Stata 15 help for arch_postestimation

[TS] arch postestimation -- Postestimation tools for arch

Postestimation commands

The following postestimation commands are available after arch:

Command Description ------------------------------------------------------------------------- estat ic Akaike's and Schwarz's Bayesian information criteria (AIC and BIC) estat summarize summary statistics for the estimation sample estat vce variance-covariance matrix of the estimators (VCE) estimates cataloging estimation results forecast dynamic forecasts and simulations lincom point estimates, standard errors, testing, and inference for linear combinations of coefficients lrtest likelihood-ratio test margins marginal means, predictive margins, marginal effects, and average marginal effects marginsplot graph the results from margins (profile plots, interaction plots, etc.) nlcom point estimates, standard errors, testing, and inference for nonlinear combinations of coefficients predict predictions, residuals, influence statistics, and other diagnostic measures predictnl point estimates, standard errors, testing, and inference for generalized predictions test Wald tests of simple and composite linear hypotheses testnl Wald tests of nonlinear hypotheses -------------------------------------------------------------------------

Syntax for predict

predict [type] newvar [if] [in] [, statistic options]

statistic Description ------------------------------------------------------------------------- Main xb predicted values for mean equation -- the differenced series; the default y predicted values for the mean equation in y -- the undifferenced series variance predicted values for the conditional variance het predicted values of the variance, considering only the multiplicative heteroskedasticity residuals residuals or predicted innovations yresiduals residuals or predicted innovations in y -- the undifferenced series ------------------------------------------------------------------------- These statistics are available both in and out of sample; type predict ... if e(sample) ... if wanted only for the estimation sample.

options Description ------------------------------------------------------------------------- Options dynamic(time_constant) how to handle the lags of y_t at(varname_e|#e varname_s2|#s2) make static predictions t0(time_constant) set starting point for the recursions to time_constant structural calculate considering the structural component only ------------------------------------------------------------------------- time_constant is a # or a time literal, such as td(1jan1995) or tq(1995q1), etc.; see Conveniently typing SIF values in [D] datetime.

Menu for predict

Statistics > Postestimation

Description for predict

predict creates a new variable containing predictions such as expected values and residuals. All predictions are available as static one-step-ahead predictions or as dynamic multistep predictions, and you can control when dynamic predictions begin.

Options for predict

+------+ ----+ Main +-------------------------------------------------------------

xb, the default, calculates the predictions from the mean equation. If D.depvar is the dependent variable, these predictions are of D.depvar and not of depvar itself.

y specifies that predictions of depvar are to be made even if the model was specified for, say, D.depvar.

variance calculates predictions of the conditional variance.

het calculates predictions of the multiplicative heteroskedasticity component of variance.

residuals calculates the residuals. If no other options are specified, these are the predicted innovations; that is, they include any ARMA component. If the structural option is specified, these are the residuals from the mean equation, ignoring any ARMA terms; see structural below. The residuals are always from the estimated equation, which may have a differenced dependent variable; if depvar is differenced, they are not the residuals of the undifferenced depvar.

yresiduals calculates the residuals for depvar, even if the model was specified for, say, D.depvar. As with residuals, the yresiduals are computed from the model, including any ARMA component. If the structural option is specified, any ARMA component is ignored and yresiduals are the residuals from the structural equation; see structural below.

+---------+ ----+ Options +----------------------------------------------------------

dynamic(time_constant) specifies how lags of y_t in the model are to be handled. If dynamic() is not specified, actual values are used everywhere lagged values of y_t appear in the model to produce one-step-ahead forecasts.

dynamic(time_constant) produces dynamic (also known as recursive) forecasts. time_constant specifies when the forecast is to switch from one step ahead to dynamic. In dynamic forecasts, references to y_t evaluate to the prediction of y_t for all periods at or after time_constant; they evaluate to the actual value of y_t for all prior periods.

dynamic(10), for example, would calculate predictions where any reference to y_t with t < 10 evaluates to the actual value of y_t and any reference to y_t with t > 10 evaluates to the prediction of y_t. This means that one-step-ahead predictions would be calculated for t < 10 and dynamic predictions would be calculated thereafter. Depending on the lag structure of the model, the dynamic predictions might still refer to some actual values of y_t.

You may also specify dynamic(.) to have predict automatically switch from one-step-ahead to dynamic predictions at p + q, where p is the maximum AR lag and q is the maximum MA lag.

at(varname_e|#e varname_s2|#s2) makes static predictions. at() and dynamic() may not be specified together.

Specifying at() allows static evaluation of results for a given set of disturbances. This is useful, for instance, in generating the news response function. at() specifies two sets of values to be used for e_t and s_t^2, the dynamic components in the model. These specifies values are treated as given. Also, any lagged values of depvar in the model are obtained from the real values of the dependent variable. All computations are based on actual data and the given values.

at() requires that you specify two arguments, which can either be a variable name or a number. The first argument supplies the values to be used for e_t; the second supplies the values to be used for s_t^2. If s_t^2 plays no role in your model, the second argument may be specified as '.' to indicate missing.

t0(time_constant) specifies the starting point for the recursions to compute the predicted statistics; disturbances are assumed to be 0 for t < t0(). The default is to set t0() to the minimum t observed in the estimation sample, meaning that observations before that are assumed to have disturbances of 0.

t0() is irrelevant if structural is specified because then all observations are assumed to have disturbances of 0.

t0(5), for example, would begin recursions at t = 5. If your data were quarterly, you might instead type t0(tq(1961q2)) to obtain the same result.

Any ARMA component in the mean equation or GARCH term in the conditional-variance equation makes arch recursive and dependent on the starting point of the predictions. This includes one-step-ahead predictions.

structural makes the calculation considering the structural component only, ignoring any ARMA terms, and producing the steady-state equilibrium predictions.

Syntax for margins

margins [marginlist] [, options]

margins [marginlist] , predict(statistic ...) [predict(statistic ...) ...] [options]

statistic Description ------------------------------------------------------------------------- xb predicted values for mean equation -- the differenced series; the default y predicted values for the mean equation in y -- the undifferenced series variance predicted values for the conditional variance het predicted values of the variance, considering only the multiplicative heteroskedasticity residuals not allowed with margins yresiduals not allowed with margins -------------------------------------------------------------------------

Statistics not allowed with margins are functions of stochastic quantities other than e(b).

For the full syntax, see [R] margins.

Menu for margins

Statistics > Postestimation

Description for margins

margins estimates margins of response for expected values.

Examples

--------------------------------------------------------------------------- Setup . webuse wpi1

Fit EGARCH model . arch D.ln_wpi, ar(1) ma(1,4) earch(1) egarch(1)

Create variable that ranges from about -4 to 4 . generate et = (_n-64)/15

Static prediction of the conditional variance assuming lagged variance is one for values of e_t ranging from -4 to 4 . predict sigma2, variance at(et 1)

---------------------------------------------------------------------------

Setup . webuse wpi1, clear

Impose declining lag structure . constraint 1 (3/4)*[ARCH]l1.arch = [ARCH]l2.arch . constraint 2 (2/4)*[ARCH]l1.arch = [ARCH]l3.arch . constraint 3 (1/4)*[ARCH]l1.arch = [ARCH]l4.arch

Fit ARCH model with constraints . arch D.ln_wpi, ar(1) ma(1 4) arch(1/4) constraints(1 2 3)

Estimate alpha parameter of the model for the conditional variance . lincom [ARCH]l1.arch/.4

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