Source code for statsmodels.tsa.tsatools

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'): """ Adds a trend and/or constant to an array. Parameters ---------- X : array_like Original array of data. trend : str {"c","t","ct","ctt"} "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 already exists in X. 'raise' will raise an error. 'add' will duplicate a constant. 'skip' will return the data without change. 'skip' is the default. Returns ------- y : array, recarray or DataFrame 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'. Notes ----- Returns columns as ["ctt","ct","c"] whenever applicable. There is currently no checking for an existing trend. See Also -------- statsmodels.tools.tools.add_constant """ prepend = bool_like(prepend, 'prepend') trend = string_like(trend, 'trend', options=('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 == "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: 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': msg = "x contains a constant. Adding a constant with " \ "trend='{0}' is not allowed.".format(trend) 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
def add_lag(x, col=None, lags=1, drop=False, insert=True): """ Returns an array with lags included given an array. Parameters ---------- x : array 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 isn't "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 specifies 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 ------- detrended data series : 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, 1d or 2d data; if 2d, observation in rows and variables in columns maxlag : int all lags from zero to maxlag are included trim : str {'forward', 'backward', 'both', 'none'} or None * '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 : str {'ex','sep','in'} * '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, optional If true, returns a DataFrame when the input is a pandas Series or DataFrame. If false, return numpy ndarrays. Returns ------- lagmat : 2d array array with lagged observations y : 2d array, optional Only returned if original == 'sep' 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.]]) 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. """ 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, 2d 2d data, observation in rows and variables in columns maxlag0 : int for first variable all lags from zero to maxlag are included maxlagex : None or int max lag for all other variables all lags from zero to maxlag are included dropex : int (default is 0) exclude first dropex lags from other variables for all variables, except the first, lags from dropex to maxlagex are included trim : string * '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, optional If true, returns a DataFrame when the input is a pandas Series or DataFrame. If false, return numpy ndarrays. Returns ------- lagmat : 2d array 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 : array 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 : array 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']