## By : Fodiyé Bakary Doucouré, Statistician Econometrician, Ph.D. Expert in Forecasting Time Series

Graduate of the IFP of Paris (Quantitative Management Techniques), the Faculty of Economics and Management of the University of Paris 10 (Nanterre), and the Paris Statistical Institute (ISUP, Pierre and Marie Curie University, Paris 6), Fodiyé Bakary Doucouré is a teacher-researcher at the Faculty of Economics and Management at Cheikh Anta Diop University in Dakar. His research focuses on time series prediction problems. He is a trainer in statistical and econometric methods and the author of around ten works in the fields of statistics, probability calculation, econometrics and mathematics. Fodiyé Bakary Doucouré is the educational manager of the Masters in “Statistical and Econometric Methods” and “Quantitative Economics and Finance”.

# “The mental work of forecasting is one of the essential bases of civilization. Foreseeing is both the origin and the means of all enterprises, large or small.” Paul Valéry

Some disgruntled people point out that the recent history of forecasting methods has been marked by some resounding failures, which have cast doubt on the effectiveness of expert forecasters. These minds denounce the forecast errors observed to condemn all forecasts a priori. It is absurd to throw “the baby out with the bathwater” in this way.

The need to anticipate the future is of great importance in many areas, and it is necessary to use forecasting methods. As the saying goes **“to govern is to anticipate”**. A current example is that of the need to properly predict the evolution of the urban population to calibrate investments in infrastructure, as illustrated by the water deficit in the Senegalese capital. In a world full of uncertainties and exposed to shocks of all kinds (geopolitical, economic, natural, etc.), forecasting makes it possible to chart the future, to frame reasoning and strategies both micro and macroeconomic, even if it rarely anticipates the exact future value of the economic growth rate, the inflation rate or the unemployment rate. The publication of the economic growth rate, the price index, or the unemployment rate; is often awaited with great impatience, because they are indicators

of the success or failure of an economic policy. Likewise, the publication of certain

monetary and financial statistics strongly influences the behavior of investors. It would therefore be very interesting to know the value of these indices before their official publication. This would make it possible in particular to make the right decisions on time, which always take a certain amount of time before being effective. These are examples of time series, the future evolution of which we would like to predict. This article presents the methods for forecasting the evolution of economic quantities.

# 1. Why plan ?

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Economic forecasting occupies a growing place in our societies. It has become essential to the conduct of economic policies by the authorities and to strategic decision-making in large companies or financial institutions.

Art or science ? The forecast often hesitates between these two poles. From science, it draws a set of rigorous methods based on algorithms. From art, the art of the forecaster that is to say, it draws the ability to detect among a multitude of data, all statistically significant, those which carry the seeds of the future. Predicting what will happen in the future is of paramount importance for both a business and an economy. For a company, production is a more or less long process depending on the type of activity, so that a sales forecast, for example, is necessary to adapt the pace of production. The production forecast will in turn be used to establish the supply policy. It is therefore seen that demand forecasting, which will translate into a company’s sales budgets, is of paramount importance in a company’s planning process.

For an economy, several examples can justify the usefulness of forecasting: Rampant urbanization creates a demand for infrastructure (roads, water, schools, health centers, etc.) in cities. If the supply of infrastructure does not keep up with this demand, the result is an infrastructure deficit which places populations in a precarious situation. It therefore appears necessary to properly predict the evolution of the urban population in order to better calibrate public investments.

The availability of food products in many African countries is dependent on climatic conditions, particularly temperature levels and precipitation. It is therefore necessary to anticipate climatic conditions and their impacts on agricultural production in order to take appropriate measures to preserve the food security of populations.

When drawing up its annual budget, the State needs to know the level of its resources in order to plan its expenditure. If the State anticipates a favorable national economic situation, this should result in significant tax revenues and, consequently, in equally significant public investments in favor of the populations. On the other hand, if the

projected economic situation is not favorable, tax revenues will be reduced and public

spending could not be carried out.

Our societies are transforming with globalization. Our social and economic conditions are subject to positive and negative shocks of all kinds. We can, in a forward-looking approach, ask ourselves what will become of our traditions in 50 years. Will future generations be respectful of the traditional, moral and religious values of our current society ? With technological innovation, what types of vehicles will we have in 30 years and how will this change the way we travel and live ?

Forecasting covers a set of very diverse methods which have in common the aim of reducing the uncertainty linked to not knowing the future.

# 2. What are we planning ?

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Forecasting can concern many areas of the life of a society, a country or a business. In the field of economics, for example, we can seek to forecast the rate of economic growth, the inflation rate, the unemployment rate, interest and exchange rates, the trade balance, tax revenues, bank liquidity, public expenditure, budget deficit and balance of payments balance.

# 3. The various forecast horizons

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The notions of growth and cycle play a structuring role, both in macroeconomic analysis and in forecasting. Economic fluctuations are traditionally identified with short-term developments. Symmetrically, the trend factors which result in a lasting increase (or decrease) in activity levels are associated with long-term developments. The logics governing these two types of horizons being relatively different, it is classic to distinguish the forecasts according to their term. In fact, five horizons are generally featured.

**The very short term :**of the latest observations up to two quarters beyond the current**The short term :**from six months to two years ;

**The medium term :**generally between two and five years, sometimes ten years ;

**The long term :**beyond five to ten years ;**The present or the immediate horizon (nowcasting) :**the next few minutes or

The very short term is the area that is commonly referred to as economic analysis. We can note a particularity of this, the objective is to report on recent developments.

The short term is the most common horizon in regular forecasting exercises (it implicitly includes the very short term). Thus, forecasts published periodically typically relate to the current year and the one that follows. Very short-term forecasts are intended to plan immediate operational activity. The goal is, for example, to plan production and resource requirements for the coming days or weeks. A very short-term forecast should not exceed a six-month horizon.

Medium and long-term projections are carried out less frequently, but nevertheless regularly, particularly within economic administrations, and sometimes large companies (for example, to evaluate an investment project). Medium-term forecasts are necessary to determine annual production plans and to plan production capacity which is not very flexible in the short term. These forecasts cover an annual time horizon. Finally, long term forecasts are intended for strategic planning and serve as a basis for investment or disinvestment decisions in production units or equipment. They are also necessary to decide on the launch of new products and entry into new markets.

With the development of statistical devices, calculation tools and forecasting techniques, a new forecasting horizon, called « immediate », is gradually being put in place, nowcasting, that is to say forecasting the present. These “now” forecasting techniques make extensive use of massive and high-frequency data (big data, high-frequency data, alternative data) and computer and algorithmic tools such as machine learning. Big data is shaking up economic prediction. The almost instantaneous analysis of economic activity gave birth to nowcasting, that is to say forecasting the present. Nowcasting is very short-term forecasting, in the next few minutes or hours. Note that nowcasting was widely used in the context of the covid crisis which had rendered most available macroeconomic forecasting models inoperative. But what forecasting methods are available ?

# 4. Forecasting methods

There are numerous forecasting methods and their diversity is based on the impossibility of taking a single look at a time series. Forecasting methods fall into two groups :the qualitative approach and the quantitative approach.

The distinction between these categories lies in the degree of mathematical formalization

both in terms of hypotheses and implementation. The scope of application is also different.

# 4.1 Qualitative methods

Qualitative methods are particularly useful when data or time series are not available. This is particularly the case for the launch of a new product by a company. It also happens that the information available does not lend itself to statistical processing: poor quality of data or insufficient number of observations. Finally, sometimes the purpose of the forecast does not easily allow the development of a mathematical model. At this level, we can cite the prediction of technological changes. In most situations, this group’s methods rely on the judgment of experts or decision makers. One objective may be to obtain consensus from a group of experts on a likely future. The scenario and Delphi methods are among the best known. These methods find applications in technological forecasting, planning in large organizations and the study of the evolution of an industrial sector.

# 4.2 Quantitative methods

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The quantitative methods that can be used for forecasting economic quantities can be roughly divided into four categories :

- subjective methods ;
- approaches based on indicators ;
- time series models ;

- structural

# 4.2.1 Subjective methods

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We speak of a subjective method when we rely exclusively on common sense, on intuition or on the experience of the forecaster, without involving an explicit model. Such predictions are not necessarily inaccurate. However, they can only take into account a limited amount of information, and are based on assumptions that remain implicit, which generally makes them difficult to discuss. These forecasts are also sensitive to the profile and personality of the forecaster.

# 4.2.2 Indicator approaches

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They consist of using indicators available one step ahead of the planned variables, in order to anticipate probable developments in them.

These approaches are mainly used in economic analysis, in particular to try to detect, as early as possible, the ascending and descending phases of activity.

An interesting indicator must have the property of being known in advance with respect to the variable of interest. It must also have a stable (or robust) static relationship with the variable considered.

We then speak of a “leading indicator”. For example, in a small open economy, export

orders are often a harbinger of general business trends.

# 4.2.3 Time series models

These methods are called statistical forecasting methods. The statistical approach consists of build a self-projective model. Thus, forecasts are calculated using only the information contained in the series to be forecast without taking into account other series that may influence its behavior. We project knowledge of the present and the past onto the future. The information allowing the series to be forecast is contained in the series itself, without exogenous input, hence the name endogenous forecast. For example, one can use the history of the gross domestic product series to forecast the future level of gross domestic product. Self-projective methods are effectively applied to very short- term, short-term or medium term forecasts. They can be grouped into two categories.

# 4.2.3.1 Univariate methods

These methods include :

- so-called naive projections ;

- moving average smoothing methods ;
- exponential smoothing methods ;
- the Box-Jenkins method ;
- non-parametric

The main advantage of smoothing methods compared to other statistical methods lies in the ease of their implementation. Smoothing methods represent an alternative to the Box- Jenkins method when the time series are too short (length less than 50) or too volatile

(changes in structure in the data are frequent), or when the number of series to be

planning is important (for example in inventory management) and we cannot devote sufficient analysis time to each of them.

# 4.2.3.2 Multivariate methods

They consist of jointly predicting a group of variables based on knowledge of the past of all the variables in this group. Vector AutoRegressive (VAR) models are the most popular framework of this type, due to their ease of use.

# 4.2.4 Structural modeling

These methods are sometimes referred to as “econometric methods”. They are distinguished by the fact that we seek here to explain at the same time as we foresee. The econometric approach also called an exogenous approach, it is possible to make medium-term or long-term forecasts. In this approach, the model that is built assumes that the observed variable (variable to be predicted or endogenous variable) depends on the explanatory variables (exogenous variables) following a linear relationship or not. The most used econometric models are: the multiple linear regression model, the general linear model, the autoregressive linear model, the staggered lag model, the ARDL model, the NARDL model, the error correction model, binary models Logit/Probit, multinomial models (ordered, unordered, sequential), Tobit model, ARCH model, simultaneous equation model, panel models, vector autoregressive models (Standard VAR, VEC, Bayesian VAR, Structural VAR ), the panel VAR model (PVAR), the counting model, the gravity model, the threshold model, quantile regression, the interaction model, etc. The forecast is calculated from a model explained over the observed period and knowledge of the values taken by the exogenous variables over the periods to be forecast. The approach is called exogenous to the extent that we use exogenous information to forecast the series. For example, one can use the variables investment, human capital, inflation rate, degree of openness, external debt, public spending, exchange rate, population, governance and political instability to forecast gross domestic product. These explanatory variables cited can be useful in developing an accelerated growth strategy. Note that the choice of an econometric model depends on the availability of data and the problem studied.

# The quality of econometric work depends closely on the quality of the theoretical work that preceded it.

We should not expect miracles from econometrics: it is only the art of making good use of data within the framework of a theory, which is already not so bad.

The construction of an econometric model is carried out according to **ten **(10) steps:

- Choice of the endogenous variable (or variable to be predicted)
- Choice of exogenous variables (or explanatory variables)
- Collection of data
- Statistical analysis of data
- Choice of econometric model
- Estimation of the parameters of the chosen econometric model
- Validation of the estimated econometric model
- Economic interpretation of estimated parameters
- Simulation of the validated model
- Prediction of the validated model if the simulation is good

The term forecast in step 10 has a different meaning here from that which it receives in everyday language. This is not about predicting the future. We are in fact seeking to characterise the simulations of economic policies that econometric estimates make possible.

**Forecasting software**

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**“Machines will one day be able to solve all problems, but none of them will ever be**

**able to cause one!”**

Albert Einstein

The forecasting methods mentioned above, except the qualitative methods, require the use of a computer both for their implementation and for the calculation of the forecasts. The most used statistical and econometric software are: EVIEWS, STATA, SPSS, R, PYTHON, SAS, RATS, MATLAB, GAUSS, LIMDEP, STATISTICA, etc.

# 6. Types of variables

We distinguish four types of variables.

# 6.1 A variable in time series

This is the most common case in econometrics and statistics. These are variables observed at regular time intervals.

Example: the gross domestic product of Senegal, over the period from 1980 to 2022.

# 6.2 A variable in cross section

The data are observed at the same time and concern the values taken by the variable for a group of individuals.

Example: the gross domestic product of the eight WAEMU countries for the year 2022.

# 6.3 A panel variable

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The variable represents the values taken by a sample of individuals over several periods.

Example: The gross domestic product of the 8 WAEMU countries, over the period from 1980 to 2022.

# 6.4 A cohort variable

Cohort data is very similar to panel data. They are distinguished from panel data by the constancy of the sample, the individuals surveyed are the same from one period to the next. A cohort designates a group of individuals who experienced the same event during the same period.

Example: The cohort of Senegalese students who passed their baccalaureate in 2014.

Cohorts constitute one of the reference instruments for epidemiological research and in public health. The Ministry of Higher Education and Research has identified them as research infrastructures, recognizing their usefulness to the public health research community, and more broadly to biomedical research as a whole.

# 7. Practice of forecasting in Senegal

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A significant number of structures carry out forecasting activities in Senegal. We can cite, without wishing to be exhaustive, the following structures.

**The National Agency for Statistics and Demography (ANSD)**which carries out forecasting activities for the needs of the Government, public administrations, the private sector, development partners and the public.

**The Department of Forecasting and Economic Studies (DPEE)**of the Ministry of Economy, Planning and Cooperation which includes a macroeconomic projections

**The Directorate of Analysis, Forecasting and Agricultural Statistics (DAPSA)**of the Ministry of Agriculture, Rural Equipment and Food Sovereignty whose mission is to collect, process and disseminate agricultural statistics.**The Directorate of Research and Statistics (DRS)**of the Central Bank of West African States (BCEAO) makes weekly forecasts of the autonomous factors of bank liquidity via a weekly model. Liquidity, in a broad sense, is any liability item on the central bank’s balance sheet that can be used for the settlement of economic Forecasting the liquidity of the banking system is an essential element of the central bank’s liquidity management framework. It allows it to determine the quantity of liquidity to inject (in the event of a deficit) or to withdraw (in the event of a surplus) from the market, with a view to smoothing out unwanted fluctuations which could hamper the effectiveness of monetary policy or lead to a financial instability. The liquidity forecast is carried out on the basis of weekly data from the BCEAO balance sheet.

# 8. Conclusion

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In this article, we presented the forecasting methods. There are numerous studies comparing forecasting methods in the literature. The choice of a method depends on the sector of activity and the desired forecast horizon. No method is better than another, each method has its advantages but also its disadvantages. It should be noted that quantitative methods are not always better than qualitative forecasting, which means that these two methods should not be considered as competing but complementary: formalized forecasting can be an element which, compared to intuition, allows us to generate forecast data. As the “ideal” forecasting method does not exist, some authors recommend combining several instead of using a single technique. Statistical forecasting methods make it difficult to develop a qualitative discourse, a “story” of the forecast: major expectations of the sponsors of a forecast. This need for history, for qualitative discourse, means that we must favor econometric methods for a better forecast of certain economic quantities such as the rate of economic growth.