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The forecast error, basics

In general, a time series forecasting model can be

µ θ

defined as y = (I , ) + e (the latter being

t+h h t t+h

the usual forecast error h-step ahead). Of course,

µ θ

the forecast f = (I , ) is feasible only if the

t+h|t h t

practitioner…

1. selects the predictors (data): I

t µ

2. approximates the function (model): (…)

h

θ µ

3. estimates parameters in model (…) using I

h t

These choices will contribute to define the

forecast error, which can be decomposed in three

parts (see slides below). 9

Decomposition of the forecast error

[ ]

( )

− = − +

y f y E y I

+ + + +

t h t h

|

t t h t h t

[ ]

( )

[ ]

( ) ( ) ( )

µ ϑ µ ϑ µ ϑ

− + − ˆ

E y I I , I , I ,

+

t h t h t h t h t

f is the h-period ahead forecast of y (with h = 1, 2, …).

t+h|t

I is the information set (data) on which the forecast is based

t ( )

E y I is the (nonlinear) unknown conditional expectation

+ ( )

t h t µ ϑ

I ,

which can be approximated by the model ( )

h t

µ ϑ

ˆ

I ,

f is based (equal to) the estimated model h t

t+h|t 10 5

[ ]

( )

y E y I

The first component of error + +

t h t h t

is the deviation of the actual outcome from its

(unknown) conditional expectations functions,

and is related to the stochastic nature of the link

between y and I

t+h t

As such, it is the source of forecast error that

cannot be eliminated.

All forecasts, no matter how, good will have

forecast errors because of future unknowable

events: “we don’t know what we don’t know”. 11

[ ]

( ) ( )

µ ϑ

E y I I ,

The 2nd component of error +

t h t h t

is the contribution of model misspecification, it

represents the error arising from using a model to

approximate the (unknown) conditional

expectations function.

As such, it measures the source of forecast error

that depends on model approximation.

The use of flexible/complex models, with many

parameters, reduces the approximation error

Simple models, such as the AR(p), increase this

source of error. 12 6

[ ]

( )

( )

µ ϑ µ ϑ

− ˆ

I , I ,

The 3rd component of error h t h t

arises from the deviation of the actual (and

unknown) parameter values to their estimates

obtained from the data.

It is the parameters’ estimation error (known

uncertainty).

The use of flexible/complex models, with many

parameters, amplifies the sources of this error.

Simple models have few parameters, and entail

smaller estimation errors. 13

Summarising the trade-off

− =

y f

+ + The first component of error

t h t h

|

t

[ ]

( )

− + is variable/period specific

y E y I

+ +

t h t h t

[ ]

( ) ( )

µ ϑ

− +

E y I I ,

+

t h t h t

[ ]

( ) The last two components

( )

µ ϑ µ ϑ

− ˆ of error entail a trade-off

I , I ,

h t h t between simple and

complex models 14 7

Unknown (model) uncertainty

Besides the known uncertainty in the parameter

estimates (the 3rd component of the forecast error),

the unknown extent of the model specification error

is only a part of the 2nd component above.

In fact, another major problem is when the future

ceases to resemble the past. In this context, both the

mean and the form of the distribution of the shocks

can shift. As a result: (a) the forecasting ability

summary measures break; (b) forecast intervals

(density) are incorrect.

Adaptation can avoid systematic forecast failure to

the unpredictable shock as occurred) a

avoid (after

sequence of poor forecasts. 15

Remedies…

Potential solution to model shifts are:

1. Update parameter estimates & make Chow tests

2. Modeling intercept shifts with dummy variables.

3. Intercept corrections, i.e. constant (residual)

adjustments.

4. Differencing models exploits random walk

adaptability

5. Nonlinear models with possible further regime

changes. Dream: to find “early warning” signals,

observing leading regions, sectors. 16 8

Data accuracy summary

Data accuracy depends on the economic phenomenon we

want to forecast. In this, we cannot do almost nothing.

This part of variable’s predictability depends on its

“economic nature” and measurement issues (e.g. errors,

timeliness, revisions, etc.), and on the forecast period.

Given the forecast target, modeling involves the big

issue of the amount of information used, i.e. the

dimension of the predictor data-set (which involves the

simple/complex models trade-off)

Finally, the researcher’s judgment about the forecast

results and her modeling skills may limit forecast

failures issue due to shift/breaks. 17

18 9


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DESCRIZIONE DISPENSA

Materiale didattico per il corso di Econometria per la politica economia del prof. Roberto Golinelli. Trattasi di slides in lingua inglese a cura del docente, all'interno delle quali sono affrontati i seguenti argomenti: l'abilità previsiva; errori di previsione; previsioni fallimentari; il vantaggio dell'overdifferentiation.


DETTAGLI
Corso di laurea: Corso di laurea magistrale in politica amministrazione e organizzazione
SSD:
Università: Bologna - Unibo
A.A.: 2011-2012

I contenuti di questa pagina costituiscono rielaborazioni personali del Publisher Atreyu di informazioni apprese con la frequenza delle lezioni di Econometria per la politica economica e studio autonomo di eventuali libri di riferimento in preparazione dell'esame finale o della tesi. Non devono intendersi come materiale ufficiale dell'università Bologna - Unibo o del prof Golinelli Roberto.

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