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The Art of Forecasting
Sam Ouliaris
NUS Business School &
Monetary Authority of Singapore
Forecasting … Definition

Forecasting is the art of predicting the
future value of a random variable (i.e.,
a variable with more than one possible
outcome).
Amalgam of Numerous
Disciplines

Forecasting uses tools from many
disciplines (statistics, economics,
computer science).
Forecasts Often Involve
Subjective Judgment

Why? Professional judgment often
improves on a forecast derived using
formal techniques.
Aim of Forecasting


In short, forecasting aims to predict the
future values of a random variable as
accurately as possible.
We usually prepare these forecasts
using all (or any part of) the relevant
information available when the forecast
is being prepared.
Forecast is Tough. So, Why
Bother?

Two reasons:


uncertainty about the future;
the lags involved in decision making.

The environment we operate in is constantly
changing. Forecasts help us by predicting
these changes ahead of time.

Critical decisions can then be made based on
rational expectations of future conditions.
Why Do We Forecast?


In particular, forecasting often provides
decision makers with time to react to
unwanted outcomes (e.g., an economic
recession).
Forecasting facilitates the formulation of
rational / consistent economic policies that
help the Singapore economy achieve
sustainable economic growth.
Lags in Decision Making…



If we could always adjust instantaneously and
costlessly to new conditions there would be no need
for forecasts.
But decisions rarely have immediate effects. In some
cases, e.g., investment decisions, the changes take
months, or years, to implement.
Organisations must therefore plan ahead, and to do
this they need forecasts of future conditions.
Quantitative Information
Needed


For example, Singapore’s exchange rate
policy relies on a sequence of forecasts of
future GDP.
To this end, the MAS has
developed a model of the Singapore economy
that predicts the future value of GDP.
Qualitative feel is not good enough for policy
formulation; policy makers need quantitative
values to properly formulate exchange rate
policy.
Forecasting: A Formal
Definition



Let the future (unknown value) of a random
variable, X, be denoted by Pt+n.
Note that “t” represents the present, and t+n
denotes “n” periods ahead of “t”.
For example, if t = 2003, and n = 2, we aim
to predict the value of X in year 2005 (=
t+n).
Information? What’s That?



Historical behaviour of the variable itself, i.e.,
Xt, for t = 1 … n.
Historical behaviour of other variables that
we think might affects the value of Xt.
Economic theory plays a critical role here.
Intuition (subjective judgment), which
typically starts with the historical behaviour of
the variable.
Let’s Get Technical


In general, a forecast may be represented as
Pt+n = f(Z1t,Z2t,a,b), where Z1t and Z2t are
variables that potentially affect the future
value, and “a” and “b” are parameters that
reflect the strength of the relationship
between the variable of interest, X, and Z1t
and Z2t.
Typically, “a” and “b” need to be estimated
for this model to be operational.
Evaluating Forecasts



We traditionally examine the size of the
forecast errors, or Xt+j - Pt+j for j = 1,…,n.
This can be stated as “actual – predicted” for
each of the periods we prepared the forecast
for X.
The smaller these are, the better.
Don’t be Too Demanding


The public tends to evaluate a forecaster on
how close the most recent forecast is to the
correct value.
Not very reasonable! Why? The probability of
predicting the actual value of a continuous
random variable is ZERO!
A Good Forecaster Is…

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Someone who consistently generates small (not
necessarily the smallest) forecast errors over time. In
other words, he/she is “reasonably” accurate on
average.
Allowed to have bad calls --- they are sure to happen
according to basic statistics.
Someone who provides a range of possible
outcomes, and assigns a probability that the range
will have the value he/she is trying to predict.
Other Important Criteria for
Evaluating Forecasts

Forecasts need to be:
timely;
 cost effective;
 consistent; and,
 comprehensible by decision makers.

Forecasting Horizon
Complicates Matters


The further out you go in the forecast
horizon, the harder it is to predict accurately.
Uncertainty tends to compound itself,
particularly as we extend the forecast
horizon.
Three Approaches to
Forecasting



Econometrics, which is an amalgam of
economic theory (“econ”) and statistics
(“metrics”).
Time-Series Analysis, which uses only the
past behaviour of a variable to predict itself.
A combination of the previous two, plus
subjective judgment.
Econometrics

Starts with an economic
relationship that connects
one variable to another.
These statements imply
causality.
For example, per capita
consumption tends to move
with disposable household
income.
9.6
Log(Consumption)

Plot of Log(C) against Log(Y)
9.4
9.2
9.0
8.8
8.6
8.4
9.0
9.5
10.0
10.5
Log(Disposable Income)
Keynesian Consumption
Function
We can express this causal
statement mathematically as
Log(C) = a + bLog(Y)+e,
where a > 0 and 0 < b < 1,
are unknown parameters,
and e is the “residual” that is
meant to be unpredictable.
9.6
Log(Consumption)

Plot of Log(C) against Log(Y)
9.4
9.2
9.0
8.8
8.6
8.4
9.0
9.5
10.0
10.5
Log(Disposable Income)
Role of Econometrics
Plot of Log(C) against Log(Y)

It is the role of econometrics
to estimate the unknown
parameters, “a” and “b”,
given the assumption that
Log(C) = a + bLog(Y) + e.
Log(Consumption)
9.6
9.4
9.2
9.0
8.8
8.6
8.4
9.0
9.5
10.0
10.5
Log(Disposable Income)
Keynesian Consumption
Function for the USA
We collected actual timeseries data on USA’s “real”
consumption and household
disposable income (1947:1
to 2002:04, quarterly) and
obtained
the
following
Keynesian
consumption
function:
C = -82.07178 + 0.92596Y,
Degree of Fit: 99.7 per cent.
9.6
Log(Consumption)

Plot of Log(C) against Log(Y)
9.4
9.2
9.0
8.8
8.6
8.4
9.0
9.5
10.0
10.5
Log(Disposable Income)
Forecasting with the USA
Consumption Function

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Household disposable income in 2003:01 was reported to be
7164.97.
If we substitute this value of income into the estimated
consumption function to forecast consumption for 2003:01, we
would obtain a predicted value of 6552.41. The actual value was
6713.58.
This implies a forecast error of 161.17 million (2.5% error relative
to actual).
It’s certainly premature to assess the value of this model --- we
presently have only one forecast error, and the probability that this
error will take on any particular value is formally ZERO!
Caveats

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The consumption function we estimated is quite
simplistic.
Interest rates, wealth can also affect current
consumption, and these variables in turn are
driven by other variables.
In other words, predicting an economic variable
often requires more than one equation. We need
to formulate a model of the entire economy (i.e.,
a system of simultaneous equations).
Time-Series Analysis


Time-Series Analysis uses the previous behavior of a
variable to predict itself.
Includes a number of well-known forecasting
techniques:



simple smoothing, trend extrapolation, and decomposition
models;
ARIMA (Box-Jenkins) models; and,
other univariate and multivariate statistical methods (e.g.,
Vector Autoregression models), Artificial Neural Networks
approaches.
Box-Jenkins (BJ) Example


For a very simple BJ example, consider
Log(Ct) = a + bLog(Ct-1), where “a” and
“b” are unknown parameters.
Notice that we do not rely on any other
variable to predict Ct.
Box-Jenkins Model for USA’s
Consumption, 1947:2-2002:4

Log(Ct)=0.0090469+0.9999Log(Ct-1).

Very good fit of 99.9%.

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Predicted C for 2003:01 is 6702.96 billion
USD (1996, $); actual reported value is
6713.58.
Forecast error is quite small, 0.16%.
Subjective Judgment


The final approach to forecasting includes the
use of subjective judgment in whole or in
part.
This approach typically involves using the
formal numbers derived from econometric
estimation and/or time-series analysis, and
then adjusting the prediction for qualitative
information that is difficult to incorporate in a
formal setting.
Skills Needed to Arrive Here…

Incidentally, to get to this point yourselves you need to
master some:
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economic theory;
time-series data collection techniques;
basic understanding of how to calculate a regression using
standard regression packages (computing);
statistical theory; and,
interpretation skills.
Most of these skills are acquired at university if you
decide to major in economics (highly recommended --or at least a minor!).