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litterman1

Temporal disaggregation using the Litterman method

CALLING SEQUENCE

[y,res]=litterman1(Y,x,ta,s,delta,typemin,optfunc,opt_optim)

PARAMETERS

Input

* Y = a (N x 1) vector of low frequency data

* x = a (n x p) matrix of high frequency indicators (without intercept)

* ta = type of disaggregation

  - ta=-1 ---> sum (flow)

  - ta=0 ---> average (index)

  - ta=i ---> i th element (stock) ---> interpolation

* s = number of high frequency data points for each low frequency data points

  - s= 4 ---> annual to quarterly

  - s=12 ---> annual to monthly

  - s= 3 ---> quarterly to monthly

* delta = the increment used for numerical derivation

* typemin = estimation method:

  - typemin='wls' ---> weighted least squares

  - typemin='llike' ---> maximum likelihood

* optfunc = a string, the name of the optimisation function ('optim' or 'optimg')

* sopt_optim = a tlist, collecting the options to the optimisation function

 

Output

* y = High frequency estimate

* res = a results tlist with:

  - res('meth') = 'Litterman'

  - res('typemod') = type of the model for the high frequency innovations

  - res('ta') = type of disaggregation

  - res('nobs_lf') = nobs. of low frequency data

  - res('nobs_hf') = nobs. of high-frequency data

  - res('pred') = number of extrapolations

  - res('s') = frequency conversion between low and high freq.

  - res('p') = number of regressors (including intercept)

  - res('y') = high frequency estimate

  - res('y_lf') = low frequency data

  - res('indicator') = high frequency indicators

  - res('y_dt') = high frequency estimate: standard deviation

  - res('y_up') = high frequency estimate: sd + sigma

  - res('y_lo') = high frequency estimate: sd - sigma

  - res('resid') = high frequency residuals

  - res('resid_lf') = low frequency residuals

  - res('beta') = estimated model parameters

  - res('sd') = standard deviation of the estimated model parameters

  - res('tstat') = estimated model parameters: t ratios

  - res('rho') = innovational parameter

  - res('aic') = Information criterion: AIC

  - res('bic') = Information criterion: BIC

  - res('llike') = Objective function used by the estimation method

  - res('typemin') = method of estimation

  - res('llike') = Log-likelihood at the estimated parameters

  - res('sigma') = Variance at the estimated parameters

DESCRIPTION

Temporal disaggregation using the Litterman method of temporal disaggregation (low level function that works only with matrices or ts and all parameters must be given).

EXAMPLE

load(GROCERDIR+'\data\xesp.dat')
opt=tlist(['optim options';'optim';'optim ineq';'nelmead';'convg'],...
[',''ar'',1e4,1e4'],',''b'',-0.99,0.99',',2*%eps,1000',1e-5)
[y,res] = litterman1(Y,x,-1,4,1e-5,'wls','optimg',opt);
// With Y and x taken from the database GROCERDIR+'\macros\grocer\db\xesp.dat',
// provides quarterly disaggregation of (22 x 1) matrix Y (representing annual Spanih exportations) with (88 x 1) matrix x.
// Annual series are built by summing quarterly series (3rd arg. set to -1);
// the order of aggregation is 4 (4th arg. set to 4);
// the increment used for the numerical derivation is 1e-5 (5th arg. set to 1e-5)
// and the estimation method is weigthed least squares (6th arg. set to 'wls').
// Optimization function is Grocer 'optimg' with parameters entered in tlist opt.

AUTHOR

Eric Dubois 2005

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