Lecture#15

Forecasting methods

The Bonch-Bruevich Saint-Petersburg State University of Telecommunications

Series of lectures “Telecommunication networks”

Instructor: Prof. Nikolay Sokolov, e-mail: sokolov@niits.ru

Main algorithm

Problem statement

Information gathering

Choice of methodology

Forecasting

Analysis of the results

Decision making

Usage of the forecast

Possible approaches

Another classification:

•objective methods (QUANTITATIVE FORECASTING METHODS)

•subjective methods (QUALITATIVE FORECASTING METHODS)

•combined methods

Considered objects

Network and its attributes

Services and corresponding traffic (some parameters)

QoS (including dependability)

Capacity of the trunks

Throughput of the switches

Forecasting and time

Main attributes

QoS parameters Services and traffic Throughput and

capacity

Short-term forecast Long-term forecastMedium-term forecast

Forecasting and lifetime

Lifetime of the access network

Lifetime of the switching equipment Post-NGN time

Lifetime of the terminals

Methods of the forecasting (1)

Genius forecasting – This method is based on a combination of intuition, insight, and luck. Psychics and crystal ball readers are the most extreme case of genius forecasting. Their forecasts are based exclusively on intuition. Science fiction writers have sometimes described new technologies with uncanny accuracy.There are many examples where men and women have been remarkable successful at predicting the future. There are also many examples of wrong forecasts. The weakness in genius forecasting is that its impossible to recognize a good forecast until the forecast has come to pass.Some psychic individuals are capable of producing consistently accurate forecasts. Mainstream science generally ignores this fact because the implications are simply too difficult to accept. Our current understanding of reality is not adequate to explain this phenomena.

Methods of the forecasting (2a) Trend extrapolation – These methods examine trends and cycles in historical data, and then use mathematical techniques to extrapolate to the future. The assumption of all these techniques is that the forces responsible for creating the past, will continue to operate in the future. This is often a valid assumption when forecasting short term horizons, but it falls short when creating medium and long term forecasts. The further out we attempt to forecast, the less certain we become of the forecast. There are many mathematical models for forecasting trends and cycles. Choosing an appropriate model for a particular forecasting application depends on the historical data. The study of the historical data is called exploratory data analysis. Its purpose is to identify the trends and cycles in the data so that appropriate model can be chosen.

Methods of the forecasting (2b) The most common mathematical models involve various forms of weighted smoothing methods. Another type of model is known as decomposition. This technique mathematically separates the historical data into trend, seasonal and random components. A process known as a "turning point analysis" is used to produce forecasts. ARIMA models such as adaptive filtering and Box-Jenkins analysis constitute a third class of mathematical model, while simple linear regression and curve fitting is a fourth.The common feature of these mathematical models is that historical data is the only criteria for producing a forecast. One might think then, that if two people use the same model on the same data that the forecasts will also be the same, but this is not necessarily the case. Mathematical models involve smoothing constants, coefficients and other parameters that must be decided by the forecaster. To a large degree, the choice of these parameters determines the forecast.

Methods of the forecasting (3a)

Consensus methods – Forecasting complex systems often involves seeking expert opinions from more than one person. Each is an expert in his own discipline, and it is through the synthesis of these opinions that a final forecast is obtained.One method of arriving at a consensus forecast would be to put all the experts in a room and let them "argue it out". This method falls short because the situation is often controlled by those individuals that have the best group interaction and persuasion skills.

Methods of the forecasting (3b)

A better method is known as the Delphi technique. This method seeks to rectify the problems of face-to-face confrontation in the group, so the responses and respondents remain anonymous. The classical technique proceeds in well-defined sequence. In the first round, the participants are asked to write their predictions. Their responses are collated and a copy is given to each of the participants. The participants are asked to comment on extreme views and to defend or modify their original opinion based on what the other participants have written. Again, the answers are collated and fed back to the participants. In the final round, participants are asked to reassess their original opinion in view of those presented by other participants.The Delphi method general produces a rapid narrowing of opinions. It provides more accurate forecasts than group discussions. Furthermore, a face-to-face discussion following the application of the Delphi method generally degrades accuracy.

Methods of the forecasting (4) Simulation methods – Simulation methods involve using analogs to model complex systems. These analogs can take on several forms. A mechanical analog might be a wind tunnel for modeling aircraft performance. An equation to predict an economic measure would be a mathematical analog. A metaphorical analog could involve using the growth of a bacteria colony to describe human population growth. Game analogs are used where the interactions of the players are symbolic of social interactions.Mathematical analogs are of particular importance to futures research. They have been extremely successful in many forecasting applications, especially in the physical sciences. In the social sciences however, their accuracy is somewhat diminished. The extraordinary complexity of social systems makes it difficult to include all the relevant factors in any model.

Methods of the forecasting (5)

Scenario – The scenario is a narrative forecast that describes a potential course of events. Like the cross-impact matrix method, it recognizes the interrelationships of system components. The scenario describes the impact on the other components and the system as a whole. It is a "script" for defining the particulars of an uncertain future. Scenarios consider events such as new technology, population shifts, and changing consumer preferences. Scenarios are written as long-term predictions of the future. A most likely scenario is usually written, along with at least one optimistic and one pessimistic scenario. The primary purpose of a scenario is to provoke thinking of decision makers who can then posture themselves for the fulfillment of the scenario(s). The three scenarios force decision makers to ask: 1) Can we survive the pessimistic scenario, 2) Are we happy with the most likely scenario, and 3) Are we ready to take advantage of the optimistic scenario?

Methods of the forecasting (6) Decision trees – Decision trees originally evolved as graphical devices to help illustrate the structural relationships between alternative choices. These trees were originally presented as a series of yes/no (dichotomous) choices. As our understanding of feedback loops improved, decision trees became more complex. Their structure became the foundation of computer flow charts. Computer technology has made it possible create very complex decision trees consisting of many subsystems and feedback loops. Decisions are no longer limited to dichotomies; they now involve assigning probabilities to the likelihood of any particular path. Decision theory is based on the concept that an expected value of a discrete variable can be calculated as the average value for that variable. The expected value is especially useful for decision makers because it represents the most likely value based on the probabilities of the distribution function.

Methods of the forecasting (7) Combining ForecastsIt seems clear that no forecasting technique is appropriate for all situations. There is substantial evidence to demonstrate that combining individual forecasts produces gains in forecasting accuracy. There is also evidence that adding quantitative forecasts to qualitative forecasts reduces accuracy. Research has not yet revealed the conditions or methods for the optimal combinations of forecasts. Judgmental forecasting usually involves combining forecasts from more than one source. Informed forecasting begins with a set of key assumptions and then uses a combination of historical data and expert opinions. Involved forecasting seeks the opinions of all those directly affected by the forecast (e.g., the sales force would be included in the forecasting process). These techniques generally produce higher quality forecasts than can be attained from a single source. Combining forecasts provides us with a way to compensate for deficiencies in a forecasting technique. By selecting complementary methods, the shortcomings of one technique can be offset by the advantages of another.

Do forecasts create the future (1)

A paradox exists in preparing a forecast. If a forecast results in an adaptive change, then the accuracy of the forecast might be modified by that change. Suppose the forecast is that our business will experience a ten percent drop in sales next month. We adapt by increasing our promotion effort to compensate for the predicted loss. This action, in turn, could affect our sales, thus changing the accuracy of the original forecast.Many futurists (de Jouvenel, Dublin, Pohl, and others) have expressed the idea that the way we contemplate the future is an expression of our desire to create that future. Physicist Dennis Gabor, discoverer of holography, claimed that the future is invented, not predicted. The implication is that the future is an expression of our present thoughts. The idea that we create our own reality is not a new concept. It is easy to imagine how thoughts might translate into actions that affect the future.

Do forecasts create the future (2)

Biblical records speak of faith as the force that could move mountains. Recent research in quantum mechanics suggests that this may be more than just a philosophical concept. At a quantum level, matter itself might simply be a manifestation of thought. Electrons and other subatomic particles seem to exist only when physicists are looking for them, otherwise, they exist only as energy.An incredible discovery was made at the University of Paris in 1982. A team of researchers lead by Alain Aspect found that under certain conditions, electrons could instantaneously communicate with each other across long distances. The results of this experiment have been confirmed by many other researchers, although the implications are exceedingly hard to accept. Three explanations are possible: 1) information can be transferred at speeds exceeding the speed of light, 2) the passage of time is an illusion, 3) the distance between the electrons is an illusion. All three explanations rock our perception of reality.

Simple linear regression Some variables are associated with each other by linear dependence. This law can be conditioned by the nature of analyzed variables. In a number of cases assumption about linear dependence is acceptable on a small interval of the approximating function argument changing. Linear dependence of two variables X and Y may be determined with the help of correlation analysis. Strength of linear dependence is determined by correlation coefficient r . If there are n values for the pairs of studied variables, then sample correlation coefficient will be evaluated in the following way:

2 22 2

n XY X Yr

n X X n Y Y

.

If 1r , then studied values are related to each other by the utter negative dependence. On the contrary, when 1r then the utter positive dependence between studied values is determined. The corresponding examples are shown on the figure – variants (a) and (b). Next two variants illustrate cases of not utter linear dependence (positive and negative). They are of most interest from the practical point of view. Variant (e) represents the example of nonlinear dependence. In the process of information research, the absence of any dependence can be determined as shown in variant (f).

Correlation examples Y

X

Y

X

a) utter positive linear b) utter negative linear

Y

X

Y

X

c) not utter positive linear d) not utter negative linear

Y

X

Y

X

e) Nonlinear f) No dependence

This methods can be directly used for other functions Y=f(x). For instance, value Y may be defined as log(Z). In this case linear function will be used as well.

There are some additional possibilities of the linear regression application for forecasting.

Smoothing methods and moving average Three groups of time series forecasting methods are considered: naïve, averaging and smoothing. Naïve method is based on the assumption, that future is best described by the latest changes. Averaging method allows develop a forecast, basing only on average value of previous observations. Smoothing methods base on the averaging of accumulated data with the help of the weighting coefficients set.Proper approach to the estimation of forecasting method includes several stages. The five important stages should be distinguished:1. Close inspection of the studied object or process nature for the choice of adequate forecasting method;2. Discrimination of two groups among available data for the development of forecasts and for check-up of obtained results; 3. Initial data refining of basic data for the purpose of error detection;4. Development of forecasts and estimation of reliability of the obtained results; 5. Interpretation of the obtained results for elaboration of the detailed forecasts (if needed).

Main approach If the initial data is represented with a small set of information, then naïve method is considered the only possible forecasting method. When using naïve forecasting, it is considered that the last period predicts the future best of all. The simple model of naïve forecasting is based on the following formula:

( 1) ( )fY t Y t .

Value ( 1)fY t represents forecast, made at the time t (initial prediction) for the time 1t .

For each period of time naïve forecast is the observation directly preceding it. The one hundred percent weight is assigned to the current observed value in the series. Therefore naïve forecast is frequently called “forecast without changes”. In fact, all the previous observations are discarded when using naïve forecasting. In this case it is important to estimate the random fluctuation of investigated object or process. Forecast error 1tr is calculated by obvious formula:

1 ( 1) ( 1)t fr Y t Y t .

Statistics analysis of values tr allows draw a conclusion about possibility of naive method utilization for the investigated object or process. It is obvious, that when sum of jr values

trends to zero, naïve forecasting application can be justified. On the other hand, condition of the total error closeness to zero can not be considered sufficient. It is also necessary, that maximal value of jr does not exceed the chosen beforehand error threshold. If study of jr

series indicates the presence of trend for the investigated process or object, then naïve method is not applicable to obtaining forecasting estimates.

Trend extrapolation (1)

Time

Analyzed processes

tr t0 tf

F2(t)

F1(t)

Trends of functions F1(t) and F2(t)

Trend extrapolation (2)

Year

0 1 2 3 4 5 6 7 8 9 10 11 12 13

Frequency bar chart N(i) and approximation F(t)

N(6)

N(10)F(t)

There is no data

For

ecas

t per

iod

Trend extrapolation (3)

Year

0 1 2 3 4 5 6 7 8 9 10 11 12 13

Frequency bar chart N(i) and approximation F(t)

N(6) N(10)

F(t)

There is no data

Trend extrapolation (4)

Year

Results

0 1 2 3 4 5 6 7 8 9 10 11 12 13

{X1} {X2} {X3}

F(t)

Trend extrapolation (5)

2

1

( )N

i ii

f x y min

x

f(x)

x

f(x)

x

f(x)

A

Estimated function

a) First example b) Second example c) Third example

Approximation ApproximationApproximation

Estimated function Estimated function

Trend extrapolation (6)

Time

PSTN capacity

T1 T2T0

F(t)

F2(t)

F1(t)

100%

Trend extrapolation (7)

Income generated by telephony

Year

90%

85%

80%

75%

70%2002 2003 2004 2005 2006 2007 2008 2009 2010

Method of Box-Jenkins (ARIMA)Changes of an object or process in different periods of time are frequently interrelated. This dependence is measured with the help of the autocorrelation coefficient. For the k periods delay, this coefficient kr between observations tY and

t kY is evaluated by the following formula:

1

2

1

n

t t kt k

k n

tt

Y Y Y Yr

Y Y

.

Upper limit of summation n determines a total number of observations. Sometimes for forecasting, the models are analyzed in which a time structure of data is used. Models of AutoRegressive Integrated Moving Average (ARIMA) are good at describing both stationary and non stationary time series. In stationary series results change in relation to a certain mean value. In nonstationary series there is no constant mean value. In ARIMA models, the information contained in studied initial data is used for the forecasting. ARIMA model relies on autocorrelated structure of data. G.E.P. Box and G.M. Jenkins have made an important contribution to the research of these models. Due to this reason, the construction of ARIMA models and forecasting on their basis are often called Method of Box-Jenkins.

Typical mistakes

Time

Prototype system

Valid data

extrapolationbifurcation point

reality situation(first scenario)

reality situation(second scenario)

Example of Delphi technique

The question is: how many Y-terminals will be installed up to 2000 year?

1. Ten experts sent the following estimations: 1 million (5 opinions), 1.2 million (3 opinions), 1.4 million (2 opinions).

2. Mean value is

(1) 1.0 5 1.2 3 1.4 21.14

10N

3. Variance is2 2 2

2 (1.0 1.14) 5 (1.2 1.14) 3 (1.4 1.14) 20.0244

10σ

4. Coefficient of variation is (1)

0.137σ

kN

Conclusion: forecast is stable.

Example of “similar forecast”1. We are needed to make a forecast about broadband

access market in the developing country X – FX(t).

2. We know the history concerning similar process in the developed country S – FS(t).

3. Let us assume: DX and DS are gross domestic product per capita in considered countries, HX and HS are tariffs for the estimated service, z is difference of the beginning of the rollout.

4. In this case forecast may be presented by the following expression:

( ) .X XX S

S S

D HF t F t z

D H

Reasons: cycles in the technologies

Substantial stages of telephony development

Time

Emergence of the telephone communications

80s of the XIX century

Automation of the telephone communications network

20s of the XX century

Utilization of the program management

60s of the XX century

Change of the transmission and switching technologies

Beginning of the XXI century

Forecasting process management (1)Notable qualitative changes are happening in infocommunication system which are reflected on statement of forecasting problems, methods of their solution, and interpretation of obtained results. Two important aspects of initial data gathering should be taken into account when stating forecasting problems:In a number of cases principles of usual data representation are changing, which can lead to occurrence of errors (in particular this situation sometimes happens when estimating traffic in IP-telephony);For new types of services there is a necessity to have the data which was not gathered because of its practical value's absence. Therefore forecasting process management includes revision of the initial data’s gathering and processing principles. On the whole, it should be noted that the initial data’s gathering and processing stage are very important for the increase of forecast’s accuracy, and the essence of these operations can change frequently.

Forecasting process management (2)Next aspect of forecasting process management lies in precise statement of corresponding problems with taking into account technical and technological changes, peculiar to infocommunication systems. Changes (sometimes radical) happen in the price ratio of single components of technical facilities. About thirty years ago main memory costs were very high. Many researches were related to minimization of necessary memory. Significant part of forecasts was also related to RAM memory space requirements. At the present time the situation has changed. Now the actual forecasts are those concerning the most expensive components of infocommunication system.Prognostic estimates are to a greater extent shifting to the field of economic indicators. This stimulates utilization of interdisciplinary approaches to the forecasting. Besides, for some forecasts analysis of global trends, determined by forming of informational society, integration of national economics, and the factors similar to these, becomes relevant.

Some forecasts (1)

Some forecasts (2)

Some forecasts (3)

Note

The book David S. Walonick, Ph.D.“An Overview of Forecasting Methodology”

was used for preparation of some slides

Instructor: Prof. Nikolay Sokolov, e-mail: sokolov@niits.ru

Questions?

Forecasting methods