p4_bc.pdf

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Business

Business cycle

cycle indicators

indicators..

Methods

Methods,

, applications

applications, and

, and limits

limits..

Enrique M. Quilis

Macroeconomic Research Department

Ministry of Economy and Finance. Spain.

[email protected]

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• Any views expressed herein are my own and

not necessarily those of the Spanish

Ministry of Economy and Finance.

• I owe Ana Abad and Juan Bógalo thanks for

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OVERVIEW

• General objective of a system of cyclical

indicators.

E.M. Quilis Workshop on Leading Indicators

indicators.

• A methodological proposal.

• Case study: Stock Index as leading indicator of

Industrial Production.

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GENERAL OBJECTIVE

What is the business cycle?

• Burns and Mitchell (1946):

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GENERAL OBJECTIVE

Measuring the business cycle

• Amplitude: size of the fluctuations.

• Persistence: speed of mean-reversion.

E.M. Quilis Workshop on Leading Indicators 5

• Persistence: speed of mean-reversion.

• Diffusion: linkages across a vector of time series,

static as well as dynamic.

• Others: asymmetry, specific role of turning points,

second order turning points, etc.

full anatomy of

the business cycle, see Camacho et al. (2005).

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GENERAL OBJECTIVE

What is not business cycle measurement

:

• Business cycle measurement is different from the

measurement of the

levels

of economic activity according to a

theoretical model (e.g., National Accounts).

• Business cycle measurement is not directly related to the

quantification of the

growth

patterns of main economic

aggregates (e.g., short-term economic activity indexes).

• Business cycle measurement is not

econometric

modeling

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GENERAL OBJECTIVE

What is not business cycle measurement

:

• But… take it easy:

–

National Accounts may play a role in a system of cyclical

indicators, although the overlap should be small if we want

to design truly independent measurement devices.

–

Growth filters (rates of growth) have some common

features with cyclical filters (e.g., detrending).

–

Econometric techniques, specially dynamic factor models

and BVAR models, have a clear quantitative function in

business cycle analysis.

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GENERAL VIEW: Basic map

Indicators

Filtering

Dating

Reference

Cycle

Dating

Cyclical

Classification

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Indicators

Filtering

Dating

Reference

Cycle

Dating

Cyclical

Classification

Composition

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GENERAL RULES (Burns-Mitchell)

• Economic significance.

• Data quality.

• Timeliness.

• Cyclical stability.

• Small irregularity.

• Diversification of sources both across sectors (demand,

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GENERAL RULES

• Use all the available information, from all available sources,

and using all the available sample (data, data, and more data).

• Monthly data rather than quarterly data. Weekly or daily

frequency even better.

• Do not impose a priori classifactions. Use loose definitions.

Business cycle measurement is empirical by nature.

• Financial-monetary indicators should play an important role,

due to their forward-looking nature. But do not overstate

them (not all the cycles are linked to them!!).

• Administrative information (e.g., from the Tax Agency): cheap,

timely, complete, reliable, and exhaustive, see Frutos (2007).

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Indicators

Filtering

Dating

Reference

Cycle

Dating

Cyclical

Classification

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Z

_t

= P

_t

+ S

_t

+ I

_t

P

_t

: Trend-Cycle S

_t

: Seasonal I

_t

: Irregular

STEP 1:

Z

)

~

,

~

;

F

,

B

(

H

P

ˆ

=

φ

θ

Overall strategy: see Kaiser & Maravall (2005)

ARIMA Model Based filtering (TRAMO-SEATS):

• Data-driven decomposition.

• Allows forecasts to be used for signal

stabilization purposes (at the end of the sample).

t

)

Z

~

,

~

;

F

,

B

(

H

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P

_t

= T

_t

+ C

_t

P

_t

: Trend-Cycle T

_t

: Trend C

_t

: Cycle

t

H

(

B

,

F

;

)

P

ˆ

C

ˆ

=

ϕ

STEP 2:

t

H

(

B

,

F

;

)

P

ˆ

C

ˆ

=

ϕ

•Band-pass filter, H(B,F) :

• Select information contained in a pre-specfied

band.

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CYCLICAL FILTERS

• Hodrick-Prescott (HP): implicit high-pass filter.

• Baxter-King: explicit band-pass filter, based on a moving

average representation.

• Other: Christiano-Fitzgerald, Chebychev, etc.

• Our favorite filter: Butterworth:

–

Explicitly band-pass.

–

ARMA form: more parsimonious and simple than pure AR or MA

filters.

–

Very flexible.

–

Include HP as a particular case.

–

Robust from input definition: applicable on trend-cycle signals or on

seasonally adjusted data providing similar results.

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1 1-

δ

₁

Design of the band-pass filter

0 0,5

1 δ

₂

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• Cyclical band:

[

w

_p1

,

w

_p2

] (2-8 years)

• Rejection band:

[0, w

_s1

]

∪

[

w

_s2

,

π

]

• 0 < w

_s1

< w

_p1

< w

_p2

< w

_s2

<

π

Design of the band-pass filter

s1

p1

p2

s2

• Set: w

_p

= w

_p2

- w

_p1

;

w

_s

= w

_s2

- w

_p1

• Set tolerances

δ

₁

and

δ

₂

.

• The band-pass filter is designed as a function of

w

_p

,

w

_s

,

δ

₁

and

δ

₂

ϕ

parameters.

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• Cyclical band:

[0.060

π

, 0.240

π

] (2-8 years)

• Rejection band:

[0 , 0.034

π ] ∪

[0.420

π

,

π

]

Design of the band-pass filter:

ϕ

• Rejection band:

[0 , 0.034

π ] ∪

[0.420

π

,

π

]

• δ

₁

= 0.10

• δ

₂

= 0.01

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Alternative filters

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Indicators

Filtering

Dating

Reference

Cycle

Dating

Cyclical

Classification

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REFERENCE CYCLE

• Usually: an exogenous indicator provided by the

analyst and/or by substantive considerations.

• It should accomplish the general rules of the basis

indicators plus a general economic significance.

• The natural choice: monthly indexes of economic

activity, designed using dynamic factor analysis

techniques.

• Careful use of QNA data: the unavoidable

combination of chain-linking, seasonal adjustment,

temporal constraints, and cross-section constraints

has important dynamic effects on their own, which

do not enhance business cycle analysis, Abad et al.

(2009).

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Indicators

Filtering

Dating

Reference

Cycle

Dating

Cyclical

Classification

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DATING

• Identification of turning points: special observations

chaterized by the transition from an upward phase to an

downward phase (peaks) or viceversa (troughs).

• May be done by means of empiricist, non-parametric

methods (e.g. Bry-Boschan approach)

simple, robust,

methods (e.g. Bry-Boschan approach)

simple, robust,

reasonable. Drawback: inference is almost impossible. Turning

points are considered exogenous (a label).

• Model-based methods (e.g., MS-AR) are an interesting

alternative than considers turning points as intrinsic features

of the business cycle. Drawback: more complex procedures,

not well suited to the filtered series provided by band-pass

filters.

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Indicators

Filtering

Dating

Reference

Cycle

Dating

Cyclical

Classification

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CYCLICAL CLASSIFICATION

• Check lead/coincident/lagged or acyclical

patterns by means of:

• Cross correlation function.

• Delays among turning points.

• Spectral methods: coherence and

phase.

• Transfer function models.

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Indicators

Filtering

Dating

Reference

Cycle

Dating

Cyclical

Classification

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COMPOSITION

• Synthetic indexes can be built by means

of:

• Factor analysis.

• Weigths proportional to correlation

with the reference series.

• Regression analysis.

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APPLICATION

• Reference series: Spanish Index of Industrial

Production (

IIP

_t

).

• Indicator: Madrid Stock Exchange General

Index (

Stock

_t

).

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APPLICATION: Software

• Seasonal adjustment: TRAMO-SEATS (TSW).

• Cycle estimation: MATLAB.

• Turning points dating and classification: <F> and <G>.

• Cross-correlation analysis and spectral analysis: SCA.

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IIP: First stage decomposition

80

100

120 RAW

TREND-CYCLE

20

40

60

80

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8 ₂₀

40

60

80

100

120 TREND-CYCLE

TREND

IIP: Second stage decomposition

-8

-4

0

4

8

0

20

65

70

75

80

85

90

95

00

05 TREND

CYCLE

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IIP: Alternative cycle estimation

4

8

12 S.A.

TREND

-8

-4

0

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IIP: Alternative cycle estimation

1

2

3

4 HP_TREND

BUTTER_T REND

-3

-2

-1

0

1

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IIP: Alternative cycle estimation

2

3

4

5 HP_TREND

HP_SA

-3

-2

-1

0

1

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IIP: growth and cycle

4

8

12 -8

-4

0

4

65

70

75

80

85

90

95

00

05

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IIP and STOCK

20 30 40

IIP Stock

Jan65 Jan70 Jan75 Jan80 Jan85 Jan90 Jan95 Jan00 Jan05 Jan10

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IIP and STOCK (standardized)

1

2

3 IIP

S T OCK

-3

-2

-1

0

65 7 0

75

80

85

90

95

00

05

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IIP and STOCK: CCF

0.2 0.3 0.4 0.5

Cross Correlation Function IIP(t) vs Stock(t+h)

-25 -20 -15 -10 -5 0 5 10 15 20 25

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1

h: Leads (h<0); Lags (h>0)

C

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IIP and STOCK: CCF

• STOCK is weakly procyclical with respect

to IIP.

• STOCK leads 5 months IIP.

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IIP: Turning points

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IIP: Deepest cycles

2 4 6 8

DEEPEST CYCLES

1974.1 1991.11 2008.1

-30 -20 -10 0 10 20 -6

-4 -2 0

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IIP: Turning points: duration

40 45 50 55 60 65

IIP

PEAKS TROUGHS

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STOCK: Turning points

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STOCK: Turning points: duration

40 45 50 55 60 65

STOCK

PEAKS TROUGHS

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IIP and STOCK: turning points

-10 -5 0 5 10

IIP

-40 -20 0 20 40

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IIP and STOCK: turning points

E.M. Quilis 49

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IIP and STOCK: turning points

4 6 8 10

TURNING POINTS: PEAKS

IIP Cycle IIP STOCK

Jan65-8 Jan70 Jan75 Jan80 Jan85 Jan90 Jan95 Jan00 Jan05 Jan10

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IIP and STOCK: turning points

4 6 8 10

TURNING POINTS: TROUGHS

IIP Cycle IIP STOCK

Jan65-8 Jan70 Jan75 Jan80 Jan85 Jan90 Jan95 Jan00 Jan05 Jan10

-6 -4 -2 0 2

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IIP and STOCK: turning points

4 5 6 7 10 15 20 25 14 15 16 17

-10 -5 0 5 10

-1 0 1 2 3 1975:09

-10 -5 0 5 10

-15 -10 -5 0 5 1993:05

-10 -5 0 5 10

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IIP and STOCK: TURNING

POINTS

• STOCK leads consistently IIP, median lead = 2

months.

• The lead is higher at troughs than at peaks: 1m vs

3m.

• The leads have noticeable variability, specially in the

case of troughs.

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IIP and STOCK: spectral analysis

Window carpentry

0.7 0.8 0.9 1 WINDOW CARPENTRY Bartlett Tukey Hamming Parzen

-15 -10 -5 0 5 10 15

0 0.1 0.2 0.3 0.4 0.5 0.6

Cross covariance lag

W

e

ig

h

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IIP and STOCK: spectral analysis

Coherence

0.112 0.114 0.116 0.118 BARTLETT HANN HAMMING PARZEN

1 2 3 4 5 6 7 8

0.1 0.102 0.104 0.106 0.108 0.11 0.112

Length of the cycle (in years)

C o h e re n c e

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IIP and STOCK: spectral analysis

Phase

8 9

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IIP and STOCK: SPECTRAL

ANALYSIS

• STOCK and IIP have weak coherence, specially at

lower frequencies (longer cycles).

• STOCK leads consistently IIP across windows. The

lead may be estimated next to 7m.

• Different quantitative measures across windows may

are consistent with varying leads.

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REFERENCES

• Abad, A., Cuevas, A. & Quilis, E.M.: “Índices trimestrales de volumen

encadenados, ajuste estacional y benchmarking”, Instituto de Estudios

Fiscales, Papeles de Trabajo n. 05.09.

• Camacho, M., Pérez-Quirós, G. & Saiz, L. (2005) “Do European business

cycles look like one?”, Bank of Spain, Working Paper n 0518.

• Frutos, R. (2007) “La estadística económica de base administrativa en

España ¿Para cuándo el gran salto adelante?”, en Marcos, C. (Ed.)

El papel

de los registros administrativos en el análisis social y económico y el

desarrollo del sistema estadístico

, Instituto de Estudios Fiscales.

• Kaiser, R. & Maravall, A. (2005) “Combining Filter Design with

Model-based Filtering: An Application to Business-cycle Estimation”,

International

Journal of Forecasting

, vol. 21, p. 691-710.

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Thanks

Thanks for

for your

your attention

attention

Thanks

Thanks for

for your

your attention

attention

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Business

Business cycle

cycle indicators

indicators..

Methods

Methods,

, applications

applications, and

, and limits

limits..

Enrique M. Quilis

Macroeconomic Research Department

Ministry of Economy and Finance. Spain.