Composite Indicators - International Workshop Beijing€¦ · Composite Indicators The advantage of...

Composite IndicatorsInternational Workshop Beijing

Klaus Abberger

Swiss Economic Institute (KOF) of the ETH Zurich

Outline

Outline I

1 Business Cycles

2 Collecting Potential Indicators

3 Seasonal Adjustment

4 Analyzing Individual Indicators

5 Composite Indicators

6 Turning Points and Composite Indicators

Outline

Outline

1 Business CyclesReferenceTypes of CyclesTime SeriesTrend Estimation with Filters

Hodrick-Prescott Filter (H-P Filter)






What is a business cycle?


Business Cycles

Business Cycles

Mitchell 1927:

Reference Series

Reference Series

To assess the quality of business cycle indicators referenceseries are needed. Usually Gross Domestic Product (GDP) isused as reference. In the absence GDP of synthetic activitymeasures or indicators of key parts of the economy (e.g.industrial production) could be considered.

The reference series should

p be reliable

p contain a broad/important range of economic activity

p be in a quarterly or monthly frequency

Example: Reference Series for the Global Economy

Example: Reference Series for the GlobalEconomy

p Global GDP of the IMF (yearly), IMF World EconomicOutlook Databases

p GDP of OECD (quarterly), OECD Database

p Industrial Production of OECD (monthly), OECD Database

http://www.imf.org/external/ns/cs.aspx?id=28


http://stats.oecd.org/Index.aspx?QueryName=350&QueryType=View&Lang=en

http://stats.oecd.org/Index.aspx?querytype=view&queryname=90

Example: Reference Series for the Global Economy

Example: Reference Series for the GlobalEconomy

p Global GDP of the IMF (yearly), IMF World Economic OutlookDatabases

p GDP of OECD (quarterly), OECD Database

p Industrial Production of OECD (monthly), OECD Database



http://stats.oecd.org/Index.aspx?QueryName=350&QueryType=View&Lang=en

http://stats.oecd.org/Index.aspx?querytype=view&queryname=90

Types of Cycles

Types of Cycles

Different Cycles

p Classic Cycle

p Growth Cycle

p Growth Rate Cycle

Why is there a trend development?

Why is there a trend development?

What drives growth?

p Population

p Capital accumulation

p Technical progress

Time Series Composition


Additive Model

Additive components model:

yt = mt + kt + st + εt , t = 1, ...,n,

with

mt trend component

kt cyclical component (business cycle)

st seasonal component

εt irregular component



Additive Model

p Sometimes trend an business cycle are put together to a smoothcomponent gt . Then the model is

yt = gt + st + εt , t = 1, ...,n.

p The additive model could in principal enlarged, adding additionaleffects of regressors xt . This leads to

yt = gt + st + xtβ + εt , t = 1, ...,n.

p In this way for example calendar effects or political measurescould be captured.



Multiplicative Model

Multiplicative components model:

yt = gt · st · εt , t = 1, ...,n.

Trend estimation with Filters

Trend estimation with Filters

A conventional definition of business cycle emphasisesfluctuations of between about 1.5 years and 8 years. Longerfluctuations are regarded as trend. Shorter fluctuations containshort term fluctuations, wether effects, random effect,measurement errors etc.

One way to extract the smooth component and the businesscycle is the application of filters like the Hodrick-Prescott filterand the Baxter-King filter.

Trend Estimation with Filters

Trend Estimation with Filters

Hodrick-Prescott Filter (H-P Filter)

Estimations result from minimizing:

T∑t=1

(yt − µt )2 + λ[(µt+1 − µt )− (µt − µt−1)]2

and is a solution to the problem of minimizing the deviationsbetween y and µ subject to a condition on the smoothness ofthe estimated component.

Example: Euro Area Manufacturing Production


1995 2000 2005 2010

80

90

100

110

1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013

Index (2010=100)

Eurostat

Seasonal and working day adjusted

Example: Growth of Euro Area Manufacturing Production

Example: Growth of Euro Area ManufacturingProduction

1995 2000 2005 2010

−0.25

−0.20

−0.15

−0.10

−0.05

0.00

0.05

0.10

1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012

AnnualMonthly

Example: Growth of Euro Area Manufacturing Production

Example: Growth of Euro Area ManufacturingProduction

1995 2000 2005 2010

−4

−2

0

2

1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012

Standardized

AnnualMonthly

Outline

Outline

1 Business Cycles

2 Collecting Potential IndicatorsCharacteristics of good indicatorsSearch for potential indicatorsComposite IndicatorsWhat others do





Searching for Indicators

Searching for Indicators

Characteristics of good indicators:

p meaningful und reliable

p timely available

p after publication no big revisions

p leading or coincident for the business cycle, so that timelysignals are given

p stable relationship with the reference series

p clear signal with minor noise

Types of Indicators

Types of Indicators

Indicators can be divided into

p leading indicators

p coincident indicators

p lagging indicators

Potential indicators


Potential leading indicators are classified to one of four types ofeconomic rationale, shown below, that can be used to assesstheir suitability as leading indicators.

p Early stage: indicators measuring early stages ofproduction, such as new orders, order books, constructionapprovals, etc.

p Rapidly responsive: indicators responding rapidly to changes ineconomic activity such as average hours worked, profits andstocks.



Potential leading indicators are classified to one of four types ofeconomic rationale, shown below, that can be used to assesstheir suitability as leading indicators.

p Early stage: indicators measuring early stages of production,such as new orders, order books, construction approvals, etc.

p Rapidly responsive: indicators responding rapidly tochanges in economic activity such as average hoursworked, profits and stocks.



p Expectation-sensitive: indicators measuring, or sensitiveto, expectations, such as stock prices, raw material pricesand expectations based on business survey dataconcerning production or the general economicsituation/climate e.g. confidence indicators.

p Prime movers: indicators relating to monetary policy and foreigneconomic developments such as money supply, terms of trade,etc.



p Expectation-sensitive: indicators measuring, or sensitive to,expectations, such as stock prices, raw material prices andexpectations based on business survey data concerningproduction or the general economic situation/climate e.g.confidence indicators.

p Prime movers: indicators relating to monetary policy andforeign economic developments such as money supply,terms of trade, etc.

Search for possible Indicators

Search for possible Indicators

The list of possible indicators should contain the followinginformation:

Indicator Source Notes Meaning Frequency Publication lag Revisions Date first publication

In column "Meaning" one should identify why this indicatorcould be important for the economy (e.g. is an important sectorwith high value added)

Later this table is expanded with results from statisticalanalyses.

Composite Indicators

Composite Indicators

The advantage of composite indicators over the individualcomponent series is that they achieve a better trade-offbetween responsiveness and stability. Composite indicatorscan be constructed to have fewer false alarms and fewermissed turning points than its individual components;moreover they tend to have more stable lead-times. Finally,the composites have the capacity to react to various sources ofeconomic fluctuations and at the same time can be resilient toperturbations affecting only one of the components.

What others do

What others do

OECD:

To get some ideas about possible indicators look for example atthe OECD website.

What others do: OECD


Look at the different country indicators. There are various typesof indicators. E.g.:

p Production, stock of orders, employment, unfilled job vacancies,new car registrations, housing starts, nights spend in hotels

p business tendency surveys

p consumer surveys

p various price figures and share prices, terms of trade, exchangerate, silver price

p interest rates (spreads), bank credits

p indicators of other countries

.... and much more.

History of OECD Composite Leading Indicators

History of OECD Composite Leading Indicators

The OECD system of composite leading indicators was firstdeveloped in the early 1970s amidst renewed interest inbusiness cycle research - a direct consequence of the1969-1970 recession in developed economies. The deeper andmore global recession that followed in the mid-70s reinforcedthe need for such a tool, leading to the creation of a dedicatedOECD Working Party on Cyclical Analysis and LeadingIndicators in 1978.

Purpose of the OECD Composite Leading Indicators

Purpose of the OECD Composite LeadingIndicators

The objective of the OECD Composite Leading Indicators is toprovide ”qualitative indicators of the business cycle outlook forthe short term future”.

So what means

p business cycle?

p qualitative?

p short term?


Purpose of the OECD Composite LeadingIndicatorsp Business cycle: Deviation from trend in GDP (since 2012,

before deviation from trend in industrial production).

p Qualitative: By design the indicators are primarily aimed atidentifying turning-points but also tries to identify phases in thecycle and, albeit to a lesser extent, the acceleration/decelerationof the business cycle. The qualitative focus means that theindicators are not optimized for precise numericforecasting. There is also a risk that one would intuitivelyinterpret higher peaks and lower troughs as stronger/weakergrowth. However, such conclusions may be misplaced, becausethe indicators are not optimized in this way.

p Short term: The indicators are designed to have a typical lead ofbetween 6 and 9 months. However, in practice the timeliness ofdata releases affects information lead times.


Purpose of the OECD Composite LeadingIndicatorsp Business cycle: Deviation from trend in GDP (since 2012, before

deviation from trend in industrial production).

p Qualitative: By design the indicators are primarily aimed atidentifying turning-points but also tries to identify phases inthe cycle and, albeit to a lesser extent, theacceleration/deceleration of the business cycle. Thequalitative focus means that the indicators are notoptimized for precise numeric forecasting. There is also arisk that one would intuitively interpret higher peaks andlower troughs as stronger/weaker growth. However, suchconclusions may be misplaced, because the indicators arenot optimized in this way.

p Short term: The indicators are designed to have a typical lead ofbetween 6 and 9 months. However, in practice the timeliness ofdata releases affects information lead times.


Purpose of the OECD Composite LeadingIndicatorsp Business cycle: Deviation from trend in GDP (since 2012, before

deviation from trend in industrial production).

p Qualitative: By design the indicators are primarily aimed atidentifying turning-points but also tries to identify phases in thecycle and, albeit to a lesser extent, the acceleration/decelerationof the business cycle. The qualitative focus means that theindicators are not optimized for precise numericforecasting. There is also a risk that one would intuitivelyinterpret higher peaks and lower troughs as stronger/weakergrowth. However, such conclusions may be misplaced, becausethe indicators are not optimized in this way.

p Short term: The indicators are designed to have a typicallead of between 6 and 9 months. However, in practice thetimeliness of data releases affects information lead times.

Building Blocks of OECD Composite Leading Indicators

Building Blocks of OECD Composite LeadingIndicators

p From the candidate component series factors like seasonalpattern, outliers, trend and noise (applying the HP-filter) areremoved.

p Candidate series are standardized.

p Assessment of components (turning point analysis withBry-Boschan procedure, cross-correlations).

p Calculation of composite indicator (equal weighting ofcomponents) and assessment (turning points,cross-correlations).

Presentation of OECD Composite Leading Indicators

Presentation of OECD Composite LeadingIndicatorsThe raw composite indicator is the average of the de-trended,smoothed and normalized component series.

p Amplitude adjusted: The amplitude adjusted indicator rescalesthe raw indicator to match the amplitudes of the business cycle(i.e. the de-trended and smoothed but notnormalized/standardized reference series).

p Trend restored: It is the product of the trend of the referenceseries and the amplitude adjusted composite indicator. Thistransformation facilitates analyses of the classical businesscycle.

p Annual growth rate: The annual growth rates, calculated fromthe rend restored composite indicator. Some analysts prefer thistype of indicator because they are used to interpret annualchanges (of the reference series).

The Conference Board


p This indicator approach originated in the mid-1930s at theNational Bureau of Economic Research (NBER) with the work ofWesley Mitchell and Arthur Burns

p Starting in the late 1960s, the U.S. Department of Commercebegan publishing the composite indexes

p In late 1995, the indicator program was privatized and TheConference Board took over



The Conference Board leading indicator for the U.S. uses thefollowing data:

p Average weekly hours, manufacturing

p Average weekly initial claims for unemployment insurance

p Manufacturers’ new orders, consumer goods and materials

p ISM new orders index

p Manufacturers’ new orders, non-defense capital goods excl.aircraft

p Building permits, new private housing units Stock prices, 500common stocks



p Leading Credit Index

p Interest rate spread, 10 year Treasury bonds less federal funds

p Avg. consumer expectations for business conditions

Standard deviations of monthly changes of the variables areused to calculate a weighted average of the variables.



The Conference Board coincident indicator for the U.S. usesthe following data:

p Employees on nonagricultural payrolls

p Personal income less transfer payments

p Industrial production

p Manufacturing and trade sales

The Conference Board U.S. Coincident Indicator

The Conference Board U.S. Coincident Indicator

www.conferenceboard.org © 2014 The Conference Board, Inc. | 16

5 recessions in 25 years

3 recessions in 30 years

Coincident index closely tracks GDP; two consecutive declines in GDP is not a good rule to define a recession

110

100

90

80

70

60

50

40

30

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

The Conference Board Coincident Economic Index® (CEI) for the United States

0

0

-2

0

0

+1

0

0

+1

+1

-1

0

-6

0

+1

0

Note: Shaded areas represent recessions as determined by the NBER Business Cycle Dating Committee.Source: The Conference Board

The Conference Board U.S. Leading Indicator

The Conference Board U.S. Leading Indicator

www.conferenceboard.org © 2014 The Conference Board, Inc. | 15

Leading Economic Index summarizes and helps to predict the state of the economy and short term cyclical forces acting in and on it

Note: Shaded areas represent recessions. Source: The Conference Board

20

30

40

50

60

70

80

90

100

110

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

The Conference Board Leading Economic Index® (LEI) for the U.S.The Conference Board Coincident Economic Index® (CEI) for the U.S.

01:301:11

90:791:3

81:782:11

80:180:7

73:1175:3

69:1270:11

60:461:2

Peak:Trough:

07:1209:6

Jun '14

-8 -6

0 0

-2 0

-9

0

0

+1

-15

-2

0

0-8

-3

-18

0

-1

0

-11

-1

-6

0

-21

-3

+1

0

+1

+1



Construction of Conference Board composite indicators. Thecomponents (variables) are

p Seasonal adjusted

p Deflated

p Volatility adjusted

p Aggregated

p In some cases trend adjusted (the leading indicator is adjustedto the trend of the coincident indicator)

p An index is calculated



Construction of Composite Index

1. Calculate month to month changes for each component. Forcomponents which are in percent form, simple arithmeticdifferences are calculated: ri,t = Xi,t − Xi,t−1. In all other cases asymmetric percentage change formula is used:ri,t = 200 · Xi,t−Xi,t−1

Xi,t+Xi,t−1.

2. Adjust the month-to-month changes by multiplying them by thecomponent’s standardization factor, wi . This results inci,t = wi · ri,t .



3. Sum up components (variables) to calculate the monthly changein the composite indicator.

4. In the leading indicator demean the monthly change of theindicator obtained in 3.

5. In the leading indicator add the mean of the monthly changes inthe coincident indicator as estimated trend component.



6. Cumulate the (trend adjusted) monthly changes to thepreliminary level of the index. The index is calculated recursively,starting from an initial value of 100 for the first month of thesample. Let I1 = 100 denote the initial value of the index for thefirst month. If s2 is the result from Step 5. in the second month,the preliminary index value is I2 = I1 · 200+s2

200−s2. Then the next

month’s preliminary index value is: I3 = I2 · 200+s3200−s3

, and so on foreach month data that are available.

7. Rebase the index to an average 100 in the chosen base year.The preliminary index levels obtained in Step 6 are multiplied by100, and divided by the mean of the preliminary levels of theindex in the base year.



The Conference Board Coincident Economic Index (CEI) forChina: Components

p Value-Added Industrial Production (Billions of 2004 Yuan,deflated by PPI, S.A.)

p Retail Sales of Consumer Goods (Billions of 2004 Yuan, deflatedby RPI, S.A.)

p Volume of Passenger Traffic (Person Bn-Kilo, S.A.)

p Electricity Production (Billions of KWH, S.A.)

p Manufacturing Employment (Person Mn, S.A.)



The Conference Board Leading Economic Index (LEI) forChina: Components

p Consumer Expectations Index

p Total Loans Issued by Financial Institutions (Billions of 2004Yuan, deflated by PPI, S.A.)

p 5000 Industry Enterprises Diffusion Index: Raw MaterialsSupply (S.A.)

p PMI: Manufacturing: Supplier Delivery (S.A.)

p PMI: Manufacturing: New Export Orders (S.A.)

p Floor Space Started: Total (Thousands of Sq M, S.A.)

KOF Economic Barometer


Indicator for the Swiss business cycle. Relies strongly oneconomic tendency survey results, but not entirely. Uses Swissindicators and foreign indicators.

KOF Economic Barometer: History


p 1976 Version

p Reference series: de-trended real GDPp Number of variables selected: 6 (construction, manufacturing

(2x), labour, money, stocks)

p 1998 Version

p Reference series: real y-o-y growth in GDPp Number of variables selected: 6 (all from Business Tendency and

Consumer surveys)p Variables were low-pass filtered and then the first principal

component was extracted



p 1976 Version

p Reference series: de-trended real GDP

p Number of variables selected: 6 (construction, manufacturing (2x),labour, money, stocks)

p 1998 Version






p 1976 Version

p Reference series: de-trended real GDPp Number of variables selected: 6 (construction, manufacturing

(2x), labour, money, stocks)

p 1998 Version






p 1976 Version

p Reference series: de-trended real GDPp Number of variables selected: 6 (construction, manufacturing (2x),

labour, money, stocks)

p 1998 Version

p Reference series: real y-o-y growth in GDPp Number of variables selected: 6 (all from Business Tendency

and Consumer surveys)p Variables were low-pass filtered and then the first principal




p 1976 Version



p 1998 Version

p Reference series: real y-o-y growth in GDP

p Number of variables selected: 6 (all from Business Tendency andConsumer surveys)

p Variables were low-pass filtered and then the first principalcomponent was extracted



p 1976 Version



p 1998 Version

p Reference series: real y-o-y growth in GDPp Number of variables selected: 6 (all from Business Tendency

and Consumer surveys)

p Variables were low-pass filtered and then the first principalcomponent was extracted



p 1976 Version



p 1998 Version






p 2006 Version

p Reference series: real y-o-y growth in financial, constructionand core GDP (3 modules)

p Number of variables selected: 25p For each module the first principle component was extractedp Aggregate is filtered using end-point stable Direct Filter

Approach (DFA) of Wildi (2008)



p 2006 Version

p Reference series: real y-o-y growth in financial, constructionand core GDP (3 modules)

p Number of variables selected: 25p For each module the first principle component was extractedp Aggregate is filtered using end-point stable Direct Filter Approach

(DFA) of Wildi (2008)



p 2006 Version

p Reference series: real y-o-y growth in financial, construction andcore GDP (3 modules)

p Number of variables selected: 25

p For each module the first principle component was extractedp Aggregate is filtered using end-point stable Direct Filter Approach

(DFA) of Wildi (2008)



p 2006 Version


p Number of variables selected: 25p For each module the first principle component was extracted

p Aggregate is filtered using end-point stable Direct Filter Approach(DFA) of Wildi (2008)



p 2006 Version


p Number of variables selected: 25p For each module the first principle component was extractedp Aggregate is filtered using end-point stable Direct Filter

Approach (DFA) of Wildi (2008)

KOF Economic Barometer: Construction of the 2004 Version

KOF Economic Barometer: Construction of the2004 Versionp Objectives

p No longer use a filter for smoothingp Broaden the set of underlying time seriesp Define a standardized procedure to select variables

(Automatize and regularly apply the variable selectionprocedure)

p Two production stages

p Variable selection procedure

p Choose business cycle conceptp Define reference seriesp Pre-select the pool of potential variablesp Fix the automated selection procedure

p Construction of the leading indicator (extract the first principlecomponent from the selected variables)


KOF Economic Barometer: Construction of the2004 Version

p Objectives

p No longer use a filter for smoothing

p Broaden the set of underlying time seriesp Define a standardized procedure to select variables (Automatize

and regularly apply the variable selection procedure)







p Objectives

p No longer use a filter for smoothingp Broaden the set of underlying time series

p Define a standardized procedure to select variables (Automatizeand regularly apply the variable selection procedure)






KOF Economic Barometer: Construction of the2004 Versionp Objectives

p No longer use a filter for smoothingp Broaden the set of underlying time seriesp Define a standardized procedure to select variables

(Automatize and regularly apply the variable selectionprocedure)







p Objectives

p No longer use a filter for smoothingp Broaden the set of underlying time seriesp Define a standardized procedure to select variables (Automatize





p Construction of the leading indicator (extract the firstprinciple component from the selected variables)



p Objectives









p Objectives




p Variable selection procedurep Choose business cycle concept

p Define reference seriesp Pre-select the pool of potential variablesp Fix the automated selection procedure




p Objectives




p Variable selection procedurep Choose business cycle conceptp Define reference series

p Pre-select the pool of potential variablesp Fix the automated selection procedure




p Objectives




p Variable selection procedurep Choose business cycle conceptp Define reference seriesp Pre-select the pool of potential variables

p Fix the automated selection procedurep Construction of the leading indicator (extract the first principle

component from the selected variables)



p Objectives




p Variable selection procedurep Choose business cycle conceptp Define reference seriesp Pre-select the pool of potential variablesp Fix the automated selection procedure




p Objectives




p Variable selection procedurep Choose business cycle conceptp Define reference seriesp Pre-select the pool of potential variablesp Fix the automated selection procedure

p Construction of the leading indicator (extract the firstprinciple component from the selected variables)

KOF Economic Barometer: Reference Series


p The KOF Barometer is an indicator published monthly

p The reference series ideally also has a monthly frequency

p The level of seasonally adjusted real GDP is interpolated usingthe Denton additive method

p M-o-m growth rates are calculated out of this and subsequentlysmoothened using a symmetric 13 months moving average

p High frequency current growth rate are highly volatile, reflectingmeasurement errors, weather effects, working day effects, andalike

p The aim of the KOF Barometer is to signal the underlyingbusiness cycle - not high frequency fluctuations





p The level of seasonally adjusted real GDP is interpolatedusing the Denton additive method









p M-o-m growth rates are calculated out of this andsubsequently smoothened using a symmetric 13 monthsmoving average

p High frequency current growth rate are highly volatile,reflecting measurement errors, weather effects, working dayeffects, and alike








p High frequency current growth rate are highly volatile,reflecting measurement errors, weather effects, working dayeffects, and alike


KOF Economic Barometer: Candidate Variables


p International variables: currently 32 variables

p Concentrate on the 11 most important trading partners: 1Business tendency and 1 consumer survey question percountry

p Ifo World Economic Survey, assessment and expectations for5 regions

p National variables: currently 444 variables

p KOF Business Tendency Surveys (411)p SECO Consumer Survey (9)p BFS, SECO, OZD, SNB (24)




p Concentrate on the 11 most important trading partners: 1Business tendency and 1 consumer survey question percountry

p Ifo World Economic Survey, assessment and expectations for 5regions






p Concentrate on the 11 most important trading partners: 1Business tendency and 1 consumer survey question per country

p Ifo World Economic Survey, assessment and expectations for5 regions









p KOF Business Tendency Surveys (411)

p SECO Consumer Survey (9)p BFS, SECO, OZD, SNB (24)







p KOF Business Tendency Surveys (411)p SECO Consumer Survey (9)

p BFS, SECO, OZD, SNB (24)



p For each of these variables we determine all

p sensible transformation (level, log level, quarterly difference,monthly difference, annual difference, balance, positive,negative) (4356)

p theoretically expected sign of the correlation with thereference series

p Except for year-over-year differences, X12-ARIMA is used toseasonally adjust all variables and their transformations.




p sensible transformation (level, log level, quarterly difference,monthly difference, annual difference, balance, positive,negative) (4356)

p theoretically expected sign of the correlation with the referenceseries





p sensible transformation (level, log level, quarterly difference,monthly difference, annual difference, balance, positive, negative)(4356)

p theoretically expected sign of the correlation with thereference series





p sensible transformation (level, log level, quarterly difference,monthly difference, annual difference, balance, positive, negative)(4356)

p theoretically expected sign of the correlation with the referenceseries


KOF Economic Barometer: Automated selection procedure

KOF Economic Barometer: Automated selectionprocedure

p A variable has valid observations throughout the defined(10-year) observation window used in the cross-correlationanalysis.

p The sign of the cross-correlation complies with the exogenouslyimposed sign restriction.

p Only those variables are retained, for which the maximum(absolute) cross-correlation is found at the lead range specifiedbetween 0 and 6 months.

p The computed cross-correlation surpasses a defined threshold.

p Of those transformations that survive, we take the one thatoptimizes: max U = |rmax| ·

√hmax + 1




p The sign of the cross-correlation complies with theexogenously imposed sign restriction.




√hmax + 1





p Only those variables are retained, for which the maximum(absolute) cross-correlation is found at the lead rangespecified between 0 and 6 months.



√hmax + 1






p The computed cross-correlation surpasses a definedthreshold.


√hmax + 1








√hmax + 1



p Finally, the variance of these variables is collapsed into acomposite indicator as the first principal component.

p This first principal component is standardised to have a mean of100 and standard deviation of 10 during the observation window.



p Finally, the variance of these variables is collapsed into acomposite indicator as the first principal component.

p This first principal component is standardised to have amean of 100 and standard deviation of 10 during theobservation window.

KOF Economic Barometer: Out of sample production

KOF Economic Barometer: Out of sampleproduction

p Except for year-over-year differences, the seasonal factorsare subtracted from all variables and their transformations.The seasonal factors are kept constant until the nextvintage is constructed.

p We standardise the variables entering the KOF Barometer usingtheir means and standard deviations estimated for the 10-yearreference window.

p The first principal component is constructed by multiplying thestandardised variables with the loading coefficients derived forthe reference period.



p Except for year-over-year differences, the seasonal factors aresubtracted from all variables and their transformations. Theseasonal factors are kept constant until the next vintage isconstructed.

p We standardise the variables entering the KOF Barometerusing their means and standard deviations estimated for the10-year reference window.

p The first principal component is constructed by multiplying thestandardised variables with the loading coefficients derived forthe reference period.



p Except for year-over-year differences, the seasonal factors aresubtracted from all variables and their transformations. Theseasonal factors are kept constant until the next vintage isconstructed.

p We standardise the variables entering the KOF Barometer usingtheir means and standard deviations estimated for the 10-yearreference window.

p The first principal component is constructed by multiplyingthe standardised variables with the loading coefficientsderived for the reference period.



p We scale the constructed first principal component by thevalue of the standard deviation of the first principalcomponent computed using the reference window.

p We construct the KOF Barometer values by multiplying thestandardised principal component by 10 and adding 100.



p We scale the constructed first principal component by the valueof the standard deviation of the first principal componentcomputed using the reference window.

p We construct the KOF Barometer values by multiplying thestandardised principal component by 10 and adding 100.

KOF Economic Barometer: Yearly updates in September

KOF Economic Barometer: Yearly updates inSeptember

p Swiss quarterly SNA is published by SECO

p Swiss annual SNA is published by SFSO

p Every summer a new vintage is releasedp This vintage contains the first release of previous yearÕs growth

by the SFSO

p The subsequent quarterly release of SECO incorporates thisannual information





p Every summer a new vintage is releasedp This vintage contains the first release of previous yearÕs

growth by the SFSO






p Every summer a new vintage is released

p This vintage contains the first release of previous yearÕs growthby the SFSO






p Every summer a new vintage is releasedp This vintage contains the first release of previous yearÕs

growth by the SFSO






p Every summer a new vintage is releasedp This vintage contains the first release of previous yearÕs growth

by the SFSO

p The subsequent quarterly release of SECO incorporatesthis annual information



2004 2006 2008 2010 2012 2014707580859095

100105110115120

-4-3-2-10123456

KOF Economic Barometer (Index values; long-term average 2004–2013=100; left scale)Month-on-month change of the Swiss business cycle (Reference series; SECO/KOF, right scale)

Economic Barometer and Reference Series

When we have collected a list of indicators, we have to look foreach series whether we need a

p seasonal adjustment

p data transformation of filtering.

Outline

Outline

1 Business Cycles


3 Seasonal AdjustmentCensus X-13ARIMA-SEATS




Seasonal Adjustment

Seasonal AdjustmentModel

p Additive model yt = gt + st + εt , t = 1, ...,n

p Multiplicative model yt = gt · st · εt , t = 1, ...,n

Adjustment

p Additive model

yt − st = gt + εt , t = 1, ...,n

p Multiplicative model

yt

st= gt · εt , t = 1, ...,n

Seasonal Adjustment

Seasonal Adjustment

Steps

To seasonally adjust we have to:

p Estimate the smooth component

p Adjust series for the smooth component

p Estimate seasonal factorsp Adjust original series for seasonal factors

Seasonal Adjustment

Seasonal Adjustment

Steps




p Estimate seasonal factors

p Adjust original series for seasonal factors

Seasonal Adjustment

Seasonal Adjustment

Steps




p Estimate seasonal factorsp Adjust original series for seasonal factors

A simple procedure for illustration


Employed Persons in Germany (red s.a. from DESTATIS)

Time

1995 2000 2005 2010

37000

38000

39000

40000



Monthplot for Employment

dtx

J F M A M J J A S O N D

-400

-300

-200

-100

0100

200



Construction (quarterly)

Time

Construction

0 20 40 60 80

4045

5055

6065

70



Series adjusted to smooth component

Time

dtC

0 20 40 60 80

-8-6

-4-2

02

4


A simple procedure for illustrationdtC

Q1 Q2 Q3 Q4

-8-6

-4-2

02

4

Oh, it seems there have been two really harsh winters!


A simple procedure for illustrationThe seasonal adjusted series:

Time

5 10 15 20

4045

5055

6065

70

But there is still seasonality!!

So iterate!


A simple procedure for illustrationThe seasonal adjusted series:

Time

5 10 15 20

4045

5055

6065

70

But there is still seasonality!! So iterate!

Census X12ARIMA

Census X12ARIMA

Census X12ARIMA is a sophisticated filter based method forseasonal adjustment.

Maintained by U.S. Census Bureau (Census Homepage)

https://www.census.gov/srd/www/x13as/

Source: Statistics New Zealand

Example Construction

Example Construction

40

45

50

55

60

65

70

1992 1994 1996 1998 2000 2002 2004 2006 2008 2010

v1v1_d11v1_d12

Example Employment

Example Employment

36500

37000

37500

38000

38500

39000

39500

40000

40500

41000

1995 2000 2005 2010

EmploymentS_A_DESTATIS

Empl_d11

Outline

Outline

1 Business Cycles



4 Analyzing Individual IndicatorsCross-CorrelationTurning Points



Autocorrelation and Cross-correlation


The common Bravais-Pearson correlation coefficient for twovariables Y and X is

rxy =

∑ni=1(xi − x)(yi − y)√∑n

i=1(xi − x)2∑n

i=1(yi − y)2

=

∑ni=1 xiyi − nxy√

(∑n

i=1 x2i − nx2)(

∑ni=1 y2

i − ny2)



For a stationary time series x1, x2, x3, ..., xn and −n < h < n theautocorrelation function is estimated with

γh =

∑n−|h|t=1 (xt+|h| − x)(xt − x)√∑nt=1(xt − x)2

∑nt=1(xt − x)2


Autocorrelation and Cross-correlationFor two jointly stationary time series x1, x2, x3, ..., xn;y1, y2, y3, ..., yn and 0 ≤ h < n the cross-correlation function isestimated with

ρxy (h) =

∑nt=1+h(xt − x)(yt−h − y)√∑n

t=1(xt − x)2∑n

t=1(yt − y)2

Resp. for −n < h ≤ 0

ρxy (h) =

∑n−|h|t=1 (xt − x)(yt−h − y)√∑n

t=1(xt − x)2∑n

t=1(yt − y)2

Example

Example

-4

-3

-2

-1

0

1

2

3

4

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006

Ifo Business Climate and Cyclical Component of Real GDP

Cyclical Component of Real GDP (1)

Ifo Business Climate for Industry and Trade (1)

1) Standardized. Source: Federal Statistical Office, Ifo Business Survey.

Example

Example

-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

-0,8

-0,6

-0,4

-0,2

0

0,2

0,4

0,6

0,8

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8

Cross Correlogramm: Ifo Business Climate and Cyclical Component of real GDP

Correlation Coeffizient ρ

Source: Statistical Office, Ifo Business Survey.

Lead of the Ifo Business Climate in Quarters <

Algorithm for dating turning points


To minimize subjective assessments and to have a fast routinefor dating turning points we use an algorithm.

An grass-route work is:G. Bry, C. Boschan (1971), ”Cyclical Analysis of Time Series:Selected Procedures and Computer Programs”, NBERTechnical Paper no 20.

Another important work is:D. Harding, A. Pagan (2002), ”Dissecting the Cycle: aMethodological Investigation”, Journal of Monetary Economics,no 49, pp. 365-381.



Harding, Pagan: Minimum needs for an algorithm



Monthly data (classical and growth cycles)A local peak (trough) is occurring at time t whenever{yt > (<)yt±k}, k = 1, ...,K , where K is generally set to five.A phase must last at least six months and a complete cycleshould have a minimum duration of fifteen months.

Quarterly dataPut K = 2 i.e. {∆2yt > 0,∆yt > 0,∆yt+1 < 0,∆2yt+2 < 0} , asthis ensures that yt is a local maximum relative to the twoquarters (six months) on either side of yt .In addition (monthly) data are sometimes smoothed beforedating. A moving average or a spencer curve is usually appliedto reduce noise.

Example

Example

-4

-3

-2

-1

0

1

2

3

4

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006

Turning Points of the German Business Cycle and Ifo Business Climate

Cyclical Component of GDP Ifo BC Turning Points of GDP Turning Points of BC

1) Standardized values

Source: Statistisches Bundesamt, ifo Konjunkturtest.

Example

Example

-4

-3

-2

-1

0

1

2

3

1978 1981 1984 1987 1990 1993 1996 1999 2002 2005 2008

Turning Points of Real Value Added in Manufacturing in Germany and Ifo Capacity Utilization

Cyclical component of value added Ifo capacity utilization (1) (2) (3)

Turning points of value added Turning points of capacity utilization

1) Standardized values.-2) Including food.-3) Smoothed with local weighted polynomial regression.

Source: DESTATIS, Ifo Business Cycle Test.

Outline

Outline

1 Business Cycles




5 Composite IndicatorsMotivationClassical Approach (NBER)Factor Analysis

Dynamic Factor AnalysisUnobserved ComponentsDynamic Factor Analysis by Forni et al.


Approaches

Approaches

Question:How can we condense information contained in variousindicators into one (or at least in a view) indicator(s)?

p Classical (NBER)

p Factor analysis and Principal Components

Steps in Classical Approach

Steps in Classical Approach

p Choose and classify indicators (detrending, cross-correlations,turning points, co-spectral analysis)

p Standardize indicators

p Average indicators (and standardize)

Factor ModelsThese models consider that a common force drives thedynamics of all variables. This common force, also known ascommon factor, is typically of low dimension and is not directlyobserved because every macroeconomic variable embodiessome idiosyncratic noise or short term movements. Factormodels clean every variable from these idiosyncraticmovements and estimate the common component in everyseries.

Three Approaches

Three Approaches

p Model based: factor estimation with unobserved componentsmodels and the Kalman filter

p Nonparametric: dynamic factor analysis by Forni et al.

p Nonparametric: principal components

Model Based: Unobserved Components

Model Based: Unobserved Components

The model consists of two stochastic components: the commonunobserved variable, or index ct and an n dimensionalcomponent, ut , that represents idiosyncratic movements in theseries and measurement error. The formulation of the model is:

zt = β + γ(L)ct + ut (measurement equation)

φ(L)ct = δ + νt (state equation)

D(L)ut = εt

Estimation is done by the Kalman filter.Literature: Stock and Watson (1988), A Probability Model of the CoincidentEconomic Indicators. Journal of Business and Economic Statistics, 147-162.

Dynamic Factor Model (Forni et al.)

Dynamic Factor Model (Forni et al.)

The dynamic factor model is:

zit = λi(L)ft + eit (1)

with λi(L) a lag polynomial.

Approximative Dynamic Model and Principal Components (Stock, Watson Approach)

Approximative Dynamic Model and PrincipalComponents (Stock, Watson Approach)

Under some assumptions the dynamic factor model

zit = λi(L)ft + eit (2)

can be rewritten asZt = ΛFt + et (3)

with Ft = (f ′t f′t−1...f

′t−q).

Estimation can be done by principal components.Literature: Stock and Watson (2002), Macroeconomic Forecasting UsingDiffusion Indexes. Journal of Business and Economic Statistics, 147-162.

Comparison of the Nonparametric Approaches

Comparison of the Nonparametric Approaches

p The static model requires only the specification of r. Thedynamic method requires input of four parameters.

p Estimation of static model is much more simple.

p A drawback of the static estimator is that it does not take intoaccount the dynamics of the factors, if they exist.

Neither estimator necessarily dominates the other.

Literature: Boivin J., Ng S. (2005), Understanding and ComparingFactor-Based Forecasts. International Journal of Central Banking, 117-151.

Outline

Outline

1 Business Cycles





6 Turning Points and Composite IndicatorsBinary response modelsMarkov-Switching Models

Turning Points in the Business Cycle

Turning Points in the Business Cycle

Generally, practitioners in business cycle analysis sometimesassume that economic cycles are constituted by an alternationof two conjonctural phases, namely a phase of high economicactivity (or expansion) and a phase of low economic activity (orcontraction). These phases can be defined in classical, growthor growth rate cycles. Sometimes also or than two phases areconsidered.

The objective of parametric models is to provide, at each date t ,an estimated probability of being in a specific phase.

Binary response models

Binary response models

If there is a reference series and if the phases (dating) of thereference series are available a binary variable can defined thattakes the value 1 when the economy belongs to one phase and0 when it belongs to the other phase. This 0− 1 variable can beused for logit or probit regressions.

Logistic Regression

Logistic Regression

Let Y be a binary variable with values 0 and 1 and X apredictor (e.g. a composite indicator), the the logisticregression model (logit) is

Log[

prob(Yt = 1)

1− prob(Yt = 1)

]= a + bxt . (4)

The model can be extended to contain lags of X and lags of Y .

Markov Switching

Markov Switching

Markov switching models consist to the class of nonlinear timeseries models. They base on the idea of probability switchingbetween various states (e.g. upswing and downswing). In thefollowing Markov switching autoregressive models arediscussed. Markov switching regression models use alsoexplanatory variables.

Markov Switching

Markov Switching

Hamilton (1989) considers the Markov switching autoregressive(MSA) model. Here the transition is driven by a two-stateMarkov chain. A time series xt follows an MSA model if itsatisfies:

xt =

{c1 +

∑pi=1 φ1,ixt−i + a1,t if st = 1,

c2 +∑p

i=1 φ2,ixt−i + a2,t if st = 2,(5)

where st assumes values in {1,2} and is a first-order Markovchain with transition probabilities

P(st = 2|st−1 = 1) = w1, P(st = 1|st−1 = 2) = w2. (6)

Markov Switching

Markov Switching

The innovational series {a1,t} and {a2,t} are sequences of iidrandom variables with mean zero and finite variance and areindependent of each other. A small wi means that to modeltends to stay longer in state i . In fact, 1/wi is the expectedduration of the process to stay in state i .

Example

Example

Source: Calculations of the Ifo Institute.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1991 FEB 1993 FEB 1995 FEB 1997 FEB 1999 FEB 2001 FEB 2003 FEB 2005 FEB 2007 FEB 2009 FEB 2011 FEB 2013 FEB

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