'================================================================================================== '================================================================================================== '================================================================================================== subroutine local fernandez (series y_lf_ser, series y_hf_ser, series x_hf_ser, scalar ta, scalar s) ' --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- ' PURPOSE: Temporal disaggregation using Fernandez method ' --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- ' SYNTAX: series y_hf_ser ' call fernandez (y_lf_ser, y_hf_ser, x_hf_ser, ta, s) ' --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- ' OUTPUT: y_hf_ser high frequency estimate series name ' --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- ' INPUT: y_lf_ser low frequency series name, series must be disaggregated ' equaly on subperiods ' x_hf_ser high frequency related series name ' ta: type of temporal disaggregation ' ta=1 sum (flow) ' ta=2 average (index) ' ta=3 last element (stock) - interpolation ' ta=4 first element (stock) - interpolation ' s: number of high frequency points ' for each low frequency data points (freq. conversion) ' s=4 annual to quarterly ' s=12 annual to monthly ' s=3 quarterly to monthly ' --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- ' LIBRARY: d:\Eviews_library\agg_help.prg: AGG() ' --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- ' writen by: ' Slawomir Dudek ' MOF ' --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- ' REFERENCE: 1) Quilis, E.M (2002) "A MATLAB library of temporal disaggregation methods: summary" ' Instituto Nacional de Estadistica, Spain ' 2) Fernandez, R.B. (1981) "Methodological note on the estimation of time series" ' Review of Economic and Statistic, vol. 63, n. 3, p. 471-478. ' --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- ' Asiggning series to vectors, only not NA observations ' Determination of forward extrapolation period: !n_up ' Determination of backward extrapolation period: !n_dn smpl @all series t=@trend+1 sample NA_smpl_y @all if y_lf_ser <> NA sample NA_smpl_x @all if x_hf_ser <> NA smpl NA_smpl_x !obs_f_x=@min(t) !obs_l_x=@max(t) smpl NA_smpl_y !obs_f_y=@min(t) !obs_l_y=@max(t) !n_up=!obs_l_x-!obs_l_y !n_dn=!obs_f_y-!obs_f_x ' --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- ' Control checking wether related series cover aggregate sample if (!n_up<0 OR !n_dn<0) then statusline ERROR!!! Fernandez subroutine() !!!*** Related series do not cover aggregate sample ***!!! stop else ' --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- ' Assigning series to matrix objects, only for NA observations stomna(y_lf_ser, y_lf_temp, NA_smpl_y) stomna(x_hf_ser, x_hf_temp, NA_smpl_x) ' --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- ' Size of the problem !n_hf=@rows(y_lf_temp) !n_lf=!n_hf/s ' Size of low frequency input !n_hf_x=@rows(x_hf_temp) ' Size of high frequency input (number of observations) !p_hf_x_temp=@columns(x_hf_temp) ' Size of high frequency input (number of variables without intercept) !p_hf_x=!p_hf_x_temp+1 ' Size of high frequency input (number of variables with intercept) ' --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- ' Aggregation of low frequency series equaly distributed in subperiods matrix AGG1 call aggreg (AGG1, 1, !n_lf, s, 0, 0) matrix y_lf=AGG1*y_lf_temp delete AGG1 ' --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- ' Generation of aggregation matrix AGG [!n_lf x !n_lf*s] for aggregation in procedure matrix AGG call aggreg (AGG, ta, !n_lf, s, !n_up, !n_dn) ' --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- ' Preparing the X matrix: including intercept matrix(!n_hf_x, !p_hf_x) x_hf=1 matplace(x_hf, x_hf_temp , 1, 1) ' --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- ' Temporal aggreagation of the indicator matrix x_lf=AGG*x_hf ' --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- ' Estimation matrix I=@identity(!n_hf_x) matrix w=I matrix(!n_hf_x, !n_hf_x) LL=0 for !i=2 to !n_hf_x LL(!i, !i-1)=-1 'Auxiliary matrix useful to simplify computations next matrix AUX=(I+LL) matrix w=@inverse(@transpose(AUX)*AUX) ' High frequency VCV matrix (without sigma_a) matrix WW=AGG*w*@transpose(AGG) ' Low frequency VCV matrix (without sigma_a) matrix Wi=@inverse(WW) matrix beta=@inverse(@transpose(x_lf)*Wi*x_lf)*@transpose(x_lf)*Wi*y_lf ' beta ML estimator matrix u_lf=y_lf-x_lf*beta ' Low frequency residuals matrix scp=@transpose(u_lf)*Wi*u_lf ' Weighted least squere matrix sigma_a=scp*(1/(!n_lf-!p_hf_x)) ' sigma_a ML estimator matrix FM=w*@transpose(AGG)*Wi ' Filtering matrix matrix u_hf=FM*u_lf ' High frequency residuals ' --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- ' Temporaly disaggregated time series matrix y_hf=x_hf*beta+u_hf ' --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- ' Information criteria ' Note: (!p_hf_x+1) is expanded to include the innovational parameter scalar aic=@log(sigma_a(1,1))+2*(!p_hf_x+1)/!n_lf scalar bic=@log(sigma_a(1,1))+@log(!n_lf)*(!p_hf_x+1)/!n_lf ' --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- ' Computation of VCV matrix of high frequency estimates matrix sigma_beta=sigma_a(1,1)*@inverse(@transpose(x_lf)*Wi*x_lf) matrix VCV_y=sigma_a(1,1)*(@identity(!n_hf_x)-FM*AGG)*w+(x_hf-FM*x_lf)*sigma_beta*@transpose(x_hf-FM*x_lf) matrix d_y = @sqrt(@getmaindiagonal(VCV_y)) ' Std. dev. of high frequency estimate matrix y_li=y_hf-d_y ' Lower lim. of high frequency estimate matrix y_ls=y_hf+d_y ' Upper lim. of high frequency estimate ' --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- ' Assigning vector to series mtos(y_hf, y_hf_ser, NA_smpl_x) endif smpl @all endsub 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