**Singapore Institute of
Statistics **

**Occasional Article, January
2009**

__Economic Forecasting
– De-Mystifying the Art of Modern Crystallomancy__

The advent of 2009 has been greeted with words of gloom and doom. The
effects of the collapse of major financial institutions in US have left the world
in deep economic despair. Attempts by policymakers around the world to salvage
the world economy seem to have met with little success, at least in the short
term. Alas, if only humans can foretell the future, then mankind would have
been spared from all the current economic malaise. Indeed, this article will
discuss an endeavour that seems to have failed most of the times - economic
forecasting.

The reason of choosing to address this topic is two-fold. First, due to
impatience and risk-aversion, experts from all cultures in the history of
mankind have used various methods to predict the future, ranging from tarot
reading, crystallomancy and five elements of divination. Hence, forecasting the
future economic performance seems relevant in this period of uncertainty and
crisis. Second, the general public tends to find forecasting like a black box;
some probably take the numbers given by economic forecasters to be god-given
and any deviation from the predicted value is grounds to accuse the professional
as incompetent and ungodly. Hence, we will try to strip away the veil and look
at the nuts and bolts behind economic forecasting. In doing so, we will
hopefully eradicate any misconceptions that the general public may have about
forecasters and their profession.

There are many methods of forecasting but we shall look at only the more
common and popular ones. Given that economic forecasting involves looking at
the future that involves time dimension, the appropriate data set to look at is
time series data, which are economic data that measures the same economic
variables that evolves over time and are collected on regular intervals. The
forecaster will construct a mathematical equation that specifies how the
variable of interest - which is commonly called the dependent variable – will depend on the other economic variables
that we are not interested to measure, i.e., the so-called independent
variables. This is what commonly known as a regression analysis and when such
technique is used to study economic events, it is classified as econometrics ^{[1]}.
It follows that if a variable y is the dependent variable while x is the
independent variable, then we say that y is regressed on x. Since the economy
is so complex and its individual variable can be affected by probably thousands
or more factors, it is not possible to specify all influencing factors in the
equation. Hence, any mathematical model has to include a disturbance or an error
term to capture all other factors that are not explicitly included in the
equation.

Generally, the objective of the users of forecasted information will determine the approaches used by forecasters. If the users are mainly concerned about the future values of economic variables such as GDP, inflation or interest rate, then methods that are based on some form of moving-averaging or smoothing method (this refers to eradicating short-term fluctuations in the data to highlight the trend and cycles) will be used and the data is then extrapolated to get the future values based on its trend. A trend in time series refers to the data of a variable to move towards certain direction that persist over time in the long-run; hence, by extracting the trend, the future value of the data can be estimated. Hence, a moving average or rolling average is a technique that constructs an average of a subset of the full data and each number in the subset can be given an equal or different statistical weight (such as allocating more weights to recent data). For instance, if the full data set consists of 10 data points, the first value of the un-weighted moving average might be the average of data points ranging from 1 to 4. The next value would be this simple average of data points 2 through 6, and the process continues. It follows that the final value would then be the same simple average of data points 7 through 10. However, such a simple method to extrapolate future values is often less meaningful and subject to more uncertainty. Currently, most professional forecasters will make use of formal statistical techniques to produce more accurate forecasts.

**COMMON FORMAL STATISTICAL METHODS FOR FORECASTING**

**Types of Variations**

Basically, there are four basic types of variation in a time series data that are of concern to forecasters. The first type is the trend, which was has been mentioned earlier. The next kind of variation that is of concern to forecasters is whether the data exhibits any seasonal pattern. For example, due to year-end festive season such as Christmas and New Year, consumer spending tends to be higher which results in higher GDP in the last quarter of the year. The third type of variation is the cyclical component, whereby certain types of pattern in the series tend to repeat over time. In economic time series, the common cycles of concern are the business cycles, consisting of recurring patterns of ups and downs in business and economic activities. They are different from seasonal variation because the causes are different and economic cycles tend to extend over longer time horizons. The last type of variations is the irregular variation which tends to arise due to unexpected events, such as wars, elections, bank failures, stock market crash or natural disasters such as earthquakes, floods and tsunamis. This type of variation is most challenging to economic forecasters because they occur randomly and there is large uncertainty about their recurrence.

**The ARIMA method**

A common method used by professionals for both forecasting and seasonal
adjustment is the Box-Jenkins approach that applies the ARIMA (Autoregressive
Integrated Moving Average) method, which is commonly classified under the
discipline of econometrics. Although the term ARIMA may sound rather daunting
to some, it is actually not a difficult concept to understand. Basically, the
dependent variable is regressed on its past (i.e., it’s lagged) values and the
moving-average value of the error term in the equation. As mentioned earlier, an
error term is always included in any mathematical equation that is used to
model real-life phenomena and it is usually assume that it captures all other
factors that are not explicitly included as explanatory variable. If the
equation only includes the last period values, then it is called autoregressive
of order one (or an AR(1) process). This way of naming can also be applied to
the moving average term.

In an economic time series model, one of the major concerns is that
whether the data is stationary or non-stationary, which has important
implications on the model. A time series is said to be stationary when its
statistical properties such as the mean, variance etc. is constant over
time. If the time series data set is
non-stationary, it also makes forecasting difficult so one way to transform the
data to make it stationary is to subtract the current value from the last
period value, a process known as differencing. Hence, if a non-stationary time
series data set becomes stationary after differencing once, we say that the
data is integrated of order one; if it requires differencing twice to achieve
stationarity, it is integrated of order two. Hence, this is why the acronym
“ARIMA” includes “I” that stands for “integrated”, which means the data is
integrated of what order while AR refers to the autoregressive process of the
dependent variable and MA stands for the moving average process of the error
term. The ARIMA^{[2]}
technique is used by the

**Causal
Macroeconometric Models**

However, at times, the users (usually policy makers) may need to
understand the quantitative contribution of various economic factors that
contribute to one or several major economic variable/s of interest. The use of causal modeling that includes other
independent variables, in addition to the lag values of the dependent variable,
will be appropriate. For example, if the government spending increase by 2
billion dollars, what will be the value of GDP next year?). In this case,
causal econometric models will be used to answer such questions. As started in
the 1940s, many national governments started collecting national income and production
data which allows economists to construct large scale macroeconometric models
that can be used for policy analysis and forecasting. Dutch economist Jan
Tinberjan produced the first comprehensive model for the

**Structural
Time Series Models**

A structural time series model is formulated with the intention to
highlight the components of interest within a set of time series data. They are
constructed directly in terms of distinctive components such as trends,
seasonal and cycles, together with other economic variables that is suppose to
affect the dependent variable based on economic theory. Compared to the classical
regression model, a structural time series model has the additional flexibility
to allow for variables to change over time because the explanatory variables
are functions of time. The estimated values of the variables of interest can be
computed by using the Kalman Filter, a type of algorithm that was being used by
control engineers in predicting rocket movements. Specifically for the purpose
of forecasting, the economist has to continuously monitor the economic system
and the estimated values must be continuously updated as new observations
becomes available so as to produce more accurate forecasts. In order to do
this, the economic forecasters has to filter the data to remove any random
component so that policy measures that is being made is based on the essential
but unobserved movement of the economic variable of interest (e.g., GDP
movements, exchange rate fluctuations etc.)

**INFORMAL JUDGEMENT**

Although modern economic forecasting procedures use formal economic
models to predict future economic events, good forecasters tend to use some
informal judgments to form their forecasts. They do not blindly follow what
formal models tell about the future but rather use the information produced by
formal models in conjunction with their own experience and analytical skills to
do their job. Hence, like most professional disciplines, economic forecasting
is both an art and a science.

**WHY ECONOMIC FORECASTS CAN FAIL…**

Despite all the most sexy computation techniques used by economic forecasters, there are times (in fact, quite often) when forecasts produced by the best economic forecasters deviate too much from the actual outcome. One of the main reasons is that economic models are bad at capturing unexpected turning points, such as stochastic shocks arising from political crisis, wars, natural disasters, bank runs etc. These events usually arise without early warning signs; hence, most standard economic models are unable to capture relevant information during such idiosyncratic episodes. As Paul Samuelson commented “The stock market has forecast nine of the last five recessions”. His quote clearly illustrated the difficulty of predicting future economic event.

**POINT FORECAST, RANGE FORECAST
AND THE **

The economy is dynamic in nature and each
outcome is the product of millions of decisions made by people. Hence, it is
very difficult to produce precise estimates of the future. In corollary, they
may also produce at least two possible scenarios and give an upper and lower
bound forecasts especially in times of high uncertainty and there are possible
regime switching events that may disrupt the usual economic activities.

Modern economic
forecasters also tend to give a range of possible numbers, such as “GDP growth in
the next quarter will range from 3 to 5 percent”, rather than report a precise
number. In addition, forecasting is even more difficult if the forecast horizon
is further into the future. A typical example is the inflation forecasts
regularly published by the Bank of England. The forecasts are presented as a
set of intervals that depicts the range of possible future inflation paths. The
professional economic forecasters in the bank refer this as the “fan chart”.
More evocatively, the news press has described the red colored shades spreading
out as “rivers of blood”. As mentioned in the
report produced the bank, …. “*the
Bank’s inflation forecast has been published explicitly in the form of a
probability distribution—presented in what is now known as ‘the fan chart’. The
aim of the fan chart has been to convey to the reader a more accurate
representation of the Bank’s subjective assessment of medium-term inflationary
pressures, without suggesting a degree of precision that would be spurious.” *^{[3]}

An example of the “rivers of blood” is given
below for the November 2008 and it reflects the expert judgment of the Bank of
England senior staff and the Monetary Policy Committee. As shown, the economists in the bank expect
inflation to fall considerably in the next two years and the forecast
uncertainty (as indicated by the “blood” red shades) increase considerably over
longer period of time. For readers who wanted to learn more about the fan
chart, you may visit the Bank
of England website.

November 2008 CPI Fan Chart

Source: Bank of

**Conclusion**

We hope that this article would help to clear
some doubts among the general public about the nature of economic forecasting
and to understand and appreciates the difficulty in predicting future economic
events. It is impossible for forecasters to incorporate all information into
their statistical models especially when information is not symmetrically known
to everyone in the society. In sum, forecasters as mortals are simply not
equipped to play the role of god. Nevertheless, quantitative models are still
indispensable for making important decisions since it generally gives a more
robust estimate about what can reasonably happen in different state of
contingencies.

The formal quantitative models that have been
illustrated in this article are just among the more common ones used for
economic forecasting. Besides using econometric and statistical approach,
professional economic forecasters may also use other computationally intensive
approach by constructing hypothetical scenario to help predict future values of
economic variables. Some common approach includes computational general
equilibrium (CGE) and dynamic stochastic general equilibrium (DSGE) models.
Given the technical nature of such approach, we shall not further illustrate
the methods here and leave the interested readers to conduct their own
research.

--Nils Bohr, Nobel
laureate in Physics

**Reference**

Harvey, Andrew., 1989, *Forecasting, Structural Time
Series Models and the Kalman Filter*,

Stock, James H., and Watson, Mark W., 2003, *Introduction to Econometrics*, Pearson
Education.

Lindbeck,
Assar – editor, (1992), *Nobel Lectures in
Economic Sciences, 1969 – 1980, *World Scientific Press.

**Endnotes**

1
One of the common definitions of econometrics is the use of statistical and
mathematical methods to study economic problems. This includes testing economic
theories and also forecasting. One salient features that differentiate it from
general regression analysis in Statistics is that econometrics tend to focus on
establishing evidence of causality rather than simply correlation.

2 There are currently 2 variants of the ARIMA method known as X-11-ARIMA
and X-12- ARIMA

3 Bank of *Inflation
Report *projections: understanding the fan chart

__________________________________

Article contributed
by Yong Soo Keong.

Edited
by Ho Yuen Ping.

The
views and opinions expressed in this article are those of the author and do not
necessarily reflect the official policy or position of the Singapore Institute
of Statistics.

Please
do not quote without attribution.

© 2009

__________________________________

[1] One of the common definitions of
econometrics is the use of statistical and mathematical methods to study
economic problems. This includes testing economic theories and also
forecasting. One salient features that differentiate it from general regression
analysis in Statistics is that econometrics tend to focus on establishing
evidence of causality rather than simply correlation.

[2] There
are currently 2 variants of the ARIMA method known as X-11-ARIMA and X-12-
ARIMA

[3] Bank of England Quarterly Bulletin (February
1998): The *Inflation
Report *projections: understanding the fan chart