Index
ACF (autocorrelation function), 86–89
ADF test. See Augmented Dickey-Fuller (ADF) test
Adjusted R2, 117
Akaike information criterion (AIC):
for characterizing time series, 147–149
to determine autocorrelation order, 194–196
formula for, 151
for model selection, 118–119, 146, 182
Anchoring bias, 3, 14, 318–319, 325–326, 337, 346–347, 361
Applications:
benchmarking housing bust, Bear Stearns, and Lehman Brothers, 172–177
judging economic volatility, 101–109
multiple-equations forecasting, 280–288
relationship characterization for Great Recession and credit benchmarks, 215–221
Applied research, tradition of, 2
Applied time series forecasting. See Characteristics of time series; Forecasting; Relationship characterization with SAS software; Relationships between time series; Time series
ARCH (autoregressive conditional heteroskedasticity), 21–22, 115, 125–126
ARCH/GARCH modeling:
for determining statistical relationships, 124–126
ARIMA (autoregressive integrated moving average), 17–18, 23–24, 154–156, 233
ARIMA (p, d, q) model, 243–244
ARMA (p, q) model, 243
AR (p) notation, 243
Asset bubble forecast, 225
Asymmetric loss functions, 227–228
Atheoretical forecasting approach. See Unconditional forecasting model
Augmented Dickey-Fuller (ADF) test:
E-G test compared to, 198
for identifying unit root, 16–17
origins of, 91
overview of, 92
of time series, 94
Autocorrelation detection test:
Autocorrelation function (ACF), 86–89
Autoregressive, defined, 18
Autoregressive conditional heteroskedasticity (ARCH), 21–22, 115, 125–126
Autoregressive integrated moving average (ARIMA), 17–18, 23–24, 154–156, 233
Autoregressive moving average (ARMA)/autoregressive integrated moving average (ARIMA), 17–18, 23–24
Availability bias, 331
Average forecast error, 236–237
Bayesian vector autoregression (BVAR):
efficacy of, 278
Great Recession and, 309
housing starts and, 296–298, 299–300
unconditional forecasting and, 293–298
Bear Stearns and overnight market for risk, 173–175
Benchmarking economic growth, 318–321
BG-LM (Breusch-Godfrey serial correlation LM) test, 117–118
Bias:
anchoring, 3, 14, 318–319, 325–326, 337, 346–347, 361
availability, 331
confirmation, 12–13, 322–324, 327
deficit, 358
interest rate expectations and, 337
normalization of deviance, 348
overconfidence, 354
recency, 9–10, 14, 64, 326–327, 331–332
sunk cost, 347
Binomial (either/or) outcomes, 24–25
B-J method. See Box-Jenkins (B-J) forecasting method
Bloomberg real-time consensus forecast, 263, 267, 280–288, 309
Bond yields and equity earnings, imbalances between, 338–345
Box-Jenkins (B-J) forecasting method:
Box-Pierce Q-statistic (Q_BP), 88–89
Breusch-Godfrey serial correlation LM (BG-LM) test, 117–118
Bubble forecast, 225
Business credit, patterns of, 347
Business cycle:
division of data into, 142
long-term forecasting and, 230–231
macroeconomic variables and, 292, 310–311
response to macroeconomic news and, 286–287
stages in, 5
BVAR (Bayesian vector autoregression):
efficacy of, 278
Great Recession and, 309
housing starts and, 296–298, 299–300
unconditional forecasting and, 293–298
Cash for Clunkers program, 309–310
Causality and correlation, 182
Causality test, 20–21. See also Granger causality test
CDS (credit default swap) premiums, 338–340
Census effect, 310
Characteristics of time series:
judging economic volatility, 101–109
separating cycle and trend, 98
simple statistical measures for, 79–81
Characterization of data:
cointegration and error correction model, 18–20
overview of, 2
structural breaks in time series, 14–15
subcycles of economic behavior, 11–14
Charge-off rates, patterns in, 218, 219
Chow test:
testing for structural breaks in time series, 98
Coefficient, standard error of, 146–147, 190
Cointegration:
Engle-Granger test, 121–122, 197–199
Johansen test, 121–122, 202–206
Cointegration analysis, 120–122
Conditional forecasting model:
long-term forecasting, 293
Taylor rule case study, 252–256
without oil price shock, 298, 300–304
Confirmation bias, 12–13, 322–324, 327
Consensus forecast compared to individual forecast, 266–268
Consumer price index (CPI), 50–53, 333–334
Consumption, government-financed, 361
Controlled forecasting experiments, 238–239
Core CPI, 52
Corporate profits:
as key economic indicator, 60–62
as percentage of GDP, 67
Correlation analysis:
causality and, 182
for determining statistical relationships, 119, 120
growth rates of variables of interest in, 186–187
overview of, 113
Cost:
Coverage ratio, 70
CPI (consumer price index), 50–53, 333–334
Credit benchmarks and Great Recession, 215–221
Credit default swap (CDS) premiums, 338–340
Credit markets, functioning of, 340–341
Cycle for time series:
identifying with SAS software, 151–156
Cyclical component in financial ratios, 64
Data. See also Characterization of data; Key economic indicators
availability and release timing of, 278–280
descriptive statistics of, 77, 79–81, 102–105, 139–142, 143
inputting into statistical software, 179–180
real-time forecasting and, 275–277
Dataset:
choice of, 231
converting from one frequency to another, 182–183
DATA step of time series analysis, 131–135
Debt ratio, 70
Deficit bias, 358
Deficits:
Deflation, 50
Degrees of freedom for error (DFE), 146
Delinquency rates on loans, 215–218
Dependent variable:
functional form of, 276–277, 289
overview of, 231
selection of, for short-term forecasting models, 277–278
traditional and nontraditional forms of, 242
Descriptive statistics of data:
calculating in PROC step of time series analysis, 139–142, 143
for characterizing time series, 79–81, 102–105
overview of, 77
DFE (degrees of freedom for error), 146
DF (Dickey-Fuller) test, 91, 92–94
Difference stationary (DS) behavior, 91, 93, 343
Directional accuracy:
in deciphering results, 236–237
in forecast evaluation, 273–274
forecast evaluation and, 25
Disinflation, 50
Dollar and exchange rates, 58–60, 351–353
DS (difference stationary) behavior, 91, 93, 343
Dummy variable approach, 14–15, 163–164
Durable goods, 31
Durbin-Watson “d” test, 117–118, 146, 192
ECM. See Error correction model
Econometrics:
applied research compared to, 2
of real-time short-term forecasting, 268–275
Economic growth. See Employment growth; Growth
Economic indicators. See Key economic indicators
Economic policy:
deficit bias in, 358
large and persistent deficits, 354–356
Economic recovery, trends in, 1–2, 317–318
Economic trends and financial ratios, 64
E-G. See Engle-Granger (E-G) cointegration test
Either/or (binomial) outcomes, 24–25
Employment growth:
economic recovery and, 1, 317–318
Employment-population ratio, 330
Employment Situation Summary:
Endogenous break date, 98
Engle-Granger (E-G) cointegration test:
for determining statistical relationships, 121–122
overview of, 20
Equity earnings and bond yields, imbalances between, 338–345
Error correction model (ECM). See also Vector error correction model
for determining statistical relationships, 122–123
Establishment (payroll) survey, 39–43
Euro crisis, 358
Evaluating forecasts, 25, 271–274
Exchange rates, 58–60, 351–353
FIML (Full Information Maximum Likelihood), 149
Financial crisis, 175–177. See also Great Recession
Financial leverage, 70
Financial ratios:
First-order autocorrelation, detecting, 192–193
Fiscal policy. See Economic policy
Forecast error:
nature of, 307
representing by time series, 235–236
Forecasting. See also Long-term forecasting; Model-based forecasting; Short-term forecasting
acknowledging cost of errors, 226–229
models for, as evolving over time, 239–240
rationalizing horizon, 229–231
rationalizing model used, 232–233
understanding cost of variables, 231–232
understanding purpose of, 226
understanding recursive methods, 238–239
F-test, 116
Full Information Maximum Likelihood (FIML), 149
Functional form of variables, 276–277, 289
GARCH (generalized autoregressive conditional heteroskedasticity), 21–22, 125–126
GDP. See Gross domestic product
GNP (gross national product), 30
Godfrey LM test of autocorrelation, 193–194
Granger causality test:
for determining statistical relationships, 123–124
Great Recession:
credit benchmarks and, 215–221
depth of, 296
housing sector and, 298
long-term forecasting and, 311–314
model-based forecasting and, 314–315
Okun's law and, 242
performance of models and, 309
Gross domestic product (GDP):
corporate profits as percentage of, 67
government consumption and, 35–36
gross private domestic investment and, 33–35
identifying trend in time series and, 2–5
personal consumption and, 31–32
relationship to unemployment rate, 75–76
trends in, 317
Gross national product (GNP), 30
Gross private domestic investment, 33–35
Group of black swans, 311, 312–314
Growth. See also Employment growth; Gross domestic product
conditional forecasting model and, 256–257
labor market and, 38
in productivity, structural periods of, 96
Heteroskedasticity, 115
Higher-order autocorrelation, detecting, 194–196
Hodrick-Prescott (HP) filter:
identifying subcycles with, 11–14
recency bias and, 64
to separate cycle and trend in time series, 98–101
Homoskedasticity, 124
Horizon for forecast, rationalizing, 229–231
Housing market. See also S&P/Case-Schiller home price index
bust, as structural break, 172–173
Housing-related data, forecasting from, 287
HP filter. See Hodrick-Prescott (HP) filter
Identification problem, 294, 301
Importing datasets into SAS, 133–134
Independent variables, 231, 232
Individual forecast compared to consensus forecast, 266–268
Industrial production, 322–324
Industrial Production (IP) data, 311–314
Inflation:
consumer price index and, 50–53
inflation expectations and, 332–333, 334, 335
personal consumption expenditure deflator and, 55–56, 112–113
producer price index and, 53–55
Initial jobless claims, 245
I (d) notation, 243
Integration (I), 18
Interest rates:
as price of credit, 56–58, 337–338
on Treasury securities, 341–345
Inventories:
Investment valuation ratio, 72–73
IP (Industrial Production) data, 311–314
Job growth and economic recovery, 1, 317–318. See also Employment growth
Johansen cointegration test:
Key economic indicators:
dollar and exchange rates, 58–60
gross domestic purchases, 37
gross private domestic investment, 33–35
personal consumption expenditure deflator, 55–56
KISS principle, 233
Kwiatkowski, Phillips, Schmidt, and Shin (KPSS) test:
for identifying unit root, 16
of time series, 95
Labor force participation rate, 46–48, 330–331
Labor market:
change in character of, 324–331
combining indicators, 48
nonfarm payrolls forecasts, 280–284, 326–328
unemployment rate and, 27–28, 29, 43–45, 75–76, 325–326
Large-scale macro models, limitations of, 293–294
Level of significance, 115
Linear loss functions, 228–229
Linear trends:
estimating, 145
reliability of forecasts and, 81
Ljung-Box Q-Statistic (Q_LB), 88–89
LM test of autocorrelation, 193–194
Loan delinquency rates, 215–218
Log-difference form of variables, 180–181
Logistic regression model, 242, 257–261
Long-term forecasting:
conditional model with oil price shock, 304–306
conditional model without oil price shock, 298, 300–304
overview of, 230–231, 291–293, 306
risks related to, 307–308, 310–314
Loss functions:
formula for, 227
overview of, 226
symmetric and asymmetric, 227–228
Lucas, Robert E., 345
MA (moving average), 18
Macroeconomic news announcements:
business cycle and response to, 286–287
MAE (mean absolute error), 25, 146
MA (q) notation, 243
MAPE (mean absolute percentage error), 146
Maximum likelihood (ML) method, 168
Maximum test of cointegration, 202–203, 205–206
Mean:
calculating in PROC step of time series analysis, 139–142, 143
overview of, 79
Mean absolute error (MAE), 25, 146
Mean absolute percentage error (MAPE), 146
Mean reverting, series as, 319–321
Mean square error (MSE), 146
Measuring volatility:
forecast evaluation, 25
forecasting recession/regime switch as either/or outcomes, 24–25
forecasting with regression model, 22–24
forecasting with vector autoregression, 25
Minnesota prior, 268, 269, 294
Model-based forecasting:
conditional approach, 251–257, 293, 298, 300–306
data and model selection, 275–280
individual compared to consensus, 266–268
overview of, 241–243, 261–262, 263–265
Probit (logistic regression) model, 24–25, 242, 257–261
unconditional approach, 242–250, 293–298, 299–300
Modeling cycle for time series, 17–18, 154–156
Models. See also Model-based forecasting; specific models
as evolving over time, 239–240
large-scale macro, limitations of, 293–294
monitoring performance of, 308–309
selection criteria, 118–119, 275, 277–278
Monetary policy, inflationary bias of, 332
Monetary policy transmission mechanism, 218–221
Money neutrality, 75, 111–112, 113
Moving average (MA), 18
MSE (mean square error), 146
Multiple-equations forecasting:
conditional model with oil price shock, 304–306
conditional model without oil price shock, 298, 300–304
data and model selection, 275–280
individual compared to consensus, 266–268
National Income and Product Accounts (NIPA), 60–62
Net exports of goods and services, 36–37
Nonfarm payrolls forecasts, 280–284, 326–328
Nonlinear loss functions, 228–229
Nonstationary time series, 89–90
Objective of forecasts:
Observations, time periods for, 180, 182–183
Oil price shock:
conditional model with, 304–306
conditional model without, 298, 300–304
Operating leverage, 70
Ordinary least squares (OLS) analysis, 157, 196
Outcome uncertain, timing certain forecast, 224–225
Overconfidence bias, 354
Overnight market for risk, 173–175
Panics, 315
Partial autocorrelation function (PACF), 86–89
Payroll (establishment) survey, 39–43
PCE (personal consumption expenditure) deflator, 55–56, 112–113
Pearson correlation coefficient, 184–185
Performance of models, monitoring, 308–309
Personal consumption, 31–32, 104–105
Personal consumption expenditure (PCE) deflator, 55–56, 112–113
Phillips-Perron (PP) test:
for identifying unit root, 16–17
SAS software and, 160
Plotting data versus time, 77–79, 101–102
Policy changes and long-term forecasting, 292, 311
PPI (producer price index), 53–55
PP test. See Phillips-Perron (PP) test
Predictors in forecast model, 251. See also Variables
Presenting forecast results, 234–235
Prices:
Price-to-earnings (P/E) ratio, 72–73
Probit model, 24–25, 242, 257–261
PROC step of time series analysis:
calculating volatility, 139–142, 143
identifying cyclical behavior, 151–156
identifying time trend, 142, 144–151
Producer price index (PPI), 53–55
Productivity growth, structural periods of, 96
Profits:
overview of, 348
as percentage of GDP, 67
Purpose of forecasting, 226
Q_BP (Box-Pierce Q-statistic), 88–89
Q_LB (Ljung-Box Q-Statistic), 88–89
Quadratic trend model, 82
Quadratic (nonlinear) trends, 3–4, 137
Quick ratio, 68
R2, 117
Random walk with drift model, 93, 159
Rationalizing:
Real final sales, 37, 38, 104–105
Real-time short-term forecasting:
comparison of methods for, 280–288
data and model selection, 275–280
Real yields and inflation, 338
Recency bias, 9–10, 14, 64, 326–327, 331–332
Recession/regime switch, forecasting, 24–25
Recessions. See also Great Recession
dating of, 39
autocorrelation tests and, 192–196
for determining statistical relationships, 119–120
overview of, 113
using OLS, 196
Relationship characterization with SAS software:
cointegration and ECM analysis, 196–209
converting dataset from one frequency to another, 182–183
Granger causality test, 209–211
Relationships between time series. See also Relationship characterization with SAS software
additional reading on, 127
cointegration analysis, 120–122
correlation analysis, 119
error correction model, 122–123
F-test, 116
Granger causality test, 123–124
level of significance and p-value, 115
model selection criteria, 118–119
R2, 117
t-value, 116
white noise/autocorrelation detection tests, 117–118
Results of forecasting:
Revisions to macroeconomic variables, 287–288
Risk:
of leveraging activity, 341
of long-term forecasting, 310–314
of model-based forecasting, 307–308
of short-term forecasting, 308–310
variance as proxy for, 211
volatility and, 107–108, 349–351
RMSE (root mean squared error):
in deciphering results, 236–238
in forecast evaluation, 271–273
forecast evaluation and, 25
simulated out-of-sample, 292–293
Root mean squared error. See RMSE
SAS software. See also PROC step; Relationship characterization with SAS software
ARCH/GARCH approach and, 126
asterisks and semicolons, 133
BVAR approach, 274–275, 295–298
conditional model with oil price shock, 304–306
conditional model without oil price shock, 301–304
correlation coefficient, 119
Granger causality test, 124
identifying cycles in time series, 86–87
identifying structural breaks, 162–169
OUTLIER tool, 166
Probit model application, 258–261
PROC AUTOREG command, 120, 144–145, 149, 187–188
PROC CORR command, 184
PROC CORR Data keywords, 136
PROC EXPAND command, 170–171, 182
PROC EXPORT command, 171
PROC IMPORT Datafile keywords, 133–134
PROC LOGISTIC command, 260
PROC MODEL command, 149–151, 302
PROC VARMAX command, 202–203, 209–210, 274
p-values, 115
references for users of, 365
Taylor rule case study, 252–256
testing for structural breaks in time series, 97–98
SBC. See Schwarz Bayesian criterion
Scenario-based analysis, 235, 251–252, 315
Schwarz Bayesian criterion (SBC):
for characterizing time series, 147–149
to determine autocorrelation order, 194–196
formula for, 151
for model selection, 146
Schwarz information criterion (SIC), 118–119, 182
Seasonal adjustment in SAS, 136–138
Services:
personal consumption of, 32
Short-term forecasting. See also Conditional forecasting model; Probit model; Unconditional forecasting model
comparison of methods for, 280–288
data and model selection, 275–280
evaluating performance of, 240
long-term forecasting compared to, 292
methods for, 262
overview of, 230
real-time, 263–264, 265–266, 288
risks related to, 307, 308–310
SIC (Schwarz information criterion), 118–119, 182
Single-equation forecasting:
Probit (logistic regression) model, 257–261
unconditional approach, 242–250
Small-scale macro model, 301–304
Software, 129–130. See also SAS software
S&P/Case-Schiller home price index (HPI), 96–97, 162, 172–173, 307–308, 313
Stability ratio:
calculating in PROC step of time series analysis, 139–142, 143
Standard deviation:
calculating in PROC step of time series analysis, 139–142, 143
Standard error of coefficient, 146–147, 190
State-space approach:
to testing for structural breaks, 166–169
Stationarity, adjusting two-year Treasury yield to achieve, 343–344
Statistical relationships between time series. See Relationships between time series
Statistical significance, determining, 115–119
Strategic vision, need for, 318
Structural breaks in time series:
dummy variable approach to testing for, 163–164
identifying with SAS software, 162–169
methods to identify, 157
state-space approach to testing for, 166–169
Structural model, 233
Sunk cost bias, 347
Symmetric loss functions, 227–228
Ten-year Treasury yields, 344–345
Testing. See also Unit root tests
for autocorrelation, 117–118, 192–196
for causality, 20–21, 114, 123–124, 209–211
for cointegration, 121–122, 197–199, 202–206
for structural breaks in time series, 97–98
Theoretical forecasting approach. See Conditional forecasting model
Theory, relying on for long-term forecasting models, 292–293
Time series. See also Characteristics of time series; Relationship characterization with SAS software; Relationships between time series
Time trend:
identifying with SAS software, 142, 144–151
Timing uncertain, outcome known forecast, 225
Trace test of cointegration, 202–205
Trade, net exports of goods and services, 36–37
Trade-weighted dollar index, 352
Treasury yields:
inflation and, 338
Trend stationary (TS) behavior, 91, 93, 343–344
Two-year Treasury yields, 341–344
Unconditional forecasting model:
BVAR approach and, 293–298, 299–300
Underemployment, 331
Unemployment rate:
Unfunded liabilities of governments, 354–356, 361
Unit root tests:
purpose of, 157
Univariate forecasting, 241
VAR. See Vector autoregression
VAR/BVAR approach, 263
Variables:
functional form of, 276–277, 289
log-difference form of, 180–181
selection of for short-term forecasting models, 277–278
VECM. See Vector error correction model
Vector autoregression (VAR). See also Bayesian vector autoregression
forecasting with, 25
multiple-equations forecasting and, 263
uses of, 233
Vector error correction model (VECM):
overview of, 123
VIX (volatility index), 176, 177
Volatility. See also Measuring volatility
calculating in PROC step of time series analysis, 139–142, 143
of financial data series, 115
interpreting, 3
macroeconomic news announcements and, 265–266
Volatility index (VIX), 176, 177
White noise detection tests, 117–118, 244–245
Worst-case scenarios, 315