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Real-Time Signalextraction (MDFA) and Algorithmic Trading marc. wildi@zhaw. ch http: //blog. zhaw. ch/idp/sefblog http: Real-Time Signalextraction (MDFA) and Algorithmic Trading marc. [email protected] ch http: //blog. zhaw. ch/idp/sefblog http: //www. idp. zhaw. ch/usri http: //www. idp. zhaw. ch/MDFA-XT http: //www. idp. zhaw. ch/sef

Background • Hybrid math/econ. • IDP-ZHAW → Projects with econ. partners • Forecasting – Background • Hybrid math/econ. • IDP-ZHAW → Projects with econ. partners • Forecasting – Health-care (cost expenditures) – Macro (real-time economic indicators: EURI Eurostatproject) – Finance (MDFA-XT, large hedge-fund) – Engineering (Telecom, load forecasts) • Eclectic/disparate range of applications • Common methodological approach(es) – In-house developments: (M)DFA – R-package “signalextraction” on CRAN

A Classical Algorithmic Trading Approach Timing System SP 500 Daily Closures MA(200), Equally Weighted A Classical Algorithmic Trading Approach Timing System SP 500 Daily Closures MA(200), Equally Weighted

P. 5 (drawdowns), p. 7 (timing system), p. 10 (performance) P. 5 (drawdowns), p. 7 (timing system), p. 10 (performance)

Problem: (Too) Long Periods with Systematic Underperformance Problem: (Too) Long Periods with Systematic Underperformance

Why do Traders Frequently Adopt/Prefer Filter Crossings? Filter Characteristics Why MDFA? http: //blog. zhaw. Why do Traders Frequently Adopt/Prefer Filter Crossings? Filter Characteristics Why MDFA? http: //blog. zhaw. ch/idp/sefblog/index. php? /archives/54 Intermezzo-Why-do-Traders-Often-Consider-Crossings-of. Trading-Filter-Pairs. html

Log-MSCI and MA(45) Log-MSCI and MA(45)

Filter Characteristics • Amplitude function: – Which signal is extracted? • Time-shift: – How Filter Characteristics • Amplitude function: – Which signal is extracted? • Time-shift: – How large is the delay?

Timing System (MSCI-Weekly) Timing System (MSCI-Weekly)

More General Crossings: MA(45, black)-MA(22, red)=crossing (blue) More General Crossings: MA(45, black)-MA(22, red)=crossing (blue)

Conclusions • Crossing-rules are (an unnecessarily cumbersome way of implementing) bandpass filters • Crossing-rules Conclusions • Crossing-rules are (an unnecessarily cumbersome way of implementing) bandpass filters • Crossing-rules (bandpass) have small time delays • Why MDFA? – Flexible efficient real-time (bandpass) design – Fast and smooth

Fundamental Trading http: //www. idp. zhaw. ch/usri SP 500 http: //blog. zhaw. ch/idp/sefblog Fundamental Trading http: //www. idp. zhaw. ch/usri SP 500 http: //blog. zhaw. ch/idp/sefblog

USRI (MDFA) and SP 500 USRI (MDFA) and SP 500

Performance in Logs Performance in Logs

Student Thesis p. 19 Long Term Performances Fundam. Trading Student Thesis p. 19 Long Term Performances Fundam. Trading

Conclusion • Damp or avoid all massive recession draw -downs effectively – Ideal for Conclusion • Damp or avoid all massive recession draw -downs effectively – Ideal for risk-averse investors (pension funds) • Fundamental Trading: truly out of sample – Focus on Macro-data (finance data ignored) – NBER • Disadvantage: `insufficiently active’ – Texto: «Difficult to justify fees»

MDFA-XT http: //www. idp. zhaw. ch/MDFA-XT MSCI (+BRIC) http: //blog. zhaw. ch/idp/sefblog MDFA-XT http: //www. idp. zhaw. ch/MDFA-XT MSCI (+BRIC) http: //blog. zhaw. ch/idp/sefblog

Log-MSCI and MA(45) Log-MSCI and MA(45)

MDFA vs. MA(45) weekly data MDFA (blue) Faster MDFA vs. MA(45) weekly data MDFA (blue) Faster

Five Trading Filters Different Trading Frequencies Five Trading Filters Different Trading Frequencies

Filter « Unfrequent » Filter « Unfrequent »

Filter « Unfrequent to Mid» Filter « Unfrequent to Mid»

Filter « Mid » Filter « Mid »

Filter « Frequent » Filter « Frequent »

Conclusion • Higher trading frequencies are associated with – Bandpass shifted to the right Conclusion • Higher trading frequencies are associated with – Bandpass shifted to the right • More flexible than traditional filter-crossings – Smaller delays/time shifts

Performances Performances

Setting • Total degenerative trading costs of 0. 3% per order (small fund) • Setting • Total degenerative trading costs of 0. 3% per order (small fund) • Long only • No risk free interest rates

Performance « Unfrequent » Performance « Unfrequent »

Performance « Unfrequent to Mid» Performance « Unfrequent to Mid»

Performance « Mid» Performance « Mid»

Performance « Mid to Frequent » Performance « Mid to Frequent »

Performance « Frequent » Performance « Frequent »

Conclusions • Higher trading frequencies are associated with – Slight reduction of performance – Conclusions • Higher trading frequencies are associated with – Slight reduction of performance – Larger draw-downs • USRI would avoid draw-downs and then the performance would improve – Increased market activity (fees!) • Combination with USRI possible (recommended) • Filters will be available on-line in late July

Real-Time Signalextraction A SEF-Blog Excel-Tutorial http: //blog. zhaw. ch/idp/sefblog Real-Time Signalextraction A SEF-Blog Excel-Tutorial http: //blog. zhaw. ch/idp/sefblog

Excel-Tutorial on SEF-Blog • http: //blog. zhaw. ch/idp/sefblog/index. php? / archives/65 -Real-Time-Detection-of. Turning-Points-a-Tutorial-Part-I-Mean. Square-Error-Norm. Excel-Tutorial on SEF-Blog • http: //blog. zhaw. ch/idp/sefblog/index. php? / archives/65 -Real-Time-Detection-of. Turning-Points-a-Tutorial-Part-I-Mean. Square-Error-Norm. html • http: //blog. zhaw. ch/idp/sefblog/index. php? / archives/67 -Real-Time-Detection-of. Turning-Points-a-Tutorial-Part-IIEmphasizing-Turning-Points. html

Purposes • Yoga exercises to detach from main-stream maximum likelihood world • First Blog-entry: Purposes • Yoga exercises to detach from main-stream maximum likelihood world • First Blog-entry: how traditional econometric approach `works’ – Intuitively straightforward – Good (optimal) mean-square performances – People have become lazy-minded • Second Blog-Entry: the early detection of turning points – Is a (strongly) counterintuitive exercise – Generates seemingly (strongly) misspecified filter designs • Warning → Learning (→ Illumination? )

Excel-Tutorial on SEF-Blog Excel-Tutorial on SEF-Blog

Real-Time Signalextraction 1. Traditional Econometrics Real-Time Signalextraction 1. Traditional Econometrics

Task: Extract the Cycle Task: Extract the Cycle

Standard Econometric Approach • Proceeding: – Identify a time-series model (ARIMA/state space) – Extend Standard Econometric Approach • Proceeding: – Identify a time-series model (ARIMA/state space) – Extend the series by optimal forecasts – Apply the symmetric filter on the extended time series • X-12 -ARIMA, TRAMO, STAMP, R/S+… • Claim: – One-sided filter is optimal (mean-square sense) – Assumption: DGP/true model

ARMA(2, 2)-Diagnostics ARMA(2, 2)-Diagnostics

Real-Time Model-Based Filter Real-Time Model-Based Filter

Real-Time Signalextraction 2. Excel Example (Replication of Model-Based Approach) Real-Time Signalextraction 2. Excel Example (Replication of Model-Based Approach)

Parameters (ARMA(2, 2)-FILTER) • ARMA(2, 2)-Filter (not model) Parameters (ARMA(2, 2)-FILTER) • ARMA(2, 2)-Filter (not model)

A Seemingly Virtuous Design (amplitude) A Seemingly Virtuous Design (amplitude)

A Seemingly Virtuous Design (time shift) A Seemingly Virtuous Design (time shift)

A Seemingly Virtuous Design (Peak Correlation) • Correlation between real-time estimate and cycle as A Seemingly Virtuous Design (Peak Correlation) • Correlation between real-time estimate and cycle as a function of time-lag k

Signal and Estimate (Estimate: Filter Tweaked by Hand) Signal and Estimate (Estimate: Filter Tweaked by Hand)

Real-Time Signalextraction 3. Excel Example (Turning Point Revelation) Real-Time Signalextraction 3. Excel Example (Turning Point Revelation)

Parameters ARMA(2, 2)-FILTER Seemingly Misspecified Design • ARMA(2, 2)-Filter (not model) Parameters ARMA(2, 2)-FILTER Seemingly Misspecified Design • ARMA(2, 2)-Filter (not model)

A Seemingly Misspecified Design Amplitude A Seemingly Misspecified Design Amplitude

A Seemingly Misspecified Design Time Shift A Seemingly Misspecified Design Time Shift

A Seemingly Misspecified Design Peak-Correlations A Seemingly Misspecified Design Peak-Correlations

A Seemingly Misspecified Design Filtered Series and Signal A Seemingly Misspecified Design Filtered Series and Signal

Comparison: Seemingly Virtuous vs. Seemingly Misspecified Comparison: Seemingly Virtuous vs. Seemingly Misspecified

Comparison: Seemingly Virtuous vs. Seemingly Misspecified Comparison: Seemingly Virtuous vs. Seemingly Misspecified

Conclusions • Seemingly misspecified design is – Faster – Smoother (less false TP’s or Conclusions • Seemingly misspecified design is – Faster – Smoother (less false TP’s or “alarms”) – Not mean-square optimal – Much better in a TP-perspective

From Excel to MDFA • Tweak filter parameters `by hand’ in Excel Tutorial • From Excel to MDFA • Tweak filter parameters `by hand’ in Excel Tutorial • Shortcomings of example – Unrealistically simple artificial simulation exercise – In practice: • more complex nuisances and/or signals – Include information from more than one time series (multivariate framework) • Wish: a formal optimization criterion • Welcome to DFA and MDFA

DFA Direct Filter Approach Mean-Square DFA Direct Filter Approach Mean-Square

DFA: Direct Filter Approach • Idea: estimate mean-square filter error efficiently DFA: Direct Filter Approach • Idea: estimate mean-square filter error efficiently

Optimization Criterion (I(0)) • Minimize a (uniformly) superconsistent estimate of an (uniformly) efficient estimate Optimization Criterion (I(0)) • Minimize a (uniformly) superconsistent estimate of an (uniformly) efficient estimate of the filter mean-square error • (Customized) Efficiency enters explicitly in the Design of the Optimization Criterion

Did You Say and/or Mean “Periodogram”? • Periodogram is a typical example of “statisticbashing” Did You Say and/or Mean “Periodogram”? • Periodogram is a typical example of “statisticbashing” – Inconsistent estimate of spectral density – Smoothing (parametric or non-parametric) • Periodogram has wonderful statistical properties – Sufficiency (Larry Brethorst) – One can derive nice formal efficiency results in realtime signalextraction • Working on a series of new Blog entries about the topic to rehabilitate – to some extent … - the periodogram

Performances (Efficiency of Univariate DFA) • Business Survey Data (KOF, FED, 2004, 2005) – Performances (Efficiency of Univariate DFA) • Business Survey Data (KOF, FED, 2004, 2005) – X-12 -ARIMA, Tramo/Seats – MSE-gain ~30% • US- and Euro-GDP (2008): – CF – turning-points anticipated by 1 -2 quarters • ESI (2006): – Dainties – TP‘s discovered 2 -3 months earlier

Performances (Efficiency) by Relying on the Periodogram • TP-filters won NN 3 (2007) and Performances (Efficiency) by Relying on the Periodogram • TP-filters won NN 3 (2007) and NN 5 (2008) forecasting competitions (~60 participants) – IIF and University of Lancaster – Monthly Macro- and Financial Data (111 time series) and daily financial data (111 time series) – Outperformed winner and runner-up of prestigious M 3 competition, X-12 -ARIMA, Tramo, Forecast-Pro, Autobox, Exponential smoothing: Simple, Holt, Damped, … – Neural nets, artificial intelligence – http: //blog. zhaw. ch/idp/sefblog

DFA Direct Filter Approach Turning Points (TP) DFA Direct Filter Approach Turning Points (TP)

Controlling the Time Delay (Customization) • λ>1: emphasize the time delay in the pass-band Controlling the Time Delay (Customization) • λ>1: emphasize the time delay in the pass-band • λ=1: best level filter

Customization: Controlling time delay and smoothness • Stronger damping of highfrequency noise in stop-band Customization: Controlling time delay and smoothness • Stronger damping of highfrequency noise in stop-band • Smaller time delays in pass-band • W(ω) is monotonic (increasing) and λ>1

Amplitude DFA TP-filter (blue) vs. seem. virtuous level filter (KOFBarometer) Amplitude DFA TP-filter (blue) vs. seem. virtuous level filter (KOFBarometer)

Delay TP-filter (blue) vs. seem. Virtuous level filter (KOF-Barometer) Delay TP-filter (blue) vs. seem. Virtuous level filter (KOF-Barometer)

TP-Detection • Smoother and Faster! • Poor Mean-Square Performances TP-Detection • Smoother and Faster! • Poor Mean-Square Performances

MDFA MDFA

Real-Time Multivariate Filter • `Direct Filter Approach’ Real-Time Multivariate Filter • `Direct Filter Approach’

Real-Time Filter Cointegration Constraints (Rank=1) Real-Time Filter Cointegration Constraints (Rank=1)

Efficiency (Theorem 4. 1, Wildi 2008, Wildi/Sturm 2008) • The error term e. T Efficiency (Theorem 4. 1, Wildi 2008, Wildi/Sturm 2008) • The error term e. T is smallest possible uniformly • Uniform efficiency ↔ Customization

Optimal (Efficient) Criterion under Cointegration (Rank=1) • Filter Restrictions are satisfied Optimal (Efficient) Criterion under Cointegration (Rank=1) • Filter Restrictions are satisfied

Performances MDFA • Output-gap US- and Euro-GDP (2008): – CF and multivariate CF – Performances MDFA • Output-gap US- and Euro-GDP (2008): – CF and multivariate CF – turning-points anticipated by 1 -2 quarters • USRI – Outperformed Markov-switching (Chauvet, Chauvet/Piger), Dynamic factor models (CFNAI), state space models (ADS), Hodrick. Prescott (OECD-CLI), Christiano-Fitzgerald – SEF-Blog • MDFA-XT • EURI

WARNING!!! • THIS IS NOT A PUSH-THE-BUTTON APPROACH • Formula 1 racer: it can WARNING!!! • THIS IS NOT A PUSH-THE-BUTTON APPROACH • Formula 1 racer: it can be fast (Ferrari) and reliable (Mercedes) but you have to tweak it carefully: Ferrades/Mercearri – – Filter design (ZPC) Filter constraints (emphasize frequency zero) Understanding/interpreting: `intelligence’ 2008 -Book: http: //www. idp. zhaw. ch/sef • Happy to provide support given financial incentives

Contact/Links Contact/Links

Contact/Links • marc. wildi@zhaw. ch • http: //blog. zhaw. ch/idp/sefblog – Illustrate methodological issues Contact/Links • marc. [email protected] ch • http: //blog. zhaw. ch/idp/sefblog – Illustrate methodological issues by relying on `realworld‘ projects with economic partners • http: //www. idp. zhaw. ch/usri – Real-Time US Recession Indicator • http: //www. idp. zhaw. ch/MDFA-XT – Experimental Trader for MSCI Emerging Markets – Filters on-line late July • http: //www. idp. zhaw. ch/sef – Signal Extraction & Forecasting Site – Books, Articles, Software