CHAPTER 16
ECONOMIC FORECASTING
Damodar Gujarati
Econometrics by Example
TIME SERIES ECONOMETRICS
 Four important topics in time series econometrics are:
 (1) Forecasting with linear regression models
 (2) Univariate time series forecasting with Box-Jenkins
methodology (ARIMA)
 (3) Multivariate time series forecasting using vector
autoregression
 (4) The nature of causality in econometrics
Damodar Gujarati
Econometrics by Example
FORECASTING WITH LINEAR REGRESSION MODELS
 Long been used in forecasting sales, production, employment, corporate
profits and host of other economic topics
 Point and interval forecasts: In point forecast a single value for each
forecast period is provided, whereas in interval forecast we obtain a range,
or an interval, that will include the realized value with some probability.
 Ex-post and ex-ante forecasts: In the ex-post forecast period (the
holdover period), we also know the values of the regressand and
regressors.
 Conditional and unconditional forecasts: In conditional forecasts
(scenario analysis or contingency analysis), we forecast the variable of
interest conditional on the assumed values of the regressors. In
unconditional forecasts, we know the values of the regressors with
certainty instead of picking some arbitrary values of them, as in
conditional forecasting.
Damodar Gujarati
Econometrics by Example
ARIMA METHOD OF FORECASTING
 The Autoregressive (AR) Model
 The following is an AR(p) model:
Yt  B0  BY
1 t 1  B2Yt 2 ,..., BpYt  p  ut
where ut is a white noise error term.
 The Moving Average (MA) Model
 We can also model Yt as an the MA(q) model, a weighted, or moving, average
of the current and past white noise error terms:
Yt  C0  C1ut  C2ut 1 ,..., C jut q
Damodar Gujarati
Econometrics by Example
ARIMA METHOD OF FORECASTING (CONT.)
 The Autoregressive Moving Average (ARMA) Model
 The ARMA (p,q) model is a combination of AR (autoregressive) and
MA (moving average) terms.
 The Autoregressive Integrated Moving Average (ARIMA)
Model
 The BJ methodology is based on the assumption that the underlying
time series is stationary or can be made stationary by differencing it
one or more times.
 This is known as the ARIMA (p, d, q) model, where d denotes the
number of times a time series has to be differenced to make it
stationary.
Damodar Gujarati
Econometrics by Example
ARIMA METHOD OF FORECASTING (CONT.)
 The BJ methodology to determine which model is appropriate follows a four-step
procedure:
 Step 1: Identification: Determine the appropriate values of p, d.
and q.
 The main tools in this search are the correlogram and partial correlogram.
 Step 2: Estimation: Estimate the parameters of the chosen model.
 Step 3: Diagnostic Checking: Check if the residuals from the fitted
model are white noise.
 If they are, accept the chosen model; if not, start afresh.
 That is why the BJ methodology is an iterative process.
 Step 4: Forecasting. The ultimate test of a successful ARIMA
model lies in its forecasting performance, within the sample period
as well as outside the sample period.
Damodar Gujarati
Econometrics by Example
VECTOR AUTOREGRESSION (VAR)
 Vector autoregressive models (VARs) are used to deal with forecasting
two or more time series.
 In VAR we have one equation for each variable and each equation
contains only the lagged values of that variable and the lagged values of
all other variables in the system.
 As in the case of the univariate time series, in VAR we also require the time series
to be stationary.
 If each variable in the VAR is already stationary, each equation in it can be
estimated by OLS.
 If each variable is not stationary, we can estimate VAR only in the firstdifferences of the series.
 If individual variables in VAR are nonstationary, but are cointegrated, we can
estimate VAR by taking into account the error correction term, which is obtained
from the cointegrating regression.
 This leads to vector error correction model (VECM).
Damodar Gujarati
Econometrics by Example
NATURE OF CAUSALITY
 VAR modes can also be used to shed light on causality among
variables.
 The basic idea behind VAR causality testing is that the past can
cause the present and the future, but not the other way around.
 Granger causality: In establishing causality, we must make sure
that the underlying variables are stationary. If they are not, we have
to difference the variables and run the causality test on the
differenced variables.
 However, if the variables are nonstationary, but are integrated, we
need to use the error correction term to account for causality, if any.
Damodar Gujarati
Econometrics by Example
GRANGER CAUSALITY TEST
 1. Regress current Y on all lagged Y terms and other variables, if any (such as
trend), but do not included the lagged X terms in this regression. This is the
restricted regression. Obtain the restricted residual sum of squares, RSSr.
 2. Reestimate the equation including the lagged X terms. This is the unrestricted
regression. From this regression obtain the unrestricted residual sum of squares,
RSSur.
 3. The null hypothesis is that the lagged X terms do not belong in the regression.
 4. To test the null hypothesis, we apply the F test, which is:
( RSSr  RSSur ) / m
F
RSSur /(n  k )
which has m and (n-k) df, where m is the number of lagged X terms, k is the number of
parameters estimated in the unrestricted regression, and n is the sample size.
 5. If the computed F value exceeds the critical F value at the chosen level of
significance, we reject the null hypothesis.
Damodar Gujarati
Econometrics by Example
GRANGER CAUSALITY TEST (CONT.)
 Run the test again switching X and Y. There are four cases:
 1. Unidirectional causality from X to Y
 2. Unidirectional causality from Y to X
 3. Feedback or Bilateral causality is indicated when the sets of
Y and X coefficients are statistically significantly different
from zero in both regressions.
 4. Independence is suggested when the sets of Y and X
coefficients are not statistically significant in either of the
regressions.
Damodar Gujarati
Econometrics by Example