everything you always wanted to know about ultra high...
TRANSCRIPT
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Everything You Always Wanted to KnowAbout Ultra High-Frequency Data
but Were Afraid to Ask
Christian T. Brownlees1 Giampiero M. Gallo1
1Dipartimento di Statistica “G. Parenti”Università degli Studi di Firenze
22nd September 2005
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Outline
1 Motivation
2 Data Structure and Exchange Market Rules & Procedures
3 Ultra High-Frequency Data ManagementData CleaningData HandlingTime Series Construction
4 Econometric Analysis of Ultra High-Frequency DataStylised FactsA MEM Approach to High Frequency Dynamics
5 Conclusions
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Ultra High-Frequency Analysis
The availability of financial data at a very high frequency hasbeen one of the most relevant innovations in the field ofquantitative analysis of the financial markets over the past fewyears.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Ultra High-Frequency Analysis
The practitioner’s world is also slowly moving towards an ultrahigh-frequency approach to financial analysis.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Ultra High-Frequency Analysis
Unfortunately the analysis of this data is not particularly simple.The main causes of this difficulty are
the need to understand the market mechanisms whichhave an impact in the series dynamics,
the operational complications which arise whenmanipulating these data,
models based on daily observations do not seem to besuccessful in capturing data patterns at higher frequencies.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Ultra High-Frequency Analysis
Unfortunately the analysis of this data is not particularly simple.The main causes of this difficulty are
the need to understand the market mechanisms whichhave an impact in the series dynamics,
the operational complications which arise whenmanipulating these data,
models based on daily observations do not seem to besuccessful in capturing data patterns at higher frequencies.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Ultra High-Frequency Analysis
Unfortunately the analysis of this data is not particularly simple.The main causes of this difficulty are
the need to understand the market mechanisms whichhave an impact in the series dynamics,
the operational complications which arise whenmanipulating these data,
models based on daily observations do not seem to besuccessful in capturing data patterns at higher frequencies.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Ultra High-Frequency Analysis
Unfortunately the analysis of this data is not particularly simple.The main causes of this difficulty are
the need to understand the market mechanisms whichhave an impact in the series dynamics,
the operational complications which arise whenmanipulating these data,
models based on daily observations do not seem to besuccessful in capturing data patterns at higher frequencies.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Ultra High-Frequency Analysis
This contribution tries to directly address these issues:
it explains the structure of the high frequency datasets andhighlights the relevant aspects of the market mechanisms;
it surveys simple and general methods for the datamanagement and manipulation which have beenimplemented in a freely available package for MATLAB;
it presents some basic stylised facts and models for highfrequency modelling.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Ultra High-Frequency Analysis
This contribution tries to directly address these issues:
it explains the structure of the high frequency datasets andhighlights the relevant aspects of the market mechanisms;
it surveys simple and general methods for the datamanagement and manipulation which have beenimplemented in a freely available package for MATLAB;
it presents some basic stylised facts and models for highfrequency modelling.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Ultra High-Frequency Analysis
This contribution tries to directly address these issues:
it explains the structure of the high frequency datasets andhighlights the relevant aspects of the market mechanisms;
it surveys simple and general methods for the datamanagement and manipulation which have beenimplemented in a freely available package for MATLAB;
it presents some basic stylised facts and models for highfrequency modelling.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
The Focus of the Analysis
There are many financial markets which produce tick data.
The focus of this research is the the New York Stock Exchange(NYSE).
A review of the ultra high-frequency datasets from this source isparticularly interesting since the type of information available forequity markets is in fact qualitatively different and much moredetailed than the one available for the OTC markets.
The empirical illustrations of this presentation will be made inreference to the time series of General Electric (GE) in 2002.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
The Focus of the Analysis
There are many financial markets which produce tick data.
The focus of this research is the the New York Stock Exchange(NYSE).
A review of the ultra high-frequency datasets from this source isparticularly interesting since the type of information available forequity markets is in fact qualitatively different and much moredetailed than the one available for the OTC markets.
The empirical illustrations of this presentation will be made inreference to the time series of General Electric (GE) in 2002.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
The Focus of the Analysis
There are many financial markets which produce tick data.
The focus of this research is the the New York Stock Exchange(NYSE).
A review of the ultra high-frequency datasets from this source isparticularly interesting since the type of information available forequity markets is in fact qualitatively different and much moredetailed than the one available for the OTC markets.
The empirical illustrations of this presentation will be made inreference to the time series of General Electric (GE) in 2002.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
The Focus of the Analysis
There are many financial markets which produce tick data.
The focus of this research is the the New York Stock Exchange(NYSE).
A review of the ultra high-frequency datasets from this source isparticularly interesting since the type of information available forequity markets is in fact qualitatively different and much moredetailed than the one available for the OTC markets.
The empirical illustrations of this presentation will be made inreference to the time series of General Electric (GE) in 2002.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Ultra High-Frequency Data Description
Ultra high-frequency databases are complex to analyse
huge number of ticks;
the time interval between ticks is random;the sequence of ticks
could contain some wrong ticks,might not be time ordered andmight have to be reconstructed from other tick sequences;
a tick contains additional information which may not be ofinterest for the specific purposes of the analysis (like NYSEsequence number, trading conditions, etc.);
the structure of the ticks depends on the rules of thefinancial institution which produces/collects the data.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Ultra High-Frequency Data Description
Ultra high-frequency databases are complex to analyse
huge number of ticks;
the time interval between ticks is random;the sequence of ticks
could contain some wrong ticks,might not be time ordered andmight have to be reconstructed from other tick sequences;
a tick contains additional information which may not be ofinterest for the specific purposes of the analysis (like NYSEsequence number, trading conditions, etc.);
the structure of the ticks depends on the rules of thefinancial institution which produces/collects the data.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Ultra High-Frequency Data Description
Ultra high-frequency databases are complex to analyse
huge number of ticks;
the time interval between ticks is random;the sequence of ticks
could contain some wrong ticks,might not be time ordered andmight have to be reconstructed from other tick sequences;
a tick contains additional information which may not be ofinterest for the specific purposes of the analysis (like NYSEsequence number, trading conditions, etc.);
the structure of the ticks depends on the rules of thefinancial institution which produces/collects the data.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Ultra High-Frequency Data Description
Ultra high-frequency databases are complex to analyse
huge number of ticks;
the time interval between ticks is random;the sequence of ticks
could contain some wrong ticks,might not be time ordered andmight have to be reconstructed from other tick sequences;
a tick contains additional information which may not be ofinterest for the specific purposes of the analysis (like NYSEsequence number, trading conditions, etc.);
the structure of the ticks depends on the rules of thefinancial institution which produces/collects the data.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Ultra High-Frequency Data Description
Ultra high-frequency databases are complex to analyse
huge number of ticks;
the time interval between ticks is random;the sequence of ticks
could contain some wrong ticks,might not be time ordered andmight have to be reconstructed from other tick sequences;
a tick contains additional information which may not be ofinterest for the specific purposes of the analysis (like NYSEsequence number, trading conditions, etc.);
the structure of the ticks depends on the rules of thefinancial institution which produces/collects the data.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Ultra High-Frequency Data Description
Ultra high-frequency databases are complex to analyse
huge number of ticks;
the time interval between ticks is random;the sequence of ticks
could contain some wrong ticks,might not be time ordered andmight have to be reconstructed from other tick sequences;
a tick contains additional information which may not be ofinterest for the specific purposes of the analysis (like NYSEsequence number, trading conditions, etc.);
the structure of the ticks depends on the rules of thefinancial institution which produces/collects the data.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Ultra High-Frequency Data Description
Ultra high-frequency databases are complex to analyse
huge number of ticks;
the time interval between ticks is random;the sequence of ticks
could contain some wrong ticks,might not be time ordered andmight have to be reconstructed from other tick sequences;
a tick contains additional information which may not be ofinterest for the specific purposes of the analysis (like NYSEsequence number, trading conditions, etc.);
the structure of the ticks depends on the rules of thefinancial institution which produces/collects the data.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Ultra High-Frequency Data Description
Ultra high-frequency databases are complex to analyse
huge number of ticks;
the time interval between ticks is random;the sequence of ticks
could contain some wrong ticks,might not be time ordered andmight have to be reconstructed from other tick sequences;
a tick contains additional information which may not be ofinterest for the specific purposes of the analysis (like NYSEsequence number, trading conditions, etc.);
the structure of the ticks depends on the rules of thefinancial institution which produces/collects the data.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
The New York Stock Exchange
The NYSE is a hybrid market, in that it is both an agency andan auction market. It is an agency market since the buy andsell orders are executed by an agent, the market maker, who inthe NYSE is called the specialist. The NYSE is also an auctionmarket, since on the exchanges’ floor the brokers participateactively in the negotiation and thus they contribute to thedetermination of the transaction price.
Despite the global trend towards computer automated tradingsystems, the “human” element has a very crucial role in thetrading mechanisms, and this fact has a deep impact on thedata.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
The New York Stock Exchange
The NYSE is a hybrid market, in that it is both an agency andan auction market. It is an agency market since the buy andsell orders are executed by an agent, the market maker, who inthe NYSE is called the specialist. The NYSE is also an auctionmarket, since on the exchanges’ floor the brokers participateactively in the negotiation and thus they contribute to thedetermination of the transaction price.
Despite the global trend towards computer automated tradingsystems, the “human” element has a very crucial role in thetrading mechanisms, and this fact has a deep impact on thedata.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Types of Data
Book The book contains detailed information on limitorders.
Quotes Quote data contains information regarding the besttrading conditions available on the exchange.Information of interest: bid/ask time stamps, prices,volumes.
Trades Trade data contains information regarding theorders which have been executed on the exchange.Information of interest: transaction time stamp, pricevolume.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Types of Data
Book The book contains detailed information on limitorders.
Quotes Quote data contains information regarding the besttrading conditions available on the exchange.Information of interest: bid/ask time stamps, prices,volumes.
Trades Trade data contains information regarding theorders which have been executed on the exchange.Information of interest: transaction time stamp, pricevolume.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Types of Data
Book The book contains detailed information on limitorders.
Quotes Quote data contains information regarding the besttrading conditions available on the exchange.Information of interest: bid/ask time stamps, prices,volumes.
Trades Trade data contains information regarding theorders which have been executed on the exchange.Information of interest: transaction time stamp, pricevolume.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
Ultra High-Frequency Data Management
The preliminary steps that have to be undertaken beforestarting the analysis of UHFD are:
detecting and removing wrong observations from the rawUHFD: Data Cleaning,
constructing the time series of interest for the objectives ofthe analysis: Data Handling.
Unfortunately these operations are far less trivial than onecould expect.The literature is not particularly clear on how these operationsare performed.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
Ultra High-Frequency Data Management
The preliminary steps that have to be undertaken beforestarting the analysis of UHFD are:
detecting and removing wrong observations from the rawUHFD: Data Cleaning,
constructing the time series of interest for the objectives ofthe analysis: Data Handling.
Unfortunately these operations are far less trivial than onecould expect.The literature is not particularly clear on how these operationsare performed.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
Ultra High-Frequency Data Management
The preliminary steps that have to be undertaken beforestarting the analysis of UHFD are:
detecting and removing wrong observations from the rawUHFD: Data Cleaning,
constructing the time series of interest for the objectives ofthe analysis: Data Handling.
Unfortunately these operations are far less trivial than onecould expect.The literature is not particularly clear on how these operationsare performed.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
Ultra High-Frequency Data Management
The preliminary steps that have to be undertaken beforestarting the analysis of UHFD are:
detecting and removing wrong observations from the rawUHFD: Data Cleaning,
constructing the time series of interest for the objectives ofthe analysis: Data Handling.
Unfortunately these operations are far less trivial than onecould expect.The literature is not particularly clear on how these operationsare performed.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
Ultra High-Frequency Data Management
The preliminary steps that have to be undertaken beforestarting the analysis of UHFD are:
detecting and removing wrong observations from the rawUHFD: Data Cleaning,
constructing the time series of interest for the objectives ofthe analysis: Data Handling.
Unfortunately these operations are far less trivial than onecould expect.The literature is not particularly clear on how these operationsare performed.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
Ultra High-Frequency Data Management
The preliminary steps that have to be undertaken beforestarting the analysis of UHFD are:
detecting and removing wrong observations from the rawUHFD: Data Cleaning,
constructing the time series of interest for the objectives ofthe analysis: Data Handling.
Unfortunately these operations are far less trivial than onecould expect.The literature is not particularly clear on how these operationsare performed.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
Data Cleaning
Raw UHFD is well known for being prone to errors.
We need methods for eliminating wrong obsevations. This kindof preliminary data manipulation is often referred as filtering ordata cleaning.
Data cleaning aims to eliminate from the ultra high-frequencytime series observations which does not reflect the marketactivity, in practise however these methods cannot go beyonddetecting outliers.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
Data Cleaning
Raw UHFD is well known for being prone to errors.
We need methods for eliminating wrong obsevations. This kindof preliminary data manipulation is often referred as filtering ordata cleaning.
Data cleaning aims to eliminate from the ultra high-frequencytime series observations which does not reflect the marketactivity, in practise however these methods cannot go beyonddetecting outliers.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
Data Cleaning
Raw UHFD is well known for being prone to errors.
We need methods for eliminating wrong obsevations. This kindof preliminary data manipulation is often referred as filtering ordata cleaning.
Data cleaning aims to eliminate from the ultra high-frequencytime series observations which does not reflect the marketactivity, in practise however these methods cannot go beyonddetecting outliers.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
Where Do Errors Come From?
It is not really clear where errors come from and whichtheir causes are.
Falkenberry (2002) reports that errors are present both infully automated and partly automated trading systemssuch as the NYSE.
According to the author, trading intensity is the maindeterminant of errors: the higher the velocity in trading, thehigher the probability that some error will be committed inreporting trading information.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
Where Do Errors Come From?
It is not really clear where errors come from and whichtheir causes are.
Falkenberry (2002) reports that errors are present both infully automated and partly automated trading systemssuch as the NYSE.
According to the author, trading intensity is the maindeterminant of errors: the higher the velocity in trading, thehigher the probability that some error will be committed inreporting trading information.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
Where Do Errors Come From?
It is not really clear where errors come from and whichtheir causes are.
Falkenberry (2002) reports that errors are present both infully automated and partly automated trading systemssuch as the NYSE.
According to the author, trading intensity is the maindeterminant of errors: the higher the velocity in trading, thehigher the probability that some error will be committed inreporting trading information.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
What Does “Raw” Data Mean?
a b
Trade and quote data for the GE stock on the 11st of November 2002from (a) 9:30 to 16:05 and (b) 10:30 to 10:31.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
Data Cleaning
Easy procedure on tick–by–tick price time series (detect a priceout of line with the current market momentum).
Volume data: no special data cleaning recipes other thanassessing the plausibility of a certain volume (either judgingupon the corresponding price or resorting to classical statisticaloutlier detection methods).
Algorithms proposed in the literature for washing away wrongobservations (e.g. algorithm used at Olsen’s -Dacorogna et al,2001). NYSE data require simpler steps.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
Data Cleaning
Easy procedure on tick–by–tick price time series (detect a priceout of line with the current market momentum).
Volume data: no special data cleaning recipes other thanassessing the plausibility of a certain volume (either judgingupon the corresponding price or resorting to classical statisticaloutlier detection methods).
Algorithms proposed in the literature for washing away wrongobservations (e.g. algorithm used at Olsen’s -Dacorogna et al,2001). NYSE data require simpler steps.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
Data Cleaning
Easy procedure on tick–by–tick price time series (detect a priceout of line with the current market momentum).
Volume data: no special data cleaning recipes other thanassessing the plausibility of a certain volume (either judgingupon the corresponding price or resorting to classical statisticaloutlier detection methods).
Algorithms proposed in the literature for washing away wrongobservations (e.g. algorithm used at Olsen’s -Dacorogna et al,2001). NYSE data require simpler steps.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
Data Cleaner
Ultra High-Frequency Cleaning Algorithm
For each observation remove the i th tick if∣∣xi − x̃[i−1:i−k−1]
∣∣ > 3√
s2[i−1:i−k−1] + γ2
k window size
γ granularity tolerance level
x̃[i−1:i−k−1] 5% trimmed sample mean of the last k ticks
s2[i−1:i−k−1] sample variance of the last k ticks
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
Data Cleaner
Ultra High-Frequency Cleaning Algorithm
For each observation remove the i th tick if∣∣xi − x̃[i−1:i−k−1]
∣∣ > 3√
s2[i−1:i−k−1] + γ2
k window size
γ granularity tolerance level
x̃[i−1:i−k−1] 5% trimmed sample mean of the last k ticks
s2[i−1:i−k−1] sample variance of the last k ticks
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
Data Cleaner
Ultra High-Frequency Cleaning Algorithm
For each observation remove the i th tick if∣∣xi − x̃[i−1:i−k−1]
∣∣ > 3√
s2[i−1:i−k−1] + γ2
k window size
γ granularity tolerance level
x̃[i−1:i−k−1] 5% trimmed sample mean of the last k ticks
s2[i−1:i−k−1] sample variance of the last k ticks
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
Data Cleaner
Ultra High-Frequency Cleaning Algorithm
For each observation remove the i th tick if∣∣xi − x̃[i−1:i−k−1]
∣∣ > 3√
s2[i−1:i−k−1] + γ2
k window size
γ granularity tolerance level
x̃[i−1:i−k−1] 5% trimmed sample mean of the last k ticks
s2[i−1:i−k−1] sample variance of the last k ticks
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
Data Cleaner
Ultra High-Frequency Cleaning Algorithm
For each observation remove the i th tick if∣∣xi − x̃[i−1:i−k−1]
∣∣ > 3√
s2[i−1:i−k−1] + γ2
k window size
γ granularity tolerance level
x̃[i−1:i−k−1] 5% trimmed sample mean of the last k ticks
s2[i−1:i−k−1] sample variance of the last k ticks
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
Some Comments
The procedure is heuristic but it has several appealing features:
it is simple,
it can be used for on-line data cleaning as it only uses pastinformation,
the impact of the use of such method is negligible if thecleaned data are further aggregated at lower frequencies.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
Some Comments
The procedure is heuristic but it has several appealing features:
it is simple,
it can be used for on-line data cleaning as it only uses pastinformation,
the impact of the use of such method is negligible if thecleaned data are further aggregated at lower frequencies.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
Some Comments
The procedure is heuristic but it has several appealing features:
it is simple,
it can be used for on-line data cleaning as it only uses pastinformation,
the impact of the use of such method is negligible if thecleaned data are further aggregated at lower frequencies.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
1-minute of Trading Activity on the NYSE
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
Spot the Differences with Daily Financial Series
Simultaneous Observations There are more transactionsreported at the same time at very different pricelevels.
Irregularly Spaced Observations The timing betweensubsequent events is random.
Bid–Ask Bounce The price changes are discrete and the pricehas a tendency to bounce around the currentmid–price.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
Spot the Differences with Daily Financial Series
Simultaneous Observations There are more transactionsreported at the same time at very different pricelevels.
Irregularly Spaced Observations The timing betweensubsequent events is random.
Bid–Ask Bounce The price changes are discrete and the pricehas a tendency to bounce around the currentmid–price.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
Spot the Differences with Daily Financial Series
Simultaneous Observations There are more transactionsreported at the same time at very different pricelevels.
Irregularly Spaced Observations The timing betweensubsequent events is random.
Bid–Ask Bounce The price changes are discrete and the pricehas a tendency to bounce around the currentmid–price.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
Opening and Closing
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
What’s a Bit Weird?
Opening The first transaction/quotation of the day is notnecessarily the opening transactions/quotation
Closing the closing does not occur at 16:00 (the officialclosing time) but some time later. The lasttransaction/quotation of the day is not necessarilythe closing transactions/quotation.
Non Synchronised trades and quotes are not synchronised.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
What’s a Bit Weird?
Opening The first transaction/quotation of the day is notnecessarily the opening transactions/quotation
Closing the closing does not occur at 16:00 (the officialclosing time) but some time later. The lasttransaction/quotation of the day is not necessarilythe closing transactions/quotation.
Non Synchronised trades and quotes are not synchronised.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
What’s a Bit Weird?
Opening The first transaction/quotation of the day is notnecessarily the opening transactions/quotation
Closing the closing does not occur at 16:00 (the officialclosing time) but some time later. The lasttransaction/quotation of the day is not necessarilythe closing transactions/quotation.
Non Synchronised trades and quotes are not synchronised.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
What to Do Then?
Simultaneous Observations → Aggregate Them
Irregularly Spaced Observations → Construct a RegularFrequency Series (if needed)
Random Closing of the Markets → “Extend” the Trading Dayuntill 16:05:00
The MATLAB toolbox for UHFD analysis contains a number ofprocedures for performing these task.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
What to Do Then?
Simultaneous Observations → Aggregate Them
Irregularly Spaced Observations → Construct a RegularFrequency Series (if needed)
Random Closing of the Markets → “Extend” the Trading Dayuntill 16:05:00
The MATLAB toolbox for UHFD analysis contains a number ofprocedures for performing these task.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
What to Do Then?
Simultaneous Observations → Aggregate Them
Irregularly Spaced Observations → Construct a RegularFrequency Series (if needed)
Random Closing of the Markets → “Extend” the Trading Dayuntill 16:05:00
The MATLAB toolbox for UHFD analysis contains a number ofprocedures for performing these task.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
What to Do Then?
Simultaneous Observations → Aggregate Them
Irregularly Spaced Observations → Construct a RegularFrequency Series (if needed)
Random Closing of the Markets → “Extend” the Trading Dayuntill 16:05:00
The MATLAB toolbox for UHFD analysis contains a number ofprocedures for performing these task.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
More on the Construction of Regular Frequency Series
Origin: irregularly spaced time series {(ti , xi)}Ni=1
Destination: regular frequency time series {(t∗j , x∗j )}N∗j=1
We propose using mapping functions like:
x∗j = f ( {(ti , xi) | ti ∈ (t∗j−1, t∗j ]} )
the value x∗j is constructed using the information available t∗j−1until t∗j
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
More on the Construction of Regular Frequency Series
Origin: irregularly spaced time series {(ti , xi)}Ni=1
Destination: regular frequency time series {(t∗j , x∗j )}N∗j=1
We propose using mapping functions like:
x∗j = f ( {(ti , xi) | ti ∈ (t∗j−1, t∗j ]} )
the value x∗j is constructed using the information available t∗j−1until t∗j
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
More on the Construction of Regular Frequency Series
Some simple but useful methods are:
First: x∗j = xf where tf = min{ti |ti ∈ (t∗j−1, t∗j ]}Minimum: x∗j = min{xi |ti ∈ (t∗j−1, t∗j ]}
Maximum: x∗j = max{xi |ti ∈ (t∗j−1, t∗j ]}Last: x∗j = xl where tl = max{ti |ti ∈ (t∗j−1, t∗j ]}Sum: x∗j =
∑ti∈(t∗j−1,t∗j ] xi
Count: x∗j = #{(xi , ti)|ti ∈ (t∗j−1, t∗j ]}
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
More on the Construction of Regular Frequency Series
Some simple but useful methods are:
First: x∗j = xf where tf = min{ti |ti ∈ (t∗j−1, t∗j ]}Minimum: x∗j = min{xi |ti ∈ (t∗j−1, t∗j ]}
Maximum: x∗j = max{xi |ti ∈ (t∗j−1, t∗j ]}Last: x∗j = xl where tl = max{ti |ti ∈ (t∗j−1, t∗j ]}Sum: x∗j =
∑ti∈(t∗j−1,t∗j ] xi
Count: x∗j = #{(xi , ti)|ti ∈ (t∗j−1, t∗j ]}
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
More on the Construction of Regular Frequency Series
Some simple but useful methods are:
First: x∗j = xf where tf = min{ti |ti ∈ (t∗j−1, t∗j ]}Minimum: x∗j = min{xi |ti ∈ (t∗j−1, t∗j ]}
Maximum: x∗j = max{xi |ti ∈ (t∗j−1, t∗j ]}Last: x∗j = xl where tl = max{ti |ti ∈ (t∗j−1, t∗j ]}Sum: x∗j =
∑ti∈(t∗j−1,t∗j ] xi
Count: x∗j = #{(xi , ti)|ti ∈ (t∗j−1, t∗j ]}
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
More on the Construction of Regular Frequency Series
Some simple but useful methods are:
First: x∗j = xf where tf = min{ti |ti ∈ (t∗j−1, t∗j ]}Minimum: x∗j = min{xi |ti ∈ (t∗j−1, t∗j ]}
Maximum: x∗j = max{xi |ti ∈ (t∗j−1, t∗j ]}Last: x∗j = xl where tl = max{ti |ti ∈ (t∗j−1, t∗j ]}Sum: x∗j =
∑ti∈(t∗j−1,t∗j ] xi
Count: x∗j = #{(xi , ti)|ti ∈ (t∗j−1, t∗j ]}
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
More on the Construction of Regular Frequency Series
Some simple but useful methods are:
First: x∗j = xf where tf = min{ti |ti ∈ (t∗j−1, t∗j ]}Minimum: x∗j = min{xi |ti ∈ (t∗j−1, t∗j ]}
Maximum: x∗j = max{xi |ti ∈ (t∗j−1, t∗j ]}Last: x∗j = xl where tl = max{ti |ti ∈ (t∗j−1, t∗j ]}Sum: x∗j =
∑ti∈(t∗j−1,t∗j ] xi
Count: x∗j = #{(xi , ti)|ti ∈ (t∗j−1, t∗j ]}
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
More on the Construction of Regular Frequency Series
Some simple but useful methods are:
First: x∗j = xf where tf = min{ti |ti ∈ (t∗j−1, t∗j ]}Minimum: x∗j = min{xi |ti ∈ (t∗j−1, t∗j ]}
Maximum: x∗j = max{xi |ti ∈ (t∗j−1, t∗j ]}Last: x∗j = xl where tl = max{ti |ti ∈ (t∗j−1, t∗j ]}Sum: x∗j =
∑ti∈(t∗j−1,t∗j ] xi
Count: x∗j = #{(xi , ti)|ti ∈ (t∗j−1, t∗j ]}
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
More on the Construction of Regular Frequency Series
This approach is very different from what has been proposedby authors such as Dacorogna et al (2001).
We believe that this approach is better than other methodswhich mix past and future information in a potentiallydangerous manner.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
More on the Construction of Regular Frequency Series
This approach is very different from what has been proposedby authors such as Dacorogna et al (2001).
We believe that this approach is better than other methodswhich mix past and future information in a potentiallydangerous manner.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
Time Series Construction
Intra-daily transaction data of the GE ticker in 2002.
Time series of interest: intra-daily returns rd ,t , volumes vd ,t
and number of transactions per interval td ,t
Frequencies: 14 different intra-daily frequencies from 1minute to 3 hours
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
Time Series Construction
Intra-daily transaction data of the GE ticker in 2002.
Time series of interest: intra-daily returns rd ,t , volumes vd ,t
and number of transactions per interval td ,t
Frequencies: 14 different intra-daily frequencies from 1minute to 3 hours
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
Time Series Construction
Intra-daily transaction data of the GE ticker in 2002.
Time series of interest: intra-daily returns rd ,t , volumes vd ,t
and number of transactions per interval td ,t
Frequencies: 14 different intra-daily frequencies from 1minute to 3 hours
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
Raw Data & Preliminary Data Treatment
Summary of the preliminary operations performed on the data.
number of raw observations 3907055 100%ticks out of time scale -14353 -0.37%filtered ticks -12262 -0.31%simultaneous ticks -1471227 -37.66%number of clean observations 2409213 61.66 %
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Data CleaningData HandlingTime Series Construction
Number of Observations and Missing Observations
Frequency Num. of Observations % of Missing1 minute 97074 4.27%2 minutes 48562 4.22%
...5 minutes 19448 4.10%6 minutes 16211 4.08%10 minutes 9735 3.99%
...30 minutes 3249 3.88%
...2 hours 1002 3.65%3 hours 752 3.59%
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Stylised FactsA MEM Approach to High Frequency Dynamics
Econometric Analysis of Transaction Data
Hourly returns rd ,t , volumes vd ,t and number of transactions td ,t .
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Stylised FactsA MEM Approach to High Frequency Dynamics
Seasonal Moments
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Stylised FactsA MEM Approach to High Frequency Dynamics
Distributional Shapes Across Frequencies
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Stylised FactsA MEM Approach to High Frequency Dynamics
Autocorrelation Across Frequencies
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Stylised FactsA MEM Approach to High Frequency Dynamics
A MEM Approach to High Frequency Dynamics
The Multiplicative Error Model (MEM)(Engle (2002), Engleand Gallo (2003)) is a generalisation of GARCH modelswhich can be useful to model non–negative time seriesprocesses such as volatility, durations, volumes, and soforththe canonical MEM specification is
xt = µt · εt εt ∼ D(1, φ)
wherethe conditional mean is given by
µt = ω +
p∑j=1
αjxt−j +
q∑j=1
βjµt−j
εt is an i.i.d disturbance with non–negative support and unitmean.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Stylised FactsA MEM Approach to High Frequency Dynamics
A MEM Approach to High Frequency Dynamics
The Multiplicative Error Model (MEM)(Engle (2002), Engleand Gallo (2003)) is a generalisation of GARCH modelswhich can be useful to model non–negative time seriesprocesses such as volatility, durations, volumes, and soforththe canonical MEM specification is
xt = µt · εt εt ∼ D(1, φ)
wherethe conditional mean is given by
µt = ω +
p∑j=1
αjxt−j +
q∑j=1
βjµt−j
εt is an i.i.d disturbance with non–negative support and unitmean.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Stylised FactsA MEM Approach to High Frequency Dynamics
A MEM Approach to High Frequency Dynamics
The Multiplicative Error Model (MEM)(Engle (2002), Engleand Gallo (2003)) is a generalisation of GARCH modelswhich can be useful to model non–negative time seriesprocesses such as volatility, durations, volumes, and soforththe canonical MEM specification is
xt = µt · εt εt ∼ D(1, φ)
wherethe conditional mean is given by
µt = ω +
p∑j=1
αjxt−j +
q∑j=1
βjµt−j
εt is an i.i.d disturbance with non–negative support and unitmean.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Stylised FactsA MEM Approach to High Frequency Dynamics
A MEM Approach to High Frequency Dynamics
The Multiplicative Error Model (MEM)(Engle (2002), Engleand Gallo (2003)) is a generalisation of GARCH modelswhich can be useful to model non–negative time seriesprocesses such as volatility, durations, volumes, and soforththe canonical MEM specification is
xt = µt · εt εt ∼ D(1, φ)
wherethe conditional mean is given by
µt = ω +
p∑j=1
αjxt−j +
q∑j=1
βjµt−j
εt is an i.i.d disturbance with non–negative support and unitmean.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Stylised FactsA MEM Approach to High Frequency Dynamics
High Frequency Multiplicative Component MEM
As in Chanda et al (2005) we adopt a Multiplicative Componentmodel for intra-daily data.We are the first ones however to employ a MultiplicativeComponent MEM for the modelling of intra-daily volumes andnumber of transactions.
xd ,t = µd ,t · εd ,t εd ,t ∼ D(1, φ)
µd ,t = mld · st · mh
d ,t
mld = ωl + αl f (xd−1,0, . . . , xd−1,T ) + β lml
d−1
mhd ,t = ωh + αhx{d ,t}−1 + βhmh
{d ,t}−1
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Stylised FactsA MEM Approach to High Frequency Dynamics
High Frequency Multiplicative Component MEM
As in Chanda et al (2005) we adopt a Multiplicative Componentmodel for intra-daily data.We are the first ones however to employ a MultiplicativeComponent MEM for the modelling of intra-daily volumes andnumber of transactions.
xd ,t = µd ,t · εd ,t εd ,t ∼ D(1, φ)
µd ,t = mld · st · mh
d ,t
mld = ωl + αl f (xd−1,0, . . . , xd−1,T ) + β lml
d−1
mhd ,t = ωh + αhx{d ,t}−1 + βhmh
{d ,t}−1
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Stylised FactsA MEM Approach to High Frequency Dynamics
High Frequency Multiplicative Component MEM
As in Chanda et al (2005) we adopt a Multiplicative Componentmodel for intra-daily data.We are the first ones however to employ a MultiplicativeComponent MEM for the modelling of intra-daily volumes andnumber of transactions.
xd ,t = µd ,t · εd ,t εd ,t ∼ D(1, φ)
µd ,t = mld · st · mh
d ,t
mld = ωl + αl f (xd−1,0, . . . , xd−1,T ) + β lml
d−1
mhd ,t = ωh + αhx{d ,t}−1 + βhmh
{d ,t}−1
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Stylised FactsA MEM Approach to High Frequency Dynamics
High Frequency Multiplicative Component MEM
As in Chanda et al (2005) we adopt a Multiplicative Componentmodel for intra-daily data.We are the first ones however to employ a MultiplicativeComponent MEM for the modelling of intra-daily volumes andnumber of transactions.
xd ,t = µd ,t · εd ,t εd ,t ∼ D(1, φ)
µd ,t = mld · st · mh
d ,t
mld = ωl + αl f (xd−1,0, . . . , xd−1,T ) + β lml
d−1
mhd ,t = ωh + αhx{d ,t}−1 + βhmh
{d ,t}−1
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Stylised FactsA MEM Approach to High Frequency Dynamics
High Frequency Multiplicative Component MEM
As in Chanda et al (2005) we adopt a Multiplicative Componentmodel for intra-daily data.We are the first ones however to employ a MultiplicativeComponent MEM for the modelling of intra-daily volumes andnumber of transactions.
xd ,t = µd ,t · εd ,t εd ,t ∼ D(1, φ)
µd ,t = mld · st · mh
d ,t
mld = ωl + αl f (xd−1,0, . . . , xd−1,T ) + β lml
d−1
mhd ,t = ωh + αhx{d ,t}−1 + βhmh
{d ,t}−1
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Stylised FactsA MEM Approach to High Frequency Dynamics
High Frequency Multiplicative Component MEM
As in Chanda et al (2005) we adopt a Multiplicative Componentmodel for intra-daily data.We are the first ones however to employ a MultiplicativeComponent MEM for the modelling of intra-daily volumes andnumber of transactions.
xd ,t = µd ,t · εd ,t εd ,t ∼ D(1, φ)
µd ,t = mld · st · mh
d ,t
mld = ωl + αl f (xd−1,0, . . . , xd−1,T ) + β lml
d−1
mhd ,t = ωh + αhx{d ,t}−1 + βhmh
{d ,t}−1
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Stylised FactsA MEM Approach to High Frequency Dynamics
Models Details
The multiplicative component MEM outlined previously will beused to model the series of intra-daily returns, volumes andnumber of transactions.
rd ,t = h1/2d ,t · εd ,t εd ,t ∼ N(0, 1)
td ,t = µtd ,t · εd ,t εd ,t ∼ Exp(1)
vd ,t = µvd ,t · εd ,t εd ,t ∼ Exp(1)
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Stylised FactsA MEM Approach to High Frequency Dynamics
Models Details
The multiplicative component MEM outlined previously will beused to model the series of intra-daily returns, volumes andnumber of transactions.
rd ,t = h1/2d ,t · εd ,t εd ,t ∼ N(0, 1)
td ,t = µtd ,t · εd ,t εd ,t ∼ Exp(1)
vd ,t = µvd ,t · εd ,t εd ,t ∼ Exp(1)
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Stylised FactsA MEM Approach to High Frequency Dynamics
Models Details
The multiplicative component MEM outlined previously will beused to model the series of intra-daily returns, volumes andnumber of transactions.
rd ,t = h1/2d ,t · εd ,t εd ,t ∼ N(0, 1)
td ,t = µtd ,t · εd ,t εd ,t ∼ Exp(1)
vd ,t = µvd ,t · εd ,t εd ,t ∼ Exp(1)
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Stylised FactsA MEM Approach to High Frequency Dynamics
Estimation Results
Time Series:high frequency component: hourlow frequency component: daily
Estimation Period: 2002-01-02 to 2002-11-29, 231 days
Estimation Method: two-step estimator of Ananda et al (2005)
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Stylised FactsA MEM Approach to High Frequency Dynamics
Estimation Results
Time Series:high frequency component: hourlow frequency component: daily
Estimation Period: 2002-01-02 to 2002-11-29, 231 days
Estimation Method: two-step estimator of Ananda et al (2005)
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Stylised FactsA MEM Approach to High Frequency Dynamics
Estimation Results
Time Series:high frequency component: hourlow frequency component: daily
Estimation Period: 2002-01-02 to 2002-11-29, 231 days
Estimation Method: two-step estimator of Ananda et al (2005)
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Stylised FactsA MEM Approach to High Frequency Dynamics
Estimation Results
Time Series:high frequency component: hourlow frequency component: daily
Estimation Period: 2002-01-02 to 2002-11-29, 231 days
Estimation Method: two-step estimator of Ananda et al (2005)
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Stylised FactsA MEM Approach to High Frequency Dynamics
Estimation Results
Time Series:high frequency component: hourlow frequency component: daily
Estimation Period: 2002-01-02 to 2002-11-29, 231 days
Estimation Method: two-step estimator of Ananda et al (2005)
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Stylised FactsA MEM Approach to High Frequency Dynamics
Estimation Results Cont’d
Returns
hld = 1.885 + 0.146r2
d−1 + 0.610hld−1
hhd ,t = 0.61 + 0.082r2
{d ,t}−1 + 0.859hh{d ,t}−1
Volumes
mld = 9324307.510 + 0.479vd−1 + 0.182ml
d−1
mhd ,t = 0.290 + 0.441v{d ,t}−1 + 0.268mh
{d ,t}−1
Number of Transactions
mld = 4562.522 + 0.535td−1 + 0.171ml
d−1
mhd ,t = 0.217 + 0.588t{d ,t}−1 + 0.196mh
{d ,t}−1
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Stylised FactsA MEM Approach to High Frequency Dynamics
Comments
the multiplicative component MEM successfully capturesthe dynamics of high-frequency series
the intra-daily stochastic component is significant in allmodels
the intra-daily dynamic appears to be similar to to its dailycounterpart
trades and volumes appear to be more volatile than returns
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Stylised FactsA MEM Approach to High Frequency Dynamics
Comments
the multiplicative component MEM successfully capturesthe dynamics of high-frequency series
the intra-daily stochastic component is significant in allmodels
the intra-daily dynamic appears to be similar to to its dailycounterpart
trades and volumes appear to be more volatile than returns
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Stylised FactsA MEM Approach to High Frequency Dynamics
Comments
the multiplicative component MEM successfully capturesthe dynamics of high-frequency series
the intra-daily stochastic component is significant in allmodels
the intra-daily dynamic appears to be similar to to its dailycounterpart
trades and volumes appear to be more volatile than returns
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Stylised FactsA MEM Approach to High Frequency Dynamics
Comments
the multiplicative component MEM successfully capturesthe dynamics of high-frequency series
the intra-daily stochastic component is significant in allmodels
the intra-daily dynamic appears to be similar to to its dailycounterpart
trades and volumes appear to be more volatile than returns
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Stylised FactsA MEM Approach to High Frequency Dynamics
Forecasting Exercise
Forecasting Period: 2002-12-02 to 2002-12-31, 21 days
Forecasting Method: static
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Stylised FactsA MEM Approach to High Frequency Dynamics
Forecasting Exercise
Forecasting Period: 2002-12-02 to 2002-12-31, 21 days
Forecasting Method: static
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Stylised FactsA MEM Approach to High Frequency Dynamics
Forecasting the Number of Trades per Hour
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Stylised FactsA MEM Approach to High Frequency Dynamics
Forecasting the Number of Trades per Hour – Cont’d
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Conclusions
We have shown some features regarding the structure ofthe high frequency datasets and highlighted some linkswith the market mechanisms,
presented simple and general methods for the datamanagement and manipulation which have beenimplemented in freely available package for MATLAB,
and presented some basic stylised facts and models forhigh frequency modelling and forecasting.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Conclusions
We have shown some features regarding the structure ofthe high frequency datasets and highlighted some linkswith the market mechanisms,
presented simple and general methods for the datamanagement and manipulation which have beenimplemented in freely available package for MATLAB,
and presented some basic stylised facts and models forhigh frequency modelling and forecasting.
Brownlees & Gallo (2005) UHFD
MotivationData Structure and Exchange Market Rules
Data ManagementEconometric Analysis
Conclusions
Conclusions
We have shown some features regarding the structure ofthe high frequency datasets and highlighted some linkswith the market mechanisms,
presented simple and general methods for the datamanagement and manipulation which have beenimplemented in freely available package for MATLAB,
and presented some basic stylised facts and models forhigh frequency modelling and forecasting.
Brownlees & Gallo (2005) UHFD