Ox version of /netlib/a/dloess

• Loess( const mXt, const vY, const mWeights, const dSpan, const iDegree, const fNormalize, const aiParametric, const aiDrop_square, const sFamily, const sSurface, const sStatistics, const dCell, const sTrace_hat, const iIterations, const avFitted, const avResiduals, const avPseudo, const vDiagonal, const vRobust, const vDivisor, const avRest);
  for: Initialize and perform smoothing
  returns: 0 (failure), 1 (success), 2 (success but with warnings)
  arguments:
  

  Arguments	In (default)	Description
  mXt	n x T matrix	matrix of predictors (data in rows)
  vY	1 x T matrix	vector of response
  mWeights	empty or 1 x T matrix (all 1)	vector of weights to be given to individual observations in the sum of squared residuals that forms the local fitting criterion. By default, an unweighted fit is carried out. If supplied, weights should be a non-negative numeric vector. If the different observations have non-equal variances, weights should be inversely proportional to the variances.
  dSpan	double (0.75)	smoothing parameter
  iDegree	1,(2)	overall degree of locally-fitted polynomial. 1 is locally-linear fitting and 2 is locally-quadratic fitting.
  fNormalize	FALSE,(TRUE)	determines if numeric predictors should be normalized. If TRUE (1) - the default - the standard normalization is used. If FALSE (0), no normalization is carried out.
  aiParametric	empty or 1 x p matrix (all FALSE)	for two or more numeric predictors, this argument specifies those variables that should be conditionally-parametric. The argument should be a logical vector of length p, specified in the order of the predictor group ordered in x. Default is a vector of 0's of length p
  aiDrop_square	empty or 1 x p matrix (all FALSE)	for cases with degree = 2, and with two or more numeric predictors, this argument specifies those numeric predictors whose squares should be dropped from the set of fitting variables. The method of specification is the same as for parametric. Default is a vector of 0's of length p.
  sFamily	string ("gaussian")	the assumed distribution of the errors. The values are "gaussian" or "symmetric". The first value is the default. If the second value is specified, a robust fitting procedure is used.
  sSurface	string ("interpolate")	determines whether the fitted surface is computed directly at all points ("direct") or whether an interpolation method is used ("interpolate"). The latter, the default, is what most users should use unless special circumstances warrant.
  sStatistics	string ("approximate")	determines whether the statistical quantities are computed exactly ("exact") or approximately ("approximate"). The latter is the default. The former should only be used for testing the approximation in statistical development and is not meant for routine usage because computation time can be horrendous.
  dCell	double (0.2)	if interpolation is used to compute the surface, this argument specifies the maximum cell size of the k-d tree. Suppose k = floor(n*cell*span) where n is the number of observations. Then a cell is further divided if the number of observations within it is greater than or equal to k.
  sTrace_hat	string ("wait.to.decide")	when surface is "approximate", determines the computational method used to compute the trace of the hat matrix, which is used in the computation of the statistical quantities. If "exact", an exact computation is done; normally this goes quite fast on the fastest machines until n, the number of observations is 1000 or more, but for very slow machines, things can slow down at n = 300. If "wait.to.decide" is selected, then a default is chosen in loess(); the default is "exact" for n < 500 and "approximate" otherwise. If surface is "exact", an exact computation is always done for the trace. Set trace_hat to "approximate" for large dataset will substantially reduce the computation time.
  iIterations	integer (4)	if family is "symmetric", the number of iterations of the robust fitting method. Default is 0 for family being "gaussian" by default.

  
  Set the input values to -1 to use the defaults.
  

  Arguments	In (default)	Out
  avFitted	0 or array	fitted values of the local regression model
  avResiduals	0 or array	residuals of the local regression fit
  avPseudo	0 or array	adjusted values of the response when robust estimation is used.
  vDiagonal	0 or array	diagonal of the operator hat matrix.
  vRobust	0 or array	robustness weights for robust fitting.
  vDivisor	0 or array	normalization divisor for numeric predictors.
  avRest	0 or array	1 x 5 matrix: - equivalent number of parameters; - estimate of the scale of the residuals; - delta 1; - delta 2; - trace of the operator hat matrix

  
  
• LoessError();
  for: in case Loess returns 0
  returns: the text of the error message
  
  
• LoessFree();
  for: fress the memory alocated by Loess (not required after StLoess or StLoessEz!)
  
  
• LoessPredict( const vXt, const avFit, const avFitse);
  for: fit loess surface
  returns: 0 (failure), 1 (success), 2 (success but with warnings)
  arguments:
  

  Arguments	In (default)	Out
  vXt	n x TF matrix of predictors
  avFit	0 or array	n x TF matrix: the evaluated loess surface
  avFitse	0 or array	n x TF matrix: estimates of the standard errors of the surface values

  
  
• LoessWarning();
  for: in case Loess returns 2
  returns: the text of the warning message
  
  
• StLoess( const vY, const cSeas, const cSmo, const cTrend, const cLowpass, const fIsdeg, const fTdeg, const fLdeg, const cSjump, const cTjump, const cLjump, const cLoop, const cItrob, const avRobust, const avSeas, const avTrend);
  for: decomposes a time series into seasonal and trend components
  no return value
  arguments:
  

  Arguments	In	Description
  vY	1 x T matrix	series to decompose
  cSeas	integer	the period of the seasonal component.
  cSmo	integer	length of the seasonal smoother. The value of cSmo should be an odd integer greater than or equal to 3; cSmo>6 is recommended. As cSmo 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.
  cTrend	integer	length of the trend smoother. The value of cTrend should be an odd integer greater than or equal to 3; a value of cTrend between 1.5*cSeas and 2*cSeas is recommended. As cTrend increases the values of the trend component become smoother.
  cLowpass	integer	length of the low-pass filter. The value of cLowpass should be an odd integer greater than or equal to 3; the smallest odd integer greater than or equal to cSeas is recommended.
  fIsdeg	0,1	degree of locally-fitted polynomial in seasonal smoothing.
  fTdeg	0,1	degree of locally-fitted polynomial in trend smoothing.
  fLdeg	0,1	degree of locally-fitted polynomial in low-pass smoothing.
  cSjump	integer	skipping value for seasonal smoothing. The seasonal smoother skips ahead cSjump points and then linearly interpolates in between. The value of cSjump should be a positive integer; if cSjump=1, a seasonal smooth is calculated at all T points. To make the procedure run faster, a reasonable choice for cSjump is 10%-20% of cSmo.
  cTjump	integer	skipping value for trend smoothing.
  cLjump	integer	skipping value for the low-pass filter.
  cLoop	integer	number of loops for updating the seasonal and trend components. The value of cLoop should be a positive integer. See the next argument for advice on the choice of cLoop.
  cItrob	integer	number of iterations of robust fitting. The value of cItrob should be a nonnegative integer. If the data are well behaved without outliers, then robustness iterations are not needed. In this case set cItrob=0, and set cLoop=2 to 5 depending on how much security you want that the seasonal-trend looping converges. If outliers are present then cItrob=3 is a very secure value unless the outliers are radical, in which case cItrob=5 or even 10 might be better. If cItrob>0 then set cLoop to 1 or 2.

  
  

  Arguments	In	Out
  avRobust	array	final robustness weights. All are 1 if cItrob=0.
  avSeas	array	seasonal component
  avTrend	array	trend component.

  
  
• StLoessEz( const vY, const cSeas, const cSmo, const fIsdeg, const fTdeg, const fRobust, const avRobust, const avSeas, const avTrend);
  for: decomposes a time series into seasonal and trend components using default for many parameters available in StLoess.
  returns:number of robustness iterations. The iterations end if a convergence criterion is met or if the number is 15.
  arguments:
  

  Arguments	In	Description
  vY	1 x T matrix	series to decompose
  cSeas	integer	the period of the seasonal component.
  cSmo	integer	length of the seasonal smoother. The value of cSmo should be an odd integer greater than or equal to 3; cSmo>6 is recommended. As cSmo 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.
  fIsdeg	0,1	degree of locally-fitted polynomial in seasonal smoothing
  fTdeg	0,1	degree of locally-fitted polynomial in trend smoothing
  fRobust	0,1	1 if robustness iterations are to be used, 0 otherwise.

  
  

  Arguments	In	Out
  avRobust	array	final robustness weights. All are 1 if cItrob=0.
  avSeas	array	seasonal component
  avTrend	array	trend component.

  The defaults relative to StLoess are:
  cTrend = smallest odd integer greater than or equal to (1.5*cSeas) / (1-(1.5/cSmo)).
  cLowpass = smallest odd integer greater than or equal to cSeas.
  cSjump = cSmo/10; cTjump = cTrend/10; cLjump = cLowpass/10.
  cLoop = 2 if fRobust=0; else cLoop=1.
  cItrob = 0 if fRobust=1; else robustness iterations are carried out until convergence of both seasonal and trend components, with 15 iterations maximum. Convergence occurs if the maximum changes in individual seasonal and trend fits are less than 1% of the component's range after the previous iteration.

Loess Example

STL Example