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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: il modello statistico, le previsioni e l'informazione; previsione e disaggregazione;... Vedi di più

Esame di Econometria per la politica economica docente Prof. R. Golinelli

Anteprima

ESTRATTO DOCUMENTO

vintage, v

1 2 3 4 f

period, t T+1 1 T+2 2 T+3 3 T+4 4 T+f f

y y y y .... y

1 1 1 1 1 1

T 1 T+1 2 T+2 3 T+3 4 T+f-1 f

2 y y y y .... y

2 2 2 2 2

T-1 1 T 2 T+1 3 T+2 4 T+f-2 f

3 y y y y .... y

3 3 3 3 3

T-2 1 T-1 2 T 3 T+1 4 T+f-3 f

4 y y y y .... y

4 4 4 4 4

.... .... .... .... .... .... ....

3 1 4 2 5 3 6 4 f+2 f

T-1 y y y y .... y

T-1 T-1 T-1 T-1 T-1

2 1 3 2 4 3 5 4 f+1 f

T y y y y .... y

T T T T T

1 1 2 2 3 3 4 4 f f

T+1 y y y y .... y

T+1 T+1 T+1 T+1 T+1

1 2 2 3 3 4 f-1 f

T+2 n.a. y y y .... y

T+2 T+2 T+2 T+2

1 3 2 4 f-2 f

T+3 n.a. n.a. y y .... y

T+3 T+3 T+3

1 4 f-3 f

T+4 n.a. n.a. n.a. y .... y

T+4 T+4

.... .... .... .... .... .... ....

st

1 release 1 f

T+f n.a. n.a. n.a. n.a. .... y T+f

nd

2 vintage Latest available

vintage 15

A real-time data-set

Alternative data to forecast

v

Vintage y series represent the state-of-art at the time of

publication. Observations are homogeneous over t (but

not in quality: old data are better than recent ones)

v

y growth rate calculation is straightforward:

×

o v o v o’ v

dy = 100 ( y / y – 1)

t t t-1

o

Release y series includes data revised for the same

number of times which come from different vintages;

observations are not homogeneous over t (but they are

in quality)

o o v

y growth rates need collecting dy (growth-within)

t

→ What is the effect of data revisions on the simulated

models predicting ability? 16 8

Comparing alternative forecasts

• We know how to compute and describe forecast errors

from pseudo out-of-sample exercises. A number of

alternative summary indicators can be obtained.

Comparisons may be only descriptive.

• Idea: our forecasts should perform at least as well as the

simplest times series models from which predictions could

have been derived. But, how to make inferences on the

statistical significance of the two sets of errors differences?

• Two testing procedures are surveyed here:

The Giacomini-White (2006) test for equal

conditional predictive ability of alternative

forecasting methods.

The Fair-Shiller (1990) test for comparing

information from alternative forecasting models.

17

Giacomini and White test

• To explore the performance of alternative ways to

forecast the target, i.e. different “forecasting methods,

which include the models as well as the estimation

procedures and the possible choices of estimation

(rolling, limited memory) windows”. GW (2006, p. 1549)

• Null hypothesis: one cannot predict which forecasting

method will be more accurate at the forecast target date

t+h using the available information set at time t. χ

2

• Under the null hypothesis, the test is distributed as a

with q degrees of freedom; q is the dimension of the test

function that ranges from the simplest case where only

the constant is contained (q = 1), to cases where other

variables (including lags) are included in order to help

distinguish between the forecasting performance of the

two methods (q > 1). 18 9

Compute GW test

• Given the sequences of forecasts errors of two

alternative forecast methods a and b ( e and

a t+h|t

e ), choose the loss function (absolute errors,

b t+h|t

or quadratic errors) in order to define the pivot:

= −

pivot e e or

+ + +

t h |

t a t h |

t b t h |

t

= −

2 2

pivot e e

+ + +

t h |

t a t h |

t b t h |

t

• Regress a column of ones against pivot

× 2

• GW statistic is equal to T R of previous

regression. 19

Fair and Shiller test

• FS’s test is related to the literature on encompassing tests

and the literature on the optimal combination of forecasts.

• Given the sequences of forecasts from 2 alternative models

f and f ), make the regression:

a and b ( a t+h|t b t+h|t

α β γ

− = + − + − +

y y ( f y ) ( f y ) u

+ + + +

t h t t h

|

t t t h

|

t t t h

a b

β γ

• Test the two nulls: =0 and =0. In the first case model a’s

forecasts contain no information relevant to forecasting h

periods ahead not in the constant term and in model b. The

same for the other test. If both forecasts contain good

independent information, they both should be significant.

• The error term u is likely to be heteroskedastic, then t-

t+h

statistics must use Newey-West HAC (or White) consistent

standard errors. 20 10

Rationality tests

• Forecast comparison determines which one has

(significantly) smaller errors. But, how to improve upon

the observed record?

• Rationality: predictions are optimal with regard to a

particular information set. Three basic inferences:

1. test for bias and weak form of informational efficiency:

α β ε α β

y = + f + (H : =0, =1); or a more

t+h t+h|t t+h 0 α ε α

– f = + (H : =0);

restrictive version: y t+h t+h|t t+h 0

2. errors e are MA(h-1). White noise if h=1.

t+h|t

3. forecast efficiency: errors are not correlated with any

information that was known at t

• Caveats: (a) beware the unit roots! (b) if the forecaster’s

loss function is asymmetric, rationality even if ME≠0

21

Combining forecasts

• It could be (and in practice it is) that most forecasting

methods yield similar results; it could be that the

forecasting performance varies over time…

• The clear implication is that there is not consistent best

performer.

• If there is not such “always best” forecasting approach, it

is quite natural to determine whether a combination of

forecasts could produce better results.

• In this context, forecast combination can be seen as a test

of the specification of the alternative models: a better

performing combination would suggest both models are

not encompassing each other (there is useful information

in both models and both models are misspecified). See

also the efficiency rationality test with a second forecast

added. 22 11

• Given the sequences of forecasts from 2 alternative models

a and b ( f and f ), how should the two forecasts

a t+h|t b t+h|t

combined to form a third forecast? Bates-Granger (1969)

suggest to regress the target on a and b forecasts and use

parameter estimates as weights.

• Problem with weights: when in regression there are n>2

forecasts (even only moderately large), better to use ad

hoc averages (i.e. with not estimated weights) such as:

sample means, medians, trimmed means, etc.

• In misspecified models, averages tend to perform better

than the majority of the single components (very often

better than all the components).

• Forecast average puzzle! 23

• Better to combine forecasts or to improve the model?

• If the alternative forecasts are the only available

information, then it is better to combine them.

• If the two information sets (upon which the two forecasts

are based) are available, better to combine the information

sets and try to improve the whole modelling process.

• Follow Clive Granger: “I always thought of combining as

the more pragmatic way of producing better forecasts

which should also indicate that there is available a better

way of actually producing a model”.

• However, averaging may produce inferior forecasts if the

different models use the same set of information, and

some of these encompass others. Whether it does or not

mainly depends on how much structural change has

occurred over the sample. 24 12

Does managers’ intuition plays a role in forecasting?

Managers cannot resist manually adjusting forecasts from

statistical models: MGF = STF + ADJ. But, what is the basis

for and how effective are their adjustments?

Can such adjustment process be improved? If a judgmental

bootstrapping equation exists, we can decompose MGF in the

predictable and in the unpredictable components. Since usually

simple models of expert decisions outperform them, often the

answer is “no”: on balance, the machines win!

β β β β

MGF = + STF + Y + (Y - STF ) +

t 0 1 t 2,k t-k 3,k t-k t-k

β (Y - MGF ) +β (MGF - STF ) + INTU

4,k t-k t-k 5,k t-k t-k t

where k lags are selected to have only known explanatory variables in t.

Results: ADJ are effective, but there is little left for INTU once

managers’ forecasts are modeled by a bootstrap equation. 25

Empirical papers (4/2/2010)

Aggregate vs disaggregate

Baffigi-Golinelli-Parigi (2004) & Golinelli-Pastorello (2002)

Bridge Models, nowcast and real time data

Golinelli- Parigi (2007) & Golinelli-Parigi (2008)

Comparing BM and Factor-based models (FM)

Bulligan-Golinelli-Parigi (2009) 26 13


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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: il modello statistico, le previsioni e l'informazione; previsione e disaggregazione; modelli factor based; il test di Giacomini e White; il test di razionalità.


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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