = levels.pop(-1)
return unintegrate(np.cumsum(np.r_[x0, x]), levels)
x0 = levels[0]
return np.cumsum(np.r_[x0, x])
def freq_to_period(freq):
"""
Convert a pandas frequency to a periodicity
Parameters
----------
freq : str or offset
Frequency to convert
Returns
-------
period : int
Periodicity of freq
Notes
-----
Annual maps to 1, quarterly maps to 4, monthly to 12, weekly to 52.
"""
if not isinstance(freq, offsets.DateOffset):
freq = to_offset(freq) # go ahead and standardize
freq = freq.rule_code.upper()
if freq == 'A' or freq.startswith(('A-', 'AS-')):
return 1
elif freq == 'Q' or freq.startswith(('Q-', 'QS-')):
return 4
elif freq == 'M' or freq.startswith(('M-', 'MS')):
return 12
elif freq == 'W' or freq.startswith('W-'):
return 52
elif freq == 'D':
return 7
elif freq == 'B':
return 5
elif freq == 'H':
return 24
else: # pragma : no cover
raise ValueError("freq {} not understood. Please report if you "
"think this is in error.".format(freq))
__all__ = ['lagmat', 'lagmat2ds','add_trend', 'duplication_matrix',
'elimination_matrix', 'commutation_matrix',
'vec', 'vech', 'unvec', 'unvech', 'freq_to_period']