def toordinal(self):
"Converts the dates from values to ordinals."
# Note: we better try to cache the result
if self._cachedinfo['toord'] is None:
# diter = (Date(self.freq, value=d).toordinal() for d in self)
if self.freq == _c.FR_UND:
diter = (d.value for d in self)
else:
diter = (d.toordinal() for d in self)
toord = numeric.fromiter(diter, dtype=float_)
self._cachedinfo['toord'] = toord
return self._cachedinfo['toord']
def fstl(y, np=12, ns=7, nt=None, nl=13, isdeg=1, itdeg=1, ildeg=1,
nsjump=None,ntjump=None,nljump=None, robust=True, ni=None,no=None):
"""Decomposes a time series into seasonal and trend components.
:Parameters:
y : Numerical array
Time Series to be decomposed.
np : Integer *[12]*
Period of the seasonal component.
For example, if the time series is monthly with a yearly cycle, then
np=12.
ns : Integer *[7]*
Length of the seasonal smoother.
The value of ns should be an odd integer greater than or equal to 3.
A value 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 : Integer *[None]*
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.
If nt is None, it is estimated as the smallest odd integer greater
or equal to (1.5*np)/[1-(1.5/ns)]
nl : Integer *[None]*
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 used by default.
isdeg : Integer *[1]*
Degree of locally-fitted polynomial in seasonal smoothing.
The value is 0 or 1.
itdeg : Integer *[1]*
Degree of locally-fitted polynomial in trend smoothing.
The value is 0 or 1.
ildeg : Integer *[1]*
Degree of locally-fitted polynomial in low-pass smoothing.
The value is 0 or 1.
nsjump : Integer *[None]*
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. By default, nsjump= 0.1*ns.
ntjump : Integer *[1]*
Skipping value for trend smoothing. If None, ntjump= 0.1*nt
nljump : Integer *[1]*
Skipping value for low-pass smoothing. If None, nljump= 0.1*nl
robust : Boolean *[True]*
Flag indicating whether robust fitting should be performed.
ni : Integer *[None]*
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.
If ni is None, ni is set to 1 for robust fitting, to 5 otherwise.
no : Integer *[0]*
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.
If None, then no is set to 15 for robust fitting, to 0 otherwise.
Returns:
A recarray of estimated trend values ('trend'), estimated seasonal
components ('seasonal'), local robust weights ('weights') and fit
residuals ('residuals').
The final local robust weights are all 1 if no=0.
Reference
---------
R. B. Cleveland, W. S. Cleveland, J. E. McRae and I. Terpenning.
1990. STL: A Seasonal-Trend Decomposition Procedure Based on LOESS
(with Discussion). Journal of Official Statistics, 6:3-73.
"""
ns = max(ns, 3)
if ns % 2 == 0:
ns += 1
np = max(2, np)
if nt is None:
nt = max(int((1.5*np/(1.-1.5/ns))+0.5), 3)
if not nt % 2:
nt += 1
if nl is None:
nl = max(3,np)
if not nl % 2:
nl += 1
if nsjump is None:
nsjump = int(0.1*ns + 0.9)
if ntjump is None:
ntjump = int(0.1*nt + 0.9)
if nljump is None:
nljump = int(0.1*nl + 0.9)
if robust:
if ni is None:
ni = 1
if no is None:
no = 15
else:
if ni is None:
ni = 5
if no is None:
no = 0
if hasattr(y,'_mask') and numpy.any(y._mask):
raise ValueError,"Missing values should first be filled !"
y = numeric.array(y, subok=True, copy=False).ravel()
(rw,szn,trn,work) = _stl.stl(y,np,ns,nt,nl,isdeg,itdeg,ildeg,
nsjump,ntjump,nljump,ni,no,)
dtyp = [('trend', float_), ('seasonal', float_),
('residuals', float_), ('weights', float_)]
result = numeric.fromiter(zip(trn,szn,y-trn-szn,rw), dtype=dtyp)
return result.view(recarray)
def flowess(x,y,span=0.5,nsteps=2,delta=0):
"""Performs a robust locally weighted regression (lowess).
Outputs a *3xN* array of fitted values, residuals and fit weights.
:Parameters:
x : ndarray
Abscissas of the points on the scatterplot; the values in X must be
ordered from smallest to largest.
y : ndarray
Ordinates of the points on the scatterplot.
span : Float *[0.5]*
Fraction of the total number of points used to compute each fitted value.
As f increases the smoothed values become smoother. Choosing f in the range
.2 to .8 usually results in a good fit.
nsteps : Integer *[2]*
Number of iterations in the robust fit. If nsteps=0, the nonrobust fit
is returned; setting nsteps=2 should serve most purposes.
delta : Integer *[0]*
Nonnegative parameter which may be used to save computations.
If N (the number of elements in x) is less than 100, set delta=0.0;
if N is greater than 100 you should find out how delta works by reading
the additional instructions section.
:Returns:
A recarray of smoothed values ('smooth'), residuals ('residuals') and local
robust weights ('weights').
Additional instructions
-----------------------
Fro the original author:
DELTA can be used to save computations. Very roughly the
algorithm is this: on the initial fit and on each of the
NSTEPS iterations locally weighted regression fitted values
are computed at points in X which are spaced, roughly, DELTA
apart; then the fitted values at the remaining points are
computed using linear interpolation. The first locally
weighted regression (l.w.r.) computation is carried out at
X(1) and the last is carried out at X(N). Suppose the
l.w.r. computation is carried out at X(I). If X(I+1) is
greater than or equal to X(I)+DELTA, the next l.w.r.
computation is carried out at X(I+1). If X(I+1) is less
than X(I)+DELTA, the next l.w.r. computation is carried out
at the largest X(J) which is greater than or equal to X(I)
but is not greater than X(I)+DELTA. Then the fitted values
for X(K) between X(I) and X(J), if there are any, are
computed by linear interpolation of the fitted values at
X(I) and X(J). If N is less than 100 then DELTA can be set
to 0.0 since the computation time will not be too great.
For larger N it is typically not necessary to carry out the
l.w.r. computation for all points, so that much computation
time can be saved by taking DELTA to be greater than 0.0.
If DELTA = Range (X)/k then, if the values in X were
uniformly scattered over the range, the full l.w.r.
computation would be carried out at approximately k points.
Taking k to be 50 often works well.
Method
------
The fitted values are computed by using the nearest neighbor
routine and robust locally weighted regression of degree 1
with the tricube weight function. A few additional features
have been added. Suppose r is FN truncated to an integer.
Let h be the distance to the r-th nearest neighbor
from X[i]. All points within h of X[i] are used. Thus if
the r-th nearest neighbor is exactly the same distance as
other points, more than r points can possibly be used for
the smooth at X[i]. There are two cases where robust
locally weighted regression of degree 0 is actually used at
X[i]. One case occurs when h is 0.0. The second case
occurs when the weighted standard error of the X[i] with
respect to the weights w[j] is less than .001 times the
range of the X[i], where w[j] is the weight assigned to the
j-th point of X (the tricube weight times the robustness
weight) divided by the sum of all of the weights. Finally,
if the w[j] are all zero for the smooth at X[i], the fitted
value is taken to be Y[i].
References
----------
W. S. Cleveland. 1978. Visual and Computational Considerations in
Smoothing Scatterplots by Locally Weighted Regression. In
Computer Science and Statistics: Eleventh Annual Symposium on the
Interface, pages 96-100. Institute of Statistics, North Carolina
State University, Raleigh, North Carolina, 1978.
W. S. Cleveland, 1979. Robust Locally Weighted Regression and
Smoothing Scatterplots. Journal of the American Statistical
Association, 74:829-836, 1979.
W. S. Cleveland, 1981. LOWESS: A Program for Smoothing Scatterplots
by Robust Locally Weighted Regression. The American Statistician,
35:54.
"""
x = narray(x, copy=False, subok=True, dtype=float_)
y = narray(y, copy=False, subok=True, dtype=float_)
if x.size != y.size:
raise ValueError("Incompatible size between observations and response!")
out_dtype = [('smooth',float_), ('weigths', float_), ('residuals', float_)]
return numeric.fromiter(zip(*_lowess.lowess(x,y,span,nsteps,delta,)),
dtype=out_dtype).view(recarray)