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NBS8301 SH Forecasting NEW2-2

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Module

Managerial Economics and Organisational Architecture (NBS8301)

University

Newcastle University

Academic year: 2022/2023

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FORECASTING.

Please read in conjunction with Handout

####### 1. TIME SERIES MODELS

The basis of time-series forecasting is that by studying past values of a variable, one can gain an insight into future values in that variable, i.

Yt = f (Yt-1,Yt-2,Yt-3,.....)

Or alternatively, it can be assumed that Yt is a deterministic function of time (t):

Yt = f (t)

Linear trend model.

If we believe that a variable will increase in constant absolute amounts each time period, we can estimate coefficients for,

Yt = b 1 + b 2 .t

You regress current and past values of Y against time t (e. t = year or t = time counter: 1,2,3,...).

If we obtained,

Yt = 27 + 3 t

we could predict that the value of Y in the next period (t+1) will be 3 units higher than the value of Y in the current period (t).

Exponential growth model.

This model implies that the value of Y grows with constant percentage increases, rather than constant absolute increases.

Yt = A

r

where A, r = parameters of the model; e = base for natural logs = 2....)

The model parameters can be estimated by OLS regression

lnYt = lnA + r

lnYt = b 1 + b 2 t

FIG. 14 P&R (Handout 1) NB. A = eb

Autoregressive trend model.

Yt = c 1 + c 2 Yt-

FIG 14 P&R (Handout 1)

Quadratic trend model.

Yt = c 1 + c2 + c3

FIG. 14 P&R (Handout 1)

Moving average model.

Yt = Mean{ Yt-1 , Yt-2 , Yt-3 , Yt-4....}

####### 2. ECONOMIC LEADING (BAROMETRIC) INDICATORS.

Please read in conjunction with Handout 2

In addition to forecasting accounting/economic numbers using models, one can also use leading or barometric indicators. Barometric indicators are variables which typically lead movements in the variable(s) in which we are interested. Therefore, by studying the time series of the barometric indicator, we can predict future changes in the variables in which we are interested.

Barometric indicators:  Leading series indicators.  Composite leading indices.  The diffusion index.

(a) Leading series indicators.

A single lead series is used to predict future changes in the variable of interest. The lead variable will experience turning points in advance of turning points in the variable of interest.

For example, it may be that proportionate changes in steel production precede proportionate changes in coal shipments. The lag is the time it takes for steel producers to become aware of the changes in demand for their product and to organise a reduction in their orders of coal.

Single series indicators are unlikely to consistently lead the variables they are intended to, and are unlikely to lead by a consistent lead period because of unexpected economic changes and random factors.

(b) Composite leading indices.

To avoid the problem of the unreliability of the single indicator, composite leading indices have been formed. Several leading indicators are aggregated to form an index, with the result that random movements in any one series tend to be offset by opposite movements in one or more of the other series. The composite indicator is a more reliable indicator of future changes and turning points than the single series.

The National Bureau of Economic Research (NBER) identifies indicators for US GNP (some single, some composite).

Leading: Average work week (production workers) Index of net business formation New orders (durable goods industries) Stock prices (500 common stocks, S&P500) Corporate profits/earnings Money supply

Coincident: Employees (non-agricultural) Industrial production Sales in retail stores

Lagging: Unemployment rate Business expenditure (new plant & equipment) Labour cost per unit of output (manufacturing)

The use of coincident and lagging indicators is their ability to indicate when the peak or trough has actually passed.

Our main focus is on LEADING indicators because these will aid our forecasting.

Handout 2 Table 11 provides a list of US leading indicators published in the 1980s – these indicators are reviewed regularly and can be removed if they are no longer working well.

####### 3. APPLICATIONS OF FORECASTING MODELS TO ACCOUNTING

####### EARNINGS NUMBERS

Forecasting earnings using only past earnings data:

Watts and Leftwich 1977 JAR;

NB. This is quite a complicated paper – you don’t need to understand all of it – just get the basic story that the RW model performs very well relative to more sophisticated Box-Jenkins (‘identified’) models.

RW model is 1st or =1st in three out of four samples.

Concludes: “The ability of random walk models to "outpredict" the identified Box-Jenkins models suggests that the random walk is still a good description of the process generating annual earnings in general, and for individual firms.”

Patz 1989 ABR.

This paper looks at a variety of simple models for forecasting company earnings numbers and different error metrics, plus forecasts from professional analysts.

Although professional (Wells Fargo) analysts tend to be more accurate, results can be sensitive to the error metric chosen. Four error metrics used:

The RW model (model 3) takes a different ranking for each of the four error metrics, from 1st place (most accurate) to 4th place.

Expanding the information set to include macro-economic data:

Chant 1980 JF

Chant adjusts random walk forecasts to take account of current trends in economic leading indicators. Models assume that indicators (money supply, stock index, bank loans) lead general economic activity (and company profits) by one year.

The percentage change in the indicator from t-1 to t is mapped onto the expected change in company earnings from t to t+1.

Forecasting performance is as follows:

Only the money supply model performs better (lower rank) than the (naive) random walk model.

Hussain ABR1998.

Extends Chant’s study to look at different lead times and UK data (rather than US) – similar findings.

Finds that one-year lead/lag best for money supply models and that ‘broad’ money supply M4 is more useful than ‘narrow’ measures M0 and M2.

Also compares money supply model forecasts with those of professional analysts. Analysts’ superiority to the models is greater for larger firms, and at shorter forecasting horizons.

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