📄 prais.hlp
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{smcl}
{* *! version 1.0.0 16may2005}{...}
{cmd:help prais}{right:dialog: {bf:{dialog prais}}{space 15}}
{right:also see: {help prais postestimation}}
{hline}
{title:Title}
{p2colset 5 19 21 2}{...}
{p2col:{hi:[TS] prais} {hline 2}}Prais-Winsten and Cochrane-Orcutt regression{p_end}
{p2colreset}{...}
{title:Syntax}
{p 8 14 2}
{cmd:prais}
{depvar}
[{indepvars}]
{ifin}
[{cmd:,}
{it:options}]
{synoptset 20 tabbed}{...}
{synopthdr}
{synoptline}
{syntab:Model}
{synopt:{cmdab:rho:type:(}{opt reg:ress}{cmd:)}}base rho on single-lag OLS of
residuals; the default{p_end}
{synopt:{cmdab:rho:type:(freg)}}base rho on single-lead OLS of residuals{p_end}
{synopt:{cmdab:rho:type:(}{opt tsc:orr}{cmd:)}}base rho on autocorrelation of
residuals{p_end}
{synopt:{cmdab:rho:type:(dw)}}base rho on autocorrelation based on
Durbin-Watson {p_end}
{synopt:{cmdab:rho:type:(}{opt th:eil}{cmd:)}}base rho on adjusted
autocorrelation{p_end}
{synopt:{cmdab:rho:type:(}{opt nag:ar}{cmd:)}}base rho on adjusted
Durbin-Watson{p_end}
{synopt:{opt corc}}use Cochrane-Orcutt transformation{p_end}
{synopt:{opt sse:search}}search for rho that minimizes SSE{p_end}
{synopt:{opt two:step}}stop after the first iteration{p_end}
{synopt:{opt nocon:stant}}suppress constant term{p_end}
{synopt:{opt h:ascons}}has user-defined constant{p_end}
{synopt:{opt save:space}}conserve memory during estimation{p_end}
{syntab:SE/Robust}
{synopt:{opt r:obust}}compute standard errors using the robust/sandwich
estimator{p_end}
{synopt:{opth cl:uster(varname)}}adjust standard errors for intragroup
correlation{p_end}
{synopt:{opt hc2}}use 1/(1 - h) bias correction for {opt robust}{p_end}
{synopt:{opt hc3}}use 1/(1 - h)^2 bias correction for {opt robust}{p_end}
{syntab:Reporting}
{synopt:{opt l:evel(#)}}set confidence level; default is {cmd:level(95)}{p_end}
{synopt:{opt nodw}}do not report the Durbin-Watson statistic{p_end}
{syntab:Opt options}
{synopt:{it:{help prais##optimize_options:optimize_options}}}control the
optimization process; seldom used{p_end}
{synoptline}
{p2colreset}{...}
{p 4 6 2}
You must {helpb tsset} your data before using {opt prais}.
{p_end}
{p 4 6 2}
{it:depvar} and {it:indepvars} may contain time-series operators; see
{help tsvarlist}.
{p_end}
{p 4 6 2}
{opt by}, {opt rolling}, {opt statsby}, and {opt xi} may be used with
{opt prais}; see {help prefix}.{p_end}
{p 4 6 2}
See {help prais postestimation} for features available after estimation.{p_end}
{title:Description}
{pstd}
{opt prais} uses the generalized least-squares method to estimate the
parameters in a linear regression model in which the errors are serially
correlated. Specifically, the errors are assumed to follow a first-order
autoregressive process.
{title:Options}
{dlgtab:Model}
{phang}
{opt rhotype(rhomethod)} selects a specific computation for
the autocorrelation parameter rho, where {it:rhomethod} can be
{p 12 34 2}{cmdab:reg:ress}{space 2}rho_reg {space 2} = B from the residual
regression e_t = B * e_(t-1){p_end}
{p 12 34 2}{cmd:freg} {space 3} rho_freg {space 1} = B from the residual
regression e_t = B * e_(t+1){p_end}
{p 12 34 2}{cmdab:tsc:orr} {space 1} rho_tscorr = e'e_(t-1)/e'e, where e is the
vector of residuals{p_end}
{p 12 34 2}{cmd:dw} {space 5} rho_dw {space 3} = 1 - dw / 2, where dw is the
Durbin-Watson d statistic{p_end}
{p 12 34 2}{cmdab:th:eil} {space 2} rho_theil{space 2}= rho_tscorr * (N - k) / N{p_end}
{p 12 34 2}{cmdab:nag:ar} {space 2} rho_nagar{space 2}= (rho_dw * N^2 + k^2) / (N^2 - k^2)
{pmore}
The {opt prais} estimator can use any consistent estimate of rho to
transform the equation, and each of these estimates meets that requirement.
The default is {opt regress}, which produces the minimum sum-of-squares
solution ({opt ssesearch} option) for the Cochrane-Orcutt
transformation{hline 2}none of these computations will produce the minimum
sum-of-square solution for the full Prais-Winsten transformation.
{phang}
{opt corc} specifies that the Cochrane-Orcutt transformation be used to
estimate the equation. With this option, the Prais-Winsten transformation
of the first observation is not performed, and the first observation is
dropped when estimating the transformed equation.
{phang}
{opt ssesearch} specifies that a search be performed for the value of
rho that minimizes the sum-of-squared errors of the transformed equation
(Cochrane-Orcutt or Prais-Winsten transformation). The search method is a
combination of quadratic and modified bisection searches using golden
sections.
{phang}
{opt twostep} specifies that {opt prais} stop on the first
iteration after the equation is transformed by rho{hline 2}the two-step
efficient estimator. Although it is customary to iterate these estimators to
convergence, they are efficient at each step.
{phang}
{opt noconstant}; see {help estimation options##noconstant:estimation options}.
{phang}
{opt hascons} indicates that a user-defined constant, or a set of
variables that in linear combination forms a constant, has been included in
the regression. For some computational concerns, see the discussion in
{helpb regress}.
{phang}
{opt savespace} specifies that {opt prais} attempt to save as much
space as possible by retaining only those variables required for
estimation. The original data are restored after estimation. This option
is rarely used and should be used only if there is insufficient space to
fit a model without the option.
{dlgtab:SE/Robust}
{phang}
{opt robust}, {opth cluster(varname)}; see {help estimation options##robust:estimation options} for
details.
{pmore}
Note that all estimates from {opt prais} are conditional on the estimated
value of rho. This means that robust variance estimates in this case are
only robust to heteroskedasticity and are not generally robust to
misspecification of the functional form or omitted variables. The
estimation of the functional form is intertwined with the estimation of
rho, and all estimates are conditional on rho. Thus estimates cannot be
robust to misspecification of functional form. For these reasons, it is
probably best to interpret {opt robust} in the spirit of White's
original paper on estimation of heteroskedastic-consistent covariance
matrices.
{phang}
{opt hc2} and {opt hc3} specify an alternative bias correction for
the {opt robust} variance calculation; for more information, see
{helpb regress}. {opt hc2} and {opt hc3} may not be specified with
{opt cluster()}. Specifying {opt hc2} or {opt hc3} implies {cmd:robust}.
{dlgtab:Reporting}
{phang}
{opt level(#)}; see {help estimation options##level():estimation options}.
{phang}
{opt nodw} suppresses reporting of the Durbin-Watson statistic.
{marker optimize_options}{...}
{dlgtab:Opt options}
{phang}
{it:optimize_options}:
{opt iter:ate(#)},
[{cmdab:no:}]{opt lo:g},
{opt tol:erance(#)}.
{opt iterate()} specifies the maximum number of iterations.
{opt log}/{opt nolog} specifies whether or not to show the iteration log.
{opt tolerance()} specifies the tolerance for the coefficient vector;
{cmd:tolerance(1e-6)} is the default. These options are seldom used.
{title:Examples}
{phang}{cmd:. prais csales isales}{p_end}
{phang}{cmd:. prais}
{phang}{cmd:. prais csales isales, corc}
{phang}{cmd:. prais csales isales, ssesearch}
{phang}{cmd:. prais csales isales, twostep}
{phang}{cmd:. prais csales isales, robust}
{title:Also see}
{psee}Manual: {bf:[TS] prais}
{psee}
Online: {help prais postestimation};{break}
{helpb arima},
{helpb regress},
{help regress postestimation ts},
{helpb tsset}
{p_end}
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