SAS/ETS 9.22 User''''s Guide 311 pps

step function,785interrupted time series analysis, see intervention model interrupted time series model, see intervention model interval functions, see time intervals, functions interval

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step function,785

interrupted time series analysis, see intervention

model

interrupted time series model, see intervention

model

interval functions, see time intervals, functions

interval functions and

calendar calculations,103

INTERVAL= option and

time intervals,84

intervals, see time intervals,2623

intervention analysis, see intervention model

intervention model

ARIMA procedure,216,219,222,301

interrupted time series analysis,220

interrupted time series model,216

intervention analysis,220

intervention model and

impulse function,220

step function,220

intervention notation,2914

intervention specification,2823,2825

interventions,2913

automatic inclusion of,2810

forecasting models,2755

point,2913

predictor variables,2913

ramp,2914

specifying,2755

step,2913

INTNX function

calendar calculations and,103

checking data periodicity,102

computing ceiling of intervals,101

computing ending date of intervals,100

computing midpoint date of intervals,100

computing widths of intervals,100

defined,97

incrementing dates,98

normalizing dates in intervals,100

INTNX function and

date values,98

time intervals,97

introduced

DIF function,104

LAG function,104

percent change calculations,109

time variables,94

inverse autocorrelation function

ARIMA procedure,243

invertibility

ARIMA procedure,259

VARMAX procedure,2141

Investment Analysis System,47

Investment Portfolio,2988 invoking the system,2612 IRoR,3050

irregular component X11 procedure,2228,2234 iterated generalized method of moments,1065 iterated seemingly unrelated regression SYSLIN procedure,1797 iterated three-stage least squares SYSLIN procedure,1797 Iterative Outlier Detection ARIMA procedure,310 Jacobi method

MODEL procedure,1190 Jacobi method with General Form Equations MODEL procedure,1191

Jacobian,1058,1077 Jarque-Bera test,354 normality tests,354 JMP,57

JOIN method EXPAND procedure,784 joint generalized least squares, see seemingly

unrelated regression jointly dependent variables SYSLIN procedure,1764 K-class estimation

SYSLIN procedure,1796 Kalman filter

AUTOREG procedure,373 STATESPACE procedure,1718 used for state space modeling,1718 KEEP in the DATA step

SASEFAME engine,2517 kernels,1062,1697

SPECTRA procedure,1697 Kolmogorov-Smirnov test,1098 normality tests,1098 KPSS (Kwiatkowski, Phillips, Schmidt, Shin) test,

357 KPSS test,357,393 unit roots,393 Kruskal-Wallis test,2270 labeling variables DATASOURCE procedure,590 LAG function

alternatives to,107 explained,105 introduced,104 MODEL procedure version,107 multiperiod lags and,108 percent change calculations and,109,110

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pitfalls of,106

LAG function and

Lags,105

lags,104,106

lag functions

functions,1209

MODEL procedure,1209

lag lengths

lag logic

lagged dependent variables

and tests for autocorrelation,331

AUTOREG procedure,331

lagged endogenous variables

SYSLIN procedure,1764

lagging

time series data,104–110

Lagrange multiplier test

heteroscedasticity,364

heteroscedasticity tests,364

linear hypotheses,694

nonlinear hypotheses,962,1056,1128,1458

Lags

LAG function and,105

lags

LAG function and,104,106

MODEL procedure and,107

multiperiod lagging,108

percent change calculations and,109,110

RETAIN statement and,107

SIMLIN procedure,1670

lambda,1078

language differences

large problems

leads

calculation of,111

multiperiod,111

time series data,111

Lee and King’s test,403

Lee and King’s test for

Heteroscedasticity,403

left-hand side expressions

nonlinear models,1201

lengths of variables

DATASOURCE procedure,578,590

level shifts

forecasting models,2760

specifying,2760

levels

contrasted with flows or rates,768

levels, of classification variable,531

LIBNAMElibref SASEHAVR ‘physical name’ on

Windows SASEFAME engine,2512 LIBNAMElibref SASEHAVR ‘physical name’on

UNIX SASEFAME engine,2512 LIBNAME interface engine for Fame database,

seeSASEFAME engine LIBNAME interface engine for Haver database,

seeSASEHAVR engine LIBNAME statement

SASECRSP engine,2398 SASEFAME engine,2500 SASEHAVR engine,2556 likelihood confidence intervals,1132 MODEL procedure,1132 Likelihood ratio test

nonlinear hypotheses,962 likelihood ratio test

linear hypotheses,694 nonlinear hypotheses,1056,1128 limitations on

ordinary differential equations (ODEs),1197 limitations on ordinary differential equations MODEL procedure,1197

Limited Dependent Variable Models QLIM procedure,1446 limited information maximum likelihood LIML estimation method,1762 SYSLIN procedure,1796 LIML estimation method, see limited information

maximum likelihood linear

trend curves,2912 linear dependencies MODEL procedure,1091 linear exponential smoothing,2902 Holt smoothing model,2902 smoothing models,2902 linear hypotheses

Lagrange multiplier test,694 likelihood ratio test,694 Wald test,694

linear hypothesis testing,1360 PANEL procedure,1360 linear models

equality restriction,692 inequality restriction,692 restricted estimation,692 linear structural equations SIMLIN procedure,1667 linear trend,2742,2912 forecasting models,2742 linearized form

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Durbin-Watson tests,361

link function

heteroscedasticity models,363

Listing the Haver selection keys,

OUTSELECT=ON

SASEHAVR engine,2557

Loan,2993

LOAN procedure

adjustable rate mortgage,871,872

amortization schedule,900

balloon payment mortgage,871,872

break even analysis,896

buydown rate loans,871,872

comparing loans,879,896,900

continuous compounding,894

fixed rate mortgage,871,872

installment loans,871

interest rates,894

internal rate of return,896

loan repayment schedule,900

loan summary table,900

loans analysis,871

minimum attractive rate of return,896

mortgage loans,871

output data sets,897,898

output table names,900

present worth of cost,896

rate adjustment cases,890

taxes,896

true interest rate,896

types of loans,872

loan repayment schedule

LOAN procedure,900

loan summary table

LOAN procedure,900

loans analysis, see LOAN procedure

log

transformations,2895

log likelihood value,354

log test,2916

log transformation, see transformations

log transformations

ARIMA procedure,262

LOGTEST macro,160

logarithmic

trend curves,2913

logarithmic trend,2913

logistic

transformations,2895

trend curves,2912

logistic trend,2912

logit

QLIM Procedure,1422

LOGTEST macro

log transformations,160 output data sets,161 SAS macros,160 long-run relations testing VARMAX procedure,2163

%MA and %AR macros combined,1149

MA Initial Conditions conditional least squares,1142 maximum likelihood,1142 unconditional least squares,1142 macros, see SAS macros

MAE AUTOREG procedure,382 main economic indicators (OECD) data files, see

DATASOURCE procedure main economic indicators (OECD) data files in

FAME.db, see SASEFAME engine managing

forecasting project,2827 managing forecasting projects,2827 MAPE

AUTOREG procedure,382 Mardia’s test,1098

normality tests,1098 Marquardt method ARIMA procedure,253 Marquardt-Levenberg method,1078 MARR, see minimum attractive rate of return,

3071 mathematical functions,51 functions,1208 matrix language SAS/IML software,54 maximizing likelihood functions,56 maximum likelihood

AR initial conditions,1141

MA Initial Conditions,1142 maximum likelihood method AUTOREG procedure,375 MDC procedure

binary data modeling example,965 binary logit example,965,968 binary probit example,965 bounds on parameter estimates,935

BY groups,936 conditional logit example,968 conditional logit model,914,915,950 goodness-of-fit measures,961 Hausman’s specification and likelihood ratio tests for nested logit,965

heteroscedastic extreme value model,925, 952

ID groups,936

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introductory examples,915

mixed logit model,930,953

multinomial discrete choice,949

multinomial probit example,971

multinomial probit model,924,955

nested logit example,978

nested logit model,920,956

restrictions on parameter estimates,946

syntax,932

Tests on Parameters,962

mean absolute error

statistics of fit,2917

mean absolute percent error

statistics of fit,2012,2917

mean percent error

mean prediction error

mean square error

mean squared error

MEANS procedure,49

measurement equation

observation equation,1717

of a state space model,1717

MELO estimation method, see minimum expected

loss estimator

memory requirements

menu interfaces

to SAS/ETS software,46,47

merging series

time series data,117

merging time series data sets,117

Michaelis-Menten Equations,1124

midpoint dates of

time intervals,100

MINIC (Minimum Information Criterion) method,

246

minimization methods

minimization summary

minimum attractive rate of return

LOAN procedure,896

MARR,896

minimum expected loss estimator

MELO estimation method,1796

minimum information criteria method

Minimum Information Criterion (MINIC) method,

246 missing observations contrasted with omitted observations,78 missing values,792,1156

COMPUTAB procedure,491 contrasted with omitted observations,78 embedded in time series,78

ENTROPY procedure,706 FORECAST procedure,839 interpolation of,122 MODEL procedure,1075,1192 smoothing models,2898 time series data,767 time series data and,77 VARMAX procedure,2104 missing values and

time series data,77,78 MISSONLY operator,793 mixed logit model MDC procedure,930,953 Mixture of Distributions example,1273 MMAE,2896 MMSE,2896 model evaluation,2890 Model Identification ARIMA procedure,303 model list,2653,2834 MODEL procedure adjacency graph,1227 adjusted R squared,1077 Almon lag polynomials,1152 analyzing models,1222 ARMA model,1138 autoregressive models,1138 auxiliary equations,1124 block structure,1227 character variables,1204 Chow tests,1131 collinearity diagnostics,1082,1091 compiler listing,1220

control variables,1202 controlling starting values,1084 convergence criteria,1078 cross-equation covariance matrix,1076 cross-reference,1219

dependency list,1223 derivatives,1207 diagnostics and debugging,1217 Durbin-Watson,1075

dynamic simulation,1118,1167 Empirical Distribution Estimation,1073 equation translations,1204

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equation variables,1201

estimation convergence problems,1088

estimation methods,1057

estimation of ordinary differential equations,

1120

forecasting,1169

full information maximum likelihood,1069

functions across time,1209

Gaussian distribution,1030

goal seeking,1187

grid search,1086

Hausman specification test,1129

initializing lags,1212

input data sets,1154

internal variables,1203

Jacobi method,1190

Jacobi method with General Form Equations,

1191

lag functions,1209

lag lengths,1211

lag logic,1210

language differences,1213

large problems,1095

likelihood confidence intervals,1132

limitations on ordinary differential equations,

1197

linear dependencies,1091

memory requirements,1096

minimization methods,1077

minimization summary,1080

missing values,1075,1192

model variables,1201

Monte Carlo simulation,1266

Moore-Penrose generalized inverse,1035

moving average models,1138

Multivariate t-Distribution Estimation,1072

n-period-ahead forecasting,1167

nested iterations,1077

Newton’s Method,1190

nonadditive errors,1109

normal distribution,1030

ODS graph names,1165

ordinary differential equations and goal

seeking,1125

output data sets,1160

parameters,1202

polynomial distributed lag models,1152

program listing,1218

program variables,1204

properties of the estimates,1075

quasi-random number generators,1179

R squared,1077,1084

random-number generating functions,1208

restrictions on parameters,1148

S matrix,1076 S-iterated methods,1077 Seidel method,1191 Seidel method with General Form Equations, 1191

SIMNLIN procedure,995 simulated nonlinear least squares,1069 simulation,1169

solution mode output,1181 solution modes,1166,1189 SOLVE Data Sets,1198 starting values,1081,1088 static simulation,1118 static simulations,1167 stochastic simulation,1170 storing programs,1216 summary statistics,1184 SYSNLIN procedure,995 systems of ordinary differential equations, 1263

tests on parameters,1128 time variable,1124 troubleshooting estimation convergence problems,1080

troubleshooting simulation problems,1192 using models to forecast,1169

using solution modes,1166 variables in model program,1200 _WEIGHT_ variable,1102 MODEL procedure and

differencing,107 lags,107 MODEL procedure version DIF function,107 LAG function,107 model selection,2849 model selection criterion,2730,2838 model selection for X-11-ARIMA method X11 procedure,2262

model selection list,2839 model variables

MODEL procedure,1201 Model Viewer,2655,2843 graphs,2647

plots,2647 saving graphs and tables,2857,2859 Monte Carlo simulation,1170,1266 examples,1266

MODEL procedure,1266 Moore-Penrose generalized inverse,1035 mortgage loans, see LOAN procedure moving average function,1209 moving average models,1139

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moving averages

percent change calculations,110

moving between computer systems

SAS data sets,49

moving product and geometric mean operators,

797

moving rank operator,796

moving seasonality test,2270

moving t-value operators,800

moving time window operators,789

moving-average parameters

ARIMA procedure,259

multinomial discrete choice

independence from irrelevant alternatives,

951

MDC procedure,949

multinomial probit model

MDC procedure,924,955

multiperiod

leads,111

multiperiod differences

differencing,108

multiperiod lagging

lags,108

multiperiod lags and

DIF function,108

LAG function,108

summation,112,113

multiple selections,2626

multiplicative model

ARIMA model,216

multiplicative seasonal smoothing,2905

smoothing models,2905

multipliers

SIMLIN procedure,1663,1664,1667,1668,

1671,1672

multipliers for higher order lags

SIMLIN procedure,1668,1682

multivariate

autocorrelations,1721

normality tests,1098

partial autocorrelations,1740

multivariate forecasting

STATESPACE procedure,1716

multivariate GARCH Modeling

Multivariate Mixture of Distributions

example,1273

multivariate model diagnostic checks

Multivariate t-Distribution Estimation

multivariate time series

STATESPACE procedure,1716 n-period-ahead forecasting

MODEL procedure,1167 naming

time intervals,84,128 naming model parameters ARIMA procedure,259 national accounts data files (OECD), see

DATASOURCE procedure national accounts data files (OECD) in FAME.db,

seeSASEFAME engine national income and product accounts, see

DATASOURCE procedure DATASOURCE procedure,634 negative log likelihood function,1070 negative log-likelihood function,1072 Nerlove

variance components,1342 nested iterations

MODEL procedure,1077 nested logit model

MDC procedure,920,956 Newton’s Method

MODEL procedure,1190 Newton-Raphson

optimization methods,524,941 Newton-Raphson method,524,941 NIPA Tables

DATASOURCE procedure,634 NLO Overview

NLO system,169 NLO system

NLO Overview,169 Options,169 output table names,187 remote monitoring,185 nominal variables, see also classification variables NOMISS operator,793

nonadditive errors MODEL procedure,1109 nonlinear hypotheses

Lagrange multiplier test,962,1056,1128, 1458

Likelihood ratio test,962 likelihood ratio test,1056,1128 Wald test,962,1056,1128,1458 nonlinear least-squares

AUTOREG procedure,375 nonlinear models

equality restriction,1049,1126 functions of parameters,1031 inequality restriction,1024,1049,1126 left-hand side expressions,1201

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restricted estimation,1024,1049,1126

test of hypotheses,1055

nonmissing observations

nonseasonal ARIMA model

notation,2908

nonseasonal transfer function

notation,2910

nonstationarity, see stationarity

normal distribution

normality tests,1098

Henze-Zirkler test,1098

Jarque-Bera test,354

Kolmogorov-Smirnov test,1098

Mardia’s test,1098

multivariate,1098

Shapiro-Wilk test,1098

normalizing dates in intervals

INTNX function,100

normalizing to intervals

date values,100

notation

nonseasonal ARIMA model,2908

nonseasonal transfer function,2910

seasonal ARIMA model,2909

seasonal transfer function,2911

notation for

ARIMA model,210

ARMA model,210

number of observations

number to use

instrumental variables,1135

numerator factors

transfer function model,221

OBJECT convergence measure,1078

objective function,1057

observation equation, see measurement equation

observation numbers,2873

as time ID,2671

time ID variable,2671

obtaining descriptive information

DATASOURCE procedure,569,573–575,

594–597

ODS graph names

ARIMA procedure,279

ENTROPY procedure,710

ESM procedure,749

EXPAND procedure,803

SEVERITY procedure,1561

SIMILARITY procedure,1631 SYSLIN procedure,1808 TIMESERIES procedure,1899 UCM procedure,2006

VARMAX procedure,2191 ODS Graphics

ARIMA procedure,228 UCM procedure,1946 X12 procedure,2308 OECD ANA data files DATASOURCE procedure,654 OECD annual national accounts DATASOURCE procedure,654 OECD data files, see DATASOURCE procedure OECD data files in FAME.db, see SASEFAME

engine OECD main economic indicators DATASOURCE procedure,656 OECD MEI data files

DATASOURCE procedure,656 OECD QNA data files

DATASOURCE procedure,655 OECD quarterly national accounts DATASOURCE procedure,655

of a state space model impulse response matrix,1748 innovation vector,1717 input matrix,1717 measurement equation,1717 state transition equation,1717 state vector,1716

transition equation,1717 transition matrix,1717

of a time series unit root,158

of interleaved time series overlay plots,89

of missing values interpolation,122,767

of time series distribution,768 overlay plots,88 sampling frequency,71,84,122 simulation,2788,2882

stationarity,213 summation,112 time ranges,77

of time series data set standard form,76 time series cross-sectional form,79

of time series observations frequency,84,122 periodicity,71,84,122 omitted observations

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contrasted with missing values,78

defined,78

replacing with missing values,102

omitted observations in

time series data,78

one-way

fixed effects model,1332

random effects model,1339

one-way fixed effects model

PANEL procedure,1332

one-way fixed-effects model,1332

one-way random effects model

one-way random-effects model,1339

operations research

SAS/OR software,55

optimization methods

Newton-Raphson,524,941

quasi-Newton,362,524,941

trust region,362,524,941

optimizations

smoothing weights,2899

Options

NLO system,169

options

automatic model selection,2796

order of calculations

COMPUTAB procedure,485

order statistics, see RANK procedure

Ordinal Discrete Choice Modeling

QLIM procedure,1443

ordinary differential equations (ODEs)

and goal seeking,1125

differential algebraic equations,1197

example,1263

explosive differential equations,1197

limitations on,1197

systems of,1263

ordinary differential equations and goal seeking

Organization for Economic Cooperation and

Development data files, see

DATASOURCE procedure

DATASOURCE procedure,654

Organization for Economic Cooperation and

Development data files in FAME.db, see

SASEFAME engine

orthogonal polynomials

PDLREG procedure,1396

OUT= data set

indexing,593

OUTALL= data set

DATASOURCE procedure,574

OUTBY= data set

DATASOURCE procedure,573 OUTCONT= data set

DATASOURCE procedure,569,575 Outlier Detection

ARIMA procedure,308 Output Data Sets

VARMAX procedure,2178 output data sets

and the OUTPUT statement,83 ARIMA procedure,265,267,270,272 AUTOREG procedure,410

BOXCOXAR macro,155 COMPUTAB procedure,491 DATASOURCE procedure,567,592,

594–597 DFTEST macro,159 different forms of,82 ENTROPY procedure,708 EXPAND procedure,801 FORECAST procedure,850,852

in standard form,83 interleaved form,82 LOAN procedure,897,898 LOGTEST macro,161 MODEL procedure,1160 PANEL procedure,1368,1370 PDLREG procedure,1409 produced by SAS/ETS procedures,82 SIMLIN procedure,1670,1671 SPECTRA procedure,1700 STATESPACE procedure,1749,1750 SYSLIN procedure,1803,1804 X11 procedure,2265,2266 Output Delivery System (ODS),2846,2886 OUTPUT statement

SAS/ETS procedures using,83 output table names

ARIMA procedure,275 AUTOREG procedure,413 COUNTREG procedure,547 ENTROPY procedure,709 LOAN procedure,900 MDC procedure,964 MODEL procedure,1163 NLO system,187 PANEL procedure,1371 PDLREG procedure,1410 QLIM procedure,1465 SIMLIN procedure,1673 SPECTRA procedure,1702 STATESPACE procedure,1752 SYSLIN procedure,1807 TSCSREG procedure,1930 X11 procedure,2279

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over identification restrictions

overlay plot of

time series data,88

overlay plots

of interleaved time series,89

of time series,88

_TYPE_ variable and,90

p-values for

Durbin-Watson test,329

panel data

TSCSREG procedure,1919

Panel GMM,1352

GMM in Panel: Arellano and Bond’s

Estimator,1352

PANEL procedure

Between Estimators,1339

BY groups,1320

Da Silva method,1350

generalized least squares,1348

HCCME =,1361

ID variables,1321

linear hypothesis testing,1360

one-way fixed effects model,1332

one-way random effects model,1339

output data sets,1368,1370

Parks method,1348

Pooled Estimator,1339

predicted values,1328

printed output,1370

R-square measure,1364

residuals,1328

specification tests,1364

two-way fixed effects model,1333

two-way random effects model,1342

Zellner’s two-stage method,1349

parameter change vector,1092

parameter estimates,2661

parameter estimation,2890

parameters

UCM procedure,1949–1960,1962–1972

Pareto charts,56

Parks method

partial autocorrelations

multivariate,1740

partial autoregression coefficient

VARMAX procedure,2091,2128

partial canonical correlation

VARMAX procedure,2091,2131

partial correlation

VARMAX procedure,2129 PDL, see polynomial distributed lags PDLREG procedure

BY groups,1402 confidence limits,1406 distributed lag regression models,1395 orthogonal polynomials,1396

output data sets,1409 output table names,1410 polynomial distributed lags,1396 predicted values,1405

residuals,1405 restricted estimation,1406 percent change calculations

at annual rates,109 introduced,109 moving averages,110 period-to-period,109 time series data,109,110 year-over-year,109 yearly averages,110 percent change calculations and DIF function,109,110 differencing,109,110 LAG function,109,110 lags,109,110

percent operators,800 period of evaluation,2734 period of fit,2734,2803,2878 period-to-period

percent change calculations,109 Periodic Equivalent, see Uniform Periodic

Equivalent periodicity

changing by interpolation,122,765

of time series observations,71,84,122 periodicity of

time series data,84,122 periodicity of time series time intervals,84,122 periodogram

SPECTRA procedure,1690,1701 PGARCH model,379

AUTOREG procedure,342 Power GARCH model,379 Phillips-Ouliaris test,355,390 Phillips-Perron test,355,389 unit roots,355–357,389 Phillips-Perron tests,234 Physical Names on Supported hosts SASEFAME engine,2512 Physical path name syntax for variety of

environments SASEFAME engine,2512

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pitfalls of

DIF function,106

LAG function,106

plot axis and

time intervals,87

plot axis for time series

SGPLOT procedure,87

PLOT procedure,50

plotting time series,91

time series data,91

plot reference lines and

time intervals,87

plots, see Model Viewer, see Time Series Viewer

plots of

interleaved time series,89

plotting

autocorrelations,197

forecasts,2664

prediction errors,2657

residual,91

time series data,86

plotting time series

PLOT procedure,91

SGPLOT procedure,86

Time Series Viewer procedure,86

point

interventions,2913

point interventions,2913

point-in-time values,765,768

polynomial distributed lag models

polynomial distributed lags

Almon lag polynomials,1395

endpoint restrictions for,1396,1402

PDL,1395

PDLREG procedure,1396

Polynomial specification,2783,2812,2851

pooled

pooled estimator,1339

Pooled Estimator

pooled estimator,1339

pooled,1339

Portfolio, see Investment Portfolio

Portmanteau Q test,402

Portmanteau Q test for

Heteroscedasticity,402

power curve

trend curves,2913

power curve trend,2913

Power GARCH model, see PGARCH model

PPC convergence measure,1078

Prais-Winsten estimates

PRED variables,1204 predetermined variables SYSLIN procedure,1764 predicted values

ARIMA procedure,260 AUTOREG procedure,369,405,406 conditional variance,407

FORECAST procedure,851 PANEL procedure,1328 PDLREG procedure,1405 SIMLIN procedure,1661,1666 STATESPACE procedure,1745,1749 structural,369,405,1405

SYSLIN procedure,1788 transformed models,1111 predicting

conditional variance,407 prediction error covariance VARMAX procedure,2089,2122,2124 prediction errors

autocorrelations,2658 plotting,2657 residuals,2726 stationarity,2659 predictions

smoothing models,2898 predictive Chow test,354,405 predictive Chow tests,1131 predictor variables

forecasting models,2739 independent variables,2739 inputs,2739

interventions,2913 seasonal dummies,2915 specifying,2739 trend curves,2912 Present Value Analysis, see Time Value Analysis present worth of cost

LOAN procedure,896 prewhitening

ARIMA procedure,250,251 principal component,1091 PRINT procedure,50 printing SAS data sets,50 printed output

ARIMA procedure,273 AUTOREG procedure,412 PANEL procedure,1370 SIMLIN procedure,1671 STATESPACE procedure,1751 SYSLIN procedure,1805 X11 procedure,2268 printing

SAS data sets,50

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