1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653
|
#cython: language_level=3, boundscheck=False, cdivision=True, wraparound=False, initializedcheck=False
"""
(c) 2019 Kevin Sheppard
License: NCSA/BSD-3 Clause
Based on NETLIB STL code
Notes: See file _stl_py.py in Git history for a pure python port for
the STL FORTRAN code
R.B. Cleveland, W.S.Cleveland, J.E. McRae, and I. Terpenning,
STL: A Seasonal-Trend Decomposition Procedure Based on Loess, Statistics
Research Report, AT&T Bell Laboratories.
"""
"""
Notes: Docstring from STL
PURPOSE
STL decomposes a time series into seasonal and trend components.
It returns the components and robustness weights.
SYNOPSIS
stl(y, n, np, ns, nt, nl, isdeg, itdeg, ildeg, nsjump, ntjump,
nljump, ni, no, rw, season, trend, work)
integer n, np, ns, nt, nl, isdeg, itdeg, ildeg, nsjump, ntjump,
nljump, ni, no
real y(n), rw(n), season(n), trend(n), work(n+2*np,5)
ARGUMENTS
y input, time series to be decomposed.
n input, number of values in y.
np input, the period of the seasonal component. For example,
if the time series is monthly with a yearly cycle, then
np=12.
ns input, length of the seasonal smoother. The value of ns
should be an odd integer greater than or equal to 3; ns>6
is recommended. As ns increases the values of the
seasonal component at a given point in the seasonal cycle
(e.g., January values of a monthly series with a yearly
cycle) become smoother.
nt input, length of the trend smoother. The value of nt
should be an odd integer greater than or equal to 3; a
value of nt between 1.5*np and 2*np is recommended. As
nt increases the values of the trend component become
smoother.
nl input, length of the low-pass filter. The value of nl
should be an odd integer greater than or equal to 3; the
smallest odd integer greater than or equal to np is
recommended.
isdeg input, degree of locally-fitted polynomial in seasonal
smoothing. The value is 0 or 1.
itdeg input, degree of locally-fitted polynomial in trend
smoothing. The value is 0 or 1.
ildeg input, degree of locally-fitted polynomial in low-pass
smoothing. The value is 0 or 1.
nsjump input, skipping value for seasonal smoothing. The
seasonal smoother skips ahead nsjump points and then
linearly interpolates in between. The value of nsjump
should be a positive integer; if nsjump=1, a seasonal
smooth is calculated at all n points. To make the
procedure run faster, a reasonable choice for nsjump is
10%-20% of ns.
ntjump input, skipping value for trend smoothing.
nljump input, skipping value for the low-pass filter.
ni input, number of loops for updating the seasonal and
trend components. The value of ni should be a positive
integer. See the next argument for advice on the choice
of ni.
no input, number of iterations of robust fitting. The value
of no should be a nonnegative integer. If the data are
well behaved without outliers, then robustness iterations
are not needed. In this case set no=0, and set ni=2 to 5
depending on how much security you want that the
seasonal-trend looping converges. If outliers are
present then no=3 is a very secure value unless the
outliers are radical, in which case no=5 or even 10 might
be better. If no>0 then set ni to 1 or 2.
rw output, final robustness weights. All rw are 1 if no=0.
season output, seasonal component.
trend output, trend component.
work workspace of (n+2*np)*5 locations.
"""
from typing import Dict, Union
import pandas as pd
import numpy as np
from libc.math cimport fabs, sqrt, isnan, NAN
from statsmodels.tsa.tsatools import freq_to_period
def _is_pos_int(x, odd):
valid = (isinstance(x, (int, np.integer))
and not isinstance(x, np.timedelta64))
valid = valid and not isinstance(x, (float, np.floating))
try:
valid = valid and x > 0
except Exception:
valid = False
if valid and odd:
valid = valid & (x % 2) == 1
return valid
cdef class STL(object):
"""
STL(endog, period=None, seasonal=7, trend=None, low_pass=None,
seasonal_deg=0, trend_deg=0, low_pass_deg=0, robust=False,
seasonal_jump=1, trend_jump=1, low_pass_jump=1)
Season-Trend decomposition using LOESS.
Parameters
----------
endog : array_like
Data to be decomposed. Must be squeezable to 1-d.
period : {int, None}, optional
Periodicity of the sequence. If None and endog is a pandas Series or
DataFrame, attempts to determine from endog. If endog is a ndarray,
period must be provided.
seasonal : int, optional
Length of the seasonal smoother. Must be an odd integer, and should
normally be >= 7 (default).
trend : {int, None}, optional
Length of the trend smoother. Must be an odd integer. If not provided
uses the smallest odd integer greater than
1.5 * period / (1 - 1.5 / seasonal), following the suggestion in
the original implementation.
low_pass : {int, None}, optional
Length of the low-pass filter. Must be an odd integer >=3. If not
provided, uses the smallest odd integer > period.
seasonal_deg : int, optional
Degree of seasonal LOESS. 0 (constant) or 1 (constant and trend).
trend_deg : int, optional
Degree of trend LOESS. 0 (constant) or 1 (constant and trend).
low_pass_deg : int, optional
Degree of low pass LOESS. 0 (constant) or 1 (constant and trend).
robust : bool, optional
Flag indicating whether to use a weighted version that is robust to
some forms of outliers.
seasonal_jump : int, optional
Positive integer determining the linear interpolation step. If larger
than 1, the LOESS is used every seasonal_jump points and linear
interpolation is between fitted points. Higher values reduce
estimation time.
trend_jump : int, optional
Positive integer determining the linear interpolation step. If larger
than 1, the LOESS is used every trend_jump points and values between
the two are linearly interpolated. Higher values reduce estimation
time.
low_pass_jump : int, optional
Positive integer determining the linear interpolation step. If larger
than 1, the LOESS is used every low_pass_jump points and values between
the two are linearly interpolated. Higher values reduce estimation
time.
See Also
--------
statsmodels.tsa.seasonal.DecomposeResult
statsmodels.tsa.seasonal.seasonal_decompose
Notes
-----
Derived from the NETLIB fortran written by [1]_. The original code
contains a bug that appears in the determination of the median that is
used in the robust weighting. This version matches the fixed version that
uses a correct partitioned sort to determine the median.
References
----------
.. [1] R. B. Cleveland, W. S. Cleveland, J.E. McRae, and I. Terpenning
(1990) STL: A Seasonal-Trend Decomposition Procedure Based on LOESS.
Journal of Official Statistics, 6, 3-73.
Examples
--------
The original example uses STL to decompose CO2 data into level, season and a
residual.
Start by aggregating to monthly, and filling any missing values
>>> from statsmodels.datasets import co2
>>> import matplotlib.pyplot as plt
>>> from pandas.plotting import register_matplotlib_converters
>>> register_matplotlib_converters()
>>> data = co2.load(True).data
>>> data = data.resample('M').mean().ffill()
The period (12) is automatically detected from the data's frequency ('M').
>>> from statsmodels.tsa.seasonal import STL
>>> res = STL(data).fit()
>>> res.plot()
>>> plt.show()
.. plot:: plots/stl_plot.py
"""
cdef object endog
cdef Py_ssize_t nobs
cdef int _period, seasonal, trend, low_pass, seasonal_deg, trend_deg
cdef int low_pass_deg, low_pass_jump, trend_jump, seasonal_jump
cdef bint robust, _use_rw
cdef double[::1] _ya, _trend, _season, _rw
cdef double[:, ::1] _work
def __init__(self, endog, period=None, seasonal=7, trend=None, low_pass=None,
seasonal_deg=1, trend_deg=1, low_pass_deg=1,
robust=False, seasonal_jump=1, trend_jump=1, low_pass_jump=1):
self.endog = endog
y = np.ascontiguousarray(np.squeeze(np.asarray(endog)), dtype=np.double)
if y.ndim != 1:
raise ValueError('y must be a 1d array')
self._ya = y
self.nobs = y.shape[0] # n
if period is None:
freq = None
if isinstance(endog, (pd.Series, pd.DataFrame)):
freq = getattr(endog.index, 'inferred_freq', None)
if freq is None:
raise ValueError('Unable to determine period from endog')
period = freq_to_period(freq)
if not _is_pos_int(period, False) or period < 2:
raise ValueError('period must be a positive integer >= 2')
self._period = period # np
if not _is_pos_int(seasonal, True) or seasonal < 3:
raise ValueError('seasonal must be an odd positive integer >= 3')
self.seasonal = seasonal # ns
if trend is None:
trend = int(np.ceil(1.5 * self._period / (1 - 1.5 / self.seasonal)))
# ensure odd
trend += ((trend % 2) == 0)
if not _is_pos_int(trend, True) or trend < 3 or trend <= period:
raise ValueError('trend must be an odd positive integer '
'>= 3 where trend > period')
self.trend = trend # nt
if low_pass is None:
low_pass = self._period + 1
low_pass += ((low_pass % 2) == 0)
if not _is_pos_int(low_pass, True) or \
low_pass < 3 or low_pass <= period:
raise ValueError('low_pass must be an odd positive integer >= 3 '
'where low_pass > period')
self.low_pass = low_pass # nl
self.seasonal_deg = seasonal_deg # isdeg
self.trend_deg = trend_deg # itdeg
self.low_pass_deg = low_pass_deg # ildeg
self.robust = robust
if not _is_pos_int(low_pass_jump, False):
raise ValueError('low_pass_jump must be a positive integer')
if not _is_pos_int(seasonal_jump, False):
raise ValueError('seasonal_jump must be a positive integer')
if not _is_pos_int(trend_jump, False):
raise ValueError('trend_jump must be a positive integer')
self.low_pass_jump = low_pass_jump
self.seasonal_jump = seasonal_jump
self.trend_jump = trend_jump
self._use_rw = False
self._trend = np.zeros(self.nobs)
self._season = np.zeros(self.nobs)
self._rw = np.ones(self.nobs)
self._work = np.zeros((7, self.nobs + 2 * period))
def __reduce__(self):
args = (
self.endog,
self._period,
self.seasonal,
self.trend,
self.low_pass,
self.seasonal_deg,
self.trend_deg,
self.low_pass_deg,
self.robust,
self.seasonal_jump,
self.trend_jump,
self.low_pass_jump,
)
return (STL, args)
@property
def period(self) -> int:
"""The period length of the time series"""
return self._period
@property
def config(self) -> Dict[str, Union[int, bool]]:
"""
The parameters used in the model.
Returns
-------
dict[str, Union[int, bool]]
The values used in the STL decomposition.
"""
return dict(period=self._period,
seasonal=self.seasonal,
seasonal_deg=self.seasonal_deg,
seasonal_jump=self.seasonal_jump,
trend=self.trend,
trend_deg=self.trend_deg,
trend_jump=self.trend_jump,
low_pass=self.low_pass,
low_pass_deg=self.low_pass_deg,
low_pass_jump=self.low_pass_jump,
robust=self.robust)
def fit(self, inner_iter=None, outer_iter=None):
"""
fit(inner_iter=None, outer_iter=None)
Estimate season, trend and residuals components.
Parameters
----------
inner_iter : {int, None}, optional
Number of iterations to perform in the inner loop. If not provided
uses 2 if ``robust`` is True, or 5 if not.
outer_iter : {int, None}, optional
Number of iterations to perform in the outer loop. If not provided
uses 15 if ``robust`` is True, or 0 if not.
Returns
-------
DecomposeResult
Estimation results.
"""
cdef Py_ssize_t i
if inner_iter is None:
inner_iter = 2 if self.robust else 5
if outer_iter is None:
outer_iter = 15 if self.robust else 0
self._use_rw = False
k = 0
for i in range(self.nobs):
self._season[i] = self._trend[i] = 0.0
self._rw[i] = 1.0
while True:
self._onestp(inner_iter)
k = k + 1
if k > outer_iter:
break
for i in range(self.nobs):
self._work[0, i] = self._trend[i] + self._season[i]
self._rwts()
self._use_rw = True
# Return pandas if pandas
season = np.asarray(self._season)
trend = np.asarray(self._trend)
rw = np.asarray(self._rw)
resid = self._ya - season - trend
if isinstance(self.endog, (pd.Series, pd.DataFrame)):
index = self.endog.index
resid = pd.Series(resid, index=index, name='resid')
season = pd.Series(season, index=index, name='season')
trend = pd.Series(trend, index=index, name='trend')
rw = pd.Series(rw, index=index, name='robust_weight')
# Avoid circular imports
from statsmodels.tsa.seasonal import DecomposeResult
return DecomposeResult(self.endog, season, trend, resid, rw)
cdef void _onestp(self, int inner_iter):
"""
y, n, np, ns, nt, nl, isdeg, itdeg, ildeg, nsjump,
ntjump, nljump, ni, userw, rw, season, trend, work
->
self._ya, self.nobs, self._period, self.seasonal,
self.trend, self.low_pass, self.seasonal_deg,
self.trend_deg, self.low_pass_deg, self.seasonal_jump,
self.trend_jump, self.low_pass_jump, inner_iter,
userw, self._rw, self._season, self._trend,
self._work
"""
cdef Py_ssize_t i, j, np
cdef double[:, ::1] work
cdef double[::1] y, season, trend, rw
# Original variable names
work = self._work
y = self._ya
trend = self._trend
n = self.nobs
nl = self.low_pass
ildeg = self.low_pass_deg
nljump = self.low_pass_jump
np = self._period
season = self._season
nt = self.trend
itdeg = self.trend_deg
ntjump = self.trend_jump
rw = self._rw
for j in range(inner_iter):
for i in range(self.nobs):
work[0, i] = y[i] - trend[i]
self._ss()
self._fts()
self._ess(work[2, :], n, nl, ildeg, nljump, False, work[3, :],
work[0, :], work[4, :])
for i in range(self.nobs):
season[i] = work[1, np+i] - work[0, i]
work[0, i] = y[i] - season[i]
self._ess(work[0, :], n, nt, itdeg, ntjump, self._use_rw, rw,
trend, work[2, :])
cdef double _est(self, double[::1] y, int n, int len_, int ideg, int xs,
int nleft, int nright, double[::1] w, bint userw,
double[::1] rw):
cdef double rng, a, b, c, h, h1, h9, r, ys
cdef Py_ssize_t j
# Removed ok and ys, which are scalar return values
rng = n - 1.0
h = max(xs - nleft, nright - xs)
if len_ > n:
h += (len_ - n) // 2.0
h9 = .999 * h
h1 = .001 * h
a = 0.0
for j in range(nleft - 1, nright):
w[j] = 0.
r = fabs(j + 1 - xs)
if r <= h9:
if r <= h1:
w[j] = 1.0
else:
w[j] = (1.0 - (r / h) ** 3) ** 3
if userw:
w[j] = w[j] * rw[j]
a = a + w[j]
if a <= 0:
return NAN
for j in range(nleft - 1, nright):
w[j] = w[j] / a
if h > 0 and ideg > 0:
a = 0.0
for j in range(nleft - 1, nright):
a = a + w[j] * (j + 1)
b = xs - a
c = 0.0
for j in range(nleft - 1, nright):
c = c + w[j] * (j + 1 - a) ** 2
if sqrt(c) > .001 * rng:
b = b / c
for j in range(nleft - 1, nright):
w[j] = w[j] * (b * (j + 1 - a) + 1.0)
ys = 0.0
for j in range(nleft - 1, nright):
ys = ys + w[j] * y[j]
return ys
cdef void _ess(self, double[::1] y, int n, int len_, int ideg, int njump,
bint userw, double[::1] rw, double[::1] ys, double[::1] res):
# TODO: Try with 1 data point!!? Establish minimums
cdef Py_ssize_t i, j, k
cdef double delta
cdef int newnj, nleft, nright, nsh
cdef bint ok
if n < 2:
ys[0] = y[0]
return
newnj = min(njump, n - 1)
if len_ >= n:
nleft = 1
nright = n
i = 0
while i < n:
# formerly: for i in range(0, n, newnj):
ys[i] = self._est(y, n, len_, ideg, i + 1, nleft, nright,
res, userw, rw)
if isnan(ys[i]):
ys[i] = y[i]
i += newnj
elif newnj == 1:
nsh = (len_ + 2) // 2
nleft = 1
nright = len_
for i in range(n):
if (i + 1) > nsh and nright != n:
nleft = nleft + 1
nright = nright + 1
ys[i] = self._est(y, n, len_, ideg, i + 1, nleft, nright,
res, userw, rw)
if isnan(ys[i]):
ys[i] = y[i]
else:
nsh = (len_ + 1) // 2
i = 0
while i < n:
# formerly: for i in range(0, n, newnj):
if (i + 1) < nsh:
nleft = 1
nright = len_
elif (i + 1) >= (n - nsh + 1):
nleft = n - len_ + 1
nright = n
else:
nleft = i + 1 - nsh + 1
nright = len_ + i + 1 - nsh
ys[i] = self._est(y, n, len_, ideg, i + 1, nleft, nright,
res, userw, rw)
if isnan(ys[i]):
ys[i] = y[i]
i += newnj
if newnj == 1:
return
# newnj > 1
i = 0
while i < (n - newnj):
# Formerly: for i in range(0, n - newnj, newnj):
delta = (ys[i + newnj] - ys[i]) / newnj
for j in range(i, i + newnj):
ys[j] = ys[i] + delta * ((j + 1) - (i + 1))
i += newnj
k = ((n - 1) // newnj) * newnj + 1
if k != n:
ys[n - 1] = self._est(y, n, len_, ideg, n, nleft, nright, res,
userw, rw)
if isnan(ys[n - 1]):
ys[n - 1] = y[n - 1]
if k != (n - 1):
delta = (ys[n - 1] - ys[k - 1]) / (n - k)
for j in range(k, n):
ys[j] = ys[k - 1] + delta * ((j + 1) - k)
cdef void _ma(self, double[::1] x, int n, int len_, double[::1] ave):
cdef int newn
cdef double flen, v
cdef Py_ssize_t i, j, k, m
newn = n - len_ + 1
flen = float(len_)
v = 0.0
for i in range(len_):
v = v + x[i]
ave[0] = v / flen
k = len_
m = 0
for j in range(1, newn):
v += x[k] - x[m]
ave[j] = v / flen
k += 1
m += 1
cdef void _fts(self):
"""
Original def:
_fts(self, x, n, np, trend, work)
Only call:
fts(work[1, :], n + 2 * np, np, work[2, :], work[0, :])
"""
cdef double[::1] x, trend, work
cdef int n, np
x = self._work[1, :]
n = self.nobs + 2 * self._period
np = self._period
trend = self._work[2, :]
work = self._work[0, :]
self._ma(x, n, np, trend)
self._ma(trend, n - np + 1, np, work)
self._ma(work, n - 2 * np + 2, 3, trend)
cdef void _ss(self):
"""
_ss(self, y, n, np, ns, isdeg, nsjump, userw, rw, season, work1, work2,
work3, work4)
ss(work[0, :], n, np, ns, isdeg, nsjump, userw, rw,
work[1, :], work[2, :], work[3, :], work[4, :], season)
"""
cdef Py_ssize_t i, j, m
cdef int n, np, ns, isdef, nsjump, k
cdef bint userw
cdef double[::1] y, work1, work2, work3, work4, rw, season
# Original variable names
y = self._work[0, :]
n = self.nobs
np = self._period
ns = self.seasonal
isdeg = self.seasonal_deg
nsjump = self.seasonal_jump
rw = self._rw
season = self._work[1, :]
work1 = self._work[2, :]
work2 = self._work[3, :]
work3 = self._work[4, :]
work4 = self._season
userw = self._use_rw
for j in range(np):
k = (n - (j + 1)) // np + 1
for i in range(k):
work1[i] = y[i * np + j]
if userw:
for i in range(k):
work3[i] = rw[i * np + j]
self._ess(work1, k, ns, isdeg, nsjump, userw, work3, work2[1:],
work4)
xs = 0
nright = min(ns, k)
work2[0] = self._est(work1, k, ns, isdeg, xs, 1, nright, work4,
userw, work3)
if isnan(work2[0]):
work2[0] = work2[1]
xs = k + 1
nleft = max(1, k - ns + 1)
work2[k + 1] = self._est(work1, k, ns, isdeg, xs, nleft, k,
work4, userw, work3)
if isnan(work2[k + 1]):
work2[k + 1] = work2[k]
for m in range(k + 2):
season[m * np + j] = work2[m]
cdef void _rwts(self):
"""
y, n, fit, rw ->
self._ya, self.nobs, self._work[0, :], self._rw
"""
cdef Py_ssize_t i
cdef double [::1] y, fit, rw
cdef double cmad, c1, c9
cdef int n
# Original variable names
y = self._ya
n = self.nobs
fit = self._work[0, :]
rw = self._rw
for i in range(self.nobs):
rw[i] = fabs(y[i] - fit[i])
mid = np.empty(2, dtype=int)
mid[0] = n // 2
mid[1] = n - mid[0] - 1
rw_part = np.partition(rw, mid)
cmad = 3.0 * (rw_part[mid[0]] + rw_part[mid[1]])
if cmad == 0:
for i in range(self.nobs):
rw[i] = 1
return
c9 = .999 * cmad
c1 = .001 * cmad
for i in range(self.nobs):
if rw[i] <= c1:
rw[i] = 1.0
elif rw[i] <= c9:
rw[i] = (1.0 - (rw[i] / cmad) ** 2) ** 2
else:
rw[i] = 0.0
|