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nrnd—569

nrnd

Series Expression

 

 

Normal random number generator.

When used in a series expression, nrnd generates (pseudo) random draws from a normal distribution with zero mean and unit variance.

Examples

smpl @first @first

series y = 0

smpl @first+1 @last

series y = .6*y(-1)+.5*nrnd

generates a Y series that follows an AR(1) process with initial value zero. The innovations are normally distributed with mean zero and standard deviation 0.5.

series u = 10+@sqr(3)*nrnd

series z = u+.5*u(-1)

generates a Z series that follows an MA(1) process. The innovations are normally distributed with mean 10 and variance 3.

series x = nrnd^2+nrnd^2+nrnd^2

generates an X series as the sum of squares of three independent standard normal random variables, which has a χ2(3) distribution. Note that adding the sum of the three series is not the same as issuing the command:

series x=3*nrnd^2

since the latter involves the generation of a single random variable.

The command:

series x=@qchisq(rnd,3)

provides an alternative method of simulating random draws from a χ2(3 ) distribution.

Cross-references

See “Statistical Distribution Functions” on page 584 for a list of other random number generating functions from various distributions.

See also rnd (p. 571), rndint (p. 425) and rndseed (p. 425).

570—Appendix C. Special Expression Reference

pdl

Equation Expression

 

 

Polynomial distributed lag specification.

This expression allows you to estimate polynomial distributed lag specifications in ls or tsls estimation. pdl forces the coefficients of a distributed lag to lie on a polynomial. The expression can only be used in estimation by list.

Syntax

Expression: pdl(series_name, lags, order[,options])

Options

The PDL specification must be provided in parentheses after the keyword pdl in the following order: the name of the series to which to fit a polynomial lag, the number of lags to include, the order (degree) of polynomial to fit, and an option number to constrain the PDL. By default, EViews does not constrain the endpoints of the PDL.

The constraint options are:

1Constrain the near end of the distribution to zero.

2Constrain the far end of the distribution to zero.

3Constrain both the near and far end of the distribution to zero.

Examples

ls sale c pdl(order,8,3) ar(1) ar(2)

fits a third degree polynomial to the coefficients of eight lags of the regressor ORDER.

tsls sale c pdl(order,12,3,2) @ c pdl(rain,12,6)

fits a third degree polynomial to the coefficients of twelve lags of ORDER, constraining the far end to be zero. Estimation is by two-stage least squares, using a constant and a sixth degree polynomial fit to twelve lags of RAIN.

tsls y c x1 x2 pdl(z,12,3,2) @ c pdl(*) z2 z3 z4

When the PDL variable is exogenous in 2SLS, you may use “pdl(*)” in the instrument list instead of repeating the full PDL specification.

sar—571

Cross-references

See “Polynomial Distributed Lags (PDLs)” on page 459 of the User’s Guide for further discussion.

rnd

Series Expression

 

 

Uniform random number generator.

Generates (pseudo) random draws from a uniform distribution on (0,1). The expression may be included in a series expression or in an equation to be used in solve.

Examples

series u=5+(12-5)*rnd

generates a U series drawn from a uniform distribution on (5, 12).

Cross-references

See the list of available random number generators in Appendix D, “Operator and Function Reference”, beginning on page 573.

See also nrnd (p. 569), rndint (p. 425) and rndseed (p. 425).

sar

Equation Expression

 

 

Seasonal autoregressive error specification.

sar can be included in ls or tsls specification to specify a multiplicative seasonal autoregressive term. A sar(p) term can be included in your equation specification to represent a seasonal autoregressive term with lag p . The lag polynomial used in estimation is the product of that specified by the ar terms and that specified by the sar terms. The purpose of the sar expression is to allow you to form the product of lag polynomials.

Examples

ls tb3 c ar(1) ar(2) sar(4)

TB3 is modeled as a second order autoregressive process with a multiplicative seasonal autoregressive term at lag four.

tsls sale c adv ar(1) sar(12) sar(24) @ c gdp

In this two-stage least squares specification, the error term is a first order autoregressive process with multiplicative seasonal autoregressive terms at lags 12 and 24.

572—Appendix C. Special Expression Reference

Cross-references

See “ARIMA Theory” beginning on page 499 of the User’s Guide for details on ARMA and seasonal ARMA modeling.

See also sma (p. 572), ar (p. 565), and ma (p. 567).

sma

Equation Expression

 

 

Seasonal moving average error specification.

sma can be included in a ls or tsls specification to specify a multiplicative seasonal moving average term. A sma(p) term can be included in your equation specification to represent a seasonal moving average term of order p . The lag polynomial used in estimation is the product of that specified by the ma terms and that specified by the sma terms. The purpose of the sma expression is to allow you to form the product of lag polynomials.

Examples

ls tb3 c ma(1) ma(2) sma(4)

TB3 is modeled as a second order moving average process with a multiplicative seasonal moving average term at lag four.

tsls(z) sale c adv ma(1) sma(12) sma(24) @ c gdp

In this two-stage least squares specification, the error term is a first order moving average process with multiplicative seasonal moving average terms at lags 12 and 24. The “z” option turns off backcasting.

Cross-references

See “ARIMA Theory” beginning on page 499 of the User’s Guide for details on ARMA and seasonal ARMA modeling.

See also sar (p. 571), ar (p. 565), and ma (p. 567).

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