-
The Bank
-
The Bank - Column 1
- About the Banco de Portugal
- Sustainability
- Foreign exchange authority
-
The Bank - Column 2
-
Organisation
- Organisation chart
- Governor
- Board of Directors
- Distribution of remits and delegation of powers of the Board of Directors
- Board of Directors' Calendars
- Advisory Board
- Board of Auditors
- Internal audit
- Data protection policy
- Valora, S.A.
- Sociedade Gestora dos Fundos de Pensões
- National Council of Financial Supervisors
- Fintech +
- Recruitment
-
Organisation
-
The Bank - Column 3
- International activity
- See more
- Public consultations
- Media
-
Media - Column 1
- Press releases
- Public speeches
-
Media - Column 2
- Calendar
- Media - Column 3
- Publications and research
-
Publications - Column 1
- Annual Report
- Economic Bulletin
- Financial Stability
- Monetary Policy
-
Publications - Column 2
- Payments
- Banknotes and coins
- See all the publications
-
Other publications
-
Publications - Column 3
- Research
- Economics in a picture
- Monographs and series
-
- Mission and tasks
-
Statistics
-
Coluna 1 - Estatística
- Introduction
-
Coluna 2 - Estatística
- Reporting obligations
- SDDS Plus
- Coluna 3 - Estatística
-
Coluna 1 - Estatística
-
Supervision
-
Column 1 - Supervision
- Single Supervisory Mechanism
- Prudential rules
- Macroprudential
- Banking conduct supervision
-
Column 2 - Supervision
-
Microprudential
- Objectives and principles
- Priorities
- Supervisory Review and Evaluation Process
- Duty to report
- Reporting obligations of supervised institutions
- Authorisations
- Supervision of culture and governance
- Suitability of members of the management and supervisory bodies and key function holders
- Adequação dos titulares de funções essenciais
- Suitability of qualifying shareholders
- European Market Infrastructure Regulation (EMIR)
- Forum on Cybersecurity and Operational Resilience
- See more
-
Microprudential
-
Column 3 - Supervision
-
Money laundering and terrorist financing
- Banco de Portugal's functions
- Financial Action Task Force
- Restrictive measures
- Registration of virtual assets service providers
- Report on the activity carried out in Portugal under the freedom to provide services
- Documents
- Legislation and rules
- Forum on the Prevention of Money Laundering and Terrorist Financing
- Illicit financial activity
- Brexit
-
Money laundering and terrorist financing
-
Column 1 - Supervision
-
Monetary policy
- Column 1 - Monetary policy
-
Column 2 - Monetary policy
- Interest rates
- Implementation
- Column 3 - Monetary policy
-
Payment systems
-
Column 1 - Payment systems
- Introduction
- Confirmation of Payee/Payer and SPIN
- Digital Euro
-
Column 2 - Payment systems
- Payment instruments
- Payment services under the PSD2
- Virtual assets
-
Column 3 - Payment systems
- Market Infrastructure
- Cooperation with the market
- See more
-
Column 1 - Payment systems
-
Banknotes and coins
- Column 1 - Banknotes and coins
-
Column 2 - Banknotes and coins
- Current coins
- Commemorative and collector coins
- Column 3 - Banknotes and coins
-
The Bank - Column 1
Anterior
-
The Bank
- voltar
- The Bank
- About the Banco de Portugal
-
Sustainability
- voltar
- Sustainability
- Approach to sustainability
- Social responsibility
-
Foreign exchange authority
- voltar
- Foreign exchange authority
- Banco de Portugal's functions
- Global code
-
Organisation
- voltar
- Organisation
- Organisation chart
- Governor
- Board of Directors
- Distribution of remits and delegation of powers of the Board of Directors
- Board of Directors' Calendars
- Advisory Board
- Board of Auditors
- Internal audit
- Data protection policy
- Valora, S.A.
- Sociedade Gestora dos Fundos de Pensões
- National Council of Financial Supervisors
-
Fintech +
- voltar
- Fintech +
- What is it and how does it work?
-
Recruitment
- voltar
- Recruitment
- See job opportunities
- International activity
- See more
-
Public consultations
- voltar
- Public consultations
- Banco de Portugal
- EBA
- Other institutions
-
Media
- voltar
- Media
-
Press releases
- voltar
- Press releases
- Banco de Portugal
- European Central Bank
- SSM
- EBA
- ESRB
-
Public speeches
- voltar
- Public speeches
- Governor
- Board members
- All
-
Calendar
- voltar
- Calendar
- Events
- Publications
- Indicators
- All
- See media contacts
-
Publications and research
- voltar
- Publications and research
- Annual Report
-
Economic Bulletin
- voltar
- Economic Bulletin
- See all
- Accessible summary
- Economic projections
- Financial Stability
-
Monetary Policy
- voltar
- Monetary Policy
- Report on Monetary Policy Implementation
- Payments
-
Banknotes and coins
- voltar
- Banknotes and coins
- Report on Cash Issuance
- See all the publications
-
Other publications
- voltar
- Other publications
- Research
- Economics in a picture
-
Monographs and series
- voltar
- Monographs and series
- Order publications
- See publications
- Publication 1
- Publication 2
-
Mission and tasks
- voltar
- Mission and tasks
-
Statistics
- voltar
- Statistics
-
Introduction
- voltar
- Introduction
- Banco de Portugal Statistics
- Statistical events
-
Reporting obligations
- voltar
- Reporting obligations
- Reporting obligations for statistical purposes
- List of entities for statistical purposes
- SDDS Plus
- Browse data
-
Supervision
- voltar
- Supervision
-
Single Supervisory Mechanism
- voltar
- Single Supervisory Mechanism
- How does it work?
- Press releases
- Prudential rules
-
Macroprudential
- voltar
- Macroprudential
- Macroprudential policy
- Macroprudential measures
-
Banking conduct supervision
- voltar
- Banking conduct supervision
- Objectives
- Regulation
- Oversight
- Financial education
- Banking Conduct Supervision Forum
-
Microprudential
- voltar
- Microprudential
- Objectives and principles
- Priorities
- Supervisory Review and Evaluation Process
- Duty to report
- Reporting obligations of supervised institutions
- Authorisations
- Supervision of culture and governance
- Suitability of members of the management and supervisory bodies and key function holders
- Adequação dos titulares de funções essenciais
- Suitability of qualifying shareholders
- European Market Infrastructure Regulation (EMIR)
- Forum on Cybersecurity and Operational Resilience
- See more
-
Money laundering and terrorist financing
- voltar
- Money laundering and terrorist financing
- Banco de Portugal's functions
- Financial Action Task Force
- Restrictive measures
- Registration of virtual assets service providers
- Report on the activity carried out in Portugal under the freedom to provide services
- Documents
- Legislation and rules
- Forum on the Prevention of Money Laundering and Terrorist Financing
-
Illicit financial activity
- voltar
- Illicit financial activity
- Unauthorised activity
- Public warnings
- Advice
- Brexit
-
Monetary policy
- voltar
- Monetary policy
- Definition and strategy
-
Information systems
- voltar
- Information systems
- SITENDER, COLMS and TEB
- Eurosystem Collateral Management System
-
Interest rates
- voltar
- Interest rates
- Official and reference interest rates
-
Implementation
- voltar
- Implementation
- Instruments
- Collateral
- Counterparties
- Other monetary policy measures
-
Payment systems
- voltar
- Payment systems
-
Introduction
- voltar
- Introduction
- Banco de Portugal's functions
-
Confirmation of Payee/Payer and SPIN
- voltar
- Confirmation of Payee/Payer and SPIN
- Confirmation of Payee/Payer
- Verification of Payee
- SPIN
- Digital Euro
-
Payment instruments
- voltar
- Payment instruments
- About
- Cards
- Cheques
- Direct debits
- Credit transfers
- Instant transfers
- IBAN
- Use of payment instruments
-
Payment services under the PSD2
- voltar
- Payment services under the PSD2
- About
- Strong customer authentication
- Account information services and payment initiation services
-
Virtual assets
- voltar
- Virtual assets
- How does it work?
- Market Infrastructure
-
Cooperation with the market
- voltar
- Cooperation with the market
- CISP
- Payment Systems Forum
- AMI-SeCo-PT
- See more
-
Banknotes and coins
- voltar
- Banknotes and coins
-
Banknote production
- voltar
- Banknote production
- Valora, S.A.
- Gestão da qualidade
- Cash and sustainability
- Banknotes
- Current coins
-
Commemorative and collector coins
- voltar
- Commemorative and collector coins
- Collector coins
- Commemorative coins
- See all
-
Training
- voltar
- Training
- Face-to-face and e-learning
- Anti-counterfeiting
- For professionals
Search
Tags
- AGIL
- Balance of Payments
- Banco de Portugal
- Bank loans and deposits
- Banknotes and coins
- Cheques
- Collector coins
- Commemorative coin
- Cooperation
- Corporations in the Central Balance-Sheet Database
- COVID-19
- Decoder
- Digital euro
- Direct debits
- Direct investment
- EBA
- Economics in a picture
- Economic studies
- EFAP
- European Central Bank
- Financial stability
- General government financing
- Governor
- Historical archive
- IBAN
- Infographics
- Interest rate
- International banking statistics
- Investment Funds
- Library
- Macroprudential measure
- National Council of Financial Supervisors
- National financial accounts
- Non-financial sector indebtedness
- Organisation
- Other financial intermediaries, financial auxiliaries and captive financial institutions and money lenders balance sheet
- Payment cards
- Payment instruments
- Podcast
- Política Monetária
- Posição de investimento internacional
- Press release
- Public debt
- Reciprocidade voluntária
- Reserva contracíclica
- Reserva de conservação
- Reserva de O-SII
- Securities holdings
- Securities issues
- SICOI
- Single Supervisory Mechanism
- Sistemas de Pagamentos
- SITENDER
- Statistical Press Release
- Statistics
- Supervisão
- Sustainability
- T2S
- TARGET2
- TARGET2-Securites
- Transferências
- Vídeo
- Virtual assets
Ano
- 2025
- 2024
- 2023
- 2022
- 2021
- 2020
- 2019
- 2018
- 2017
- 2016
- 2015
- 2014
- 2013
- 2012
- 2011
- 2010
- 2009
- 2008
- 2007
- 2006
- 2005
- 2004
- 2003
- 2002
- 2001
- 2000
- 1999
- 1998
- 1997
- 1996
- 1995
- 1994
- 1993
- 1992
- 1991
- 1990
- 1989
- 1988
- 1987
- 1986
- 1985
- 1984
- 1983
- 1982
- 1981
- 1979
- 1978
- 1974
- 1969
- 1962
- 1957
- 1953
- 1950
- 1947
- 1940
- 1933
- 1932
- 1929
- 1927
- 1926
- 1922
- 1920
- 1917
- 1916
- 1915
- 1914
- 1913
- 1912
- 1911
- 1896
- 1876
- 1864
- 1844
Related Pages
Código JEL
E32 - Business Fluctuations; Cycles
C22 - Time-Series Models
We resort to a rigorous definition of spectrum of an integrated time series in order to characterise the implications of applying linear filters to such series. We conclude that in the presence of integrated series the transfer function of the filters has exactly the same interpretation as in the covariance stationary case, contrary to what many authors suggest. This disagreement leads to different conclusions regarding the link of the original fluctuations with the transformed fluctuations in the time series data, embodied in various unjustified criticisms to the application of detrending filters. Despite this, and given the frequency domain characteristics of filtered macroeconomic integrated series, we acknowledge that the choice of a particular detrending filter is far from being a neutral task.
Documents