Factor Analyses and Time-Lagged Regressions
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Factor Analyses and Time-Factor Analyses and Time-Lagged RegressionsLagged Regressions
Zed LambaZed Lamba
3/26/083/26/08
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Tech Stocks in S&P 100 (besides MSFT)Tech Stocks in S&P 100 (besides MSFT)
AAPL – Apple, ignored due to lack of trustworthy dataAAPL – Apple, ignored due to lack of trustworthy data CSCO – Cisco SystemsCSCO – Cisco Systems DELL – DellDELL – Dell EMC – EMC Corporation (data storage, competes with EMC – EMC Corporation (data storage, competes with
IBM, HP, etc.)IBM, HP, etc.) GOOG – ignored for now due to limited dataGOOG – ignored for now due to limited data HPQ – HPHPQ – HP IBM – IBMIBM – IBM INTC – IntelINTC – Intel ORCL – OracleORCL – Oracle TXN – Texas InstrumentsTXN – Texas Instruments XRX – XeroxXRX – Xerox
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Realized VarianceRealized Variance
Daily Realized Variance, whereDaily Realized Variance, where rrt,jt,j = log return = log returnM = # returns/dayM = # returns/day
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Realized Variance Summary Realized Variance Summary Statistics (Mean, Corr with MSFT)Statistics (Mean, Corr with MSFT)
MSFT 0.000314, 1.0000
CSCO 0.000572, 0.7278
DELL 0.000579, 0.6095
IBM 0.000252, 0.6829
HPQ 0.000494, 0.6399
EMC 0.000787, 0.5709
INTC 0.000503, 0.6206
ORCL 0.000761, 0.7261
TXN 0.000719, 0.6705
XRX 0.00072, 0.5441
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Factor Analysis IFactor Analysis I
Only Factor 1 should be consideredOnly Factor 1 should be considered
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Factor Analysis IIFactor Analysis II
Most variables well explained, except XRXMost variables well explained, except XRX
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Time-Lagged Regressions ITime-Lagged Regressions I
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Time-Lagged Regressions IIaTime-Lagged Regressions IIa
DELL lagged 1DELL lagged 1
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Time-Lagged Regressions IIbTime-Lagged Regressions IIb
INTC, ORCL, and TXN lagged 1; ORCL lagged 22INTC, ORCL, and TXN lagged 1; ORCL lagged 22
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Time-Lagged Regressions IIIaTime-Lagged Regressions IIIa
DELL lagged 1, but coefficient reduced => OVBDELL lagged 1, but coefficient reduced => OVB
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Time-Lagged Regressions IIIbTime-Lagged Regressions IIIb
INTC and MSFT lagged 1; MSFT lagged 5; more OVBINTC and MSFT lagged 1; MSFT lagged 5; more OVB
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Bipower VariationBipower Variation
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BV Summary Statistics (Mean, Corr BV Summary Statistics (Mean, Corr with MSFT)with MSFT)
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MSFT 0.000297, 1.000
CSCO 0.000547, 0.7211
DELL 0.000543, 0.6154
IBM 0.000238, 0.6719
HPQ 0.000453, 0.6581
EMC 0.000743, 0.5721
INTC 0.000478, 0.6195
ORCL 0.00071, 0.7087
TXN 0.000675, 0.6765
XRX 0.000635, 0.5320
Factor Analysis IFactor Analysis I
Only Factor 1 should be consideredOnly Factor 1 should be considered
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Factor Analysis IIFactor Analysis II
Most variables well explained, except XRXMost variables well explained, except XRX
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Time-Lagged Regressions ITime-Lagged Regressions I
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Time-Lagged Regressions IIaTime-Lagged Regressions IIa
DELL lagged 1DELL lagged 1
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Time-Lagged Regressions IIbTime-Lagged Regressions IIb
INTC and ORCL lagged 1; HPQ lagged 5; ORCL lagged 22INTC and ORCL lagged 1; HPQ lagged 5; ORCL lagged 22
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Time-Lagged Regressions IIIaTime-Lagged Regressions IIIa
DELL lagged 1, but coefficient reduced => OVBDELL lagged 1, but coefficient reduced => OVB
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Time-Lagged Regressions IIIbTime-Lagged Regressions IIIb
INTC and MSFT lagged 1; MSFT lagged 5; more OVBINTC and MSFT lagged 1; MSFT lagged 5; more OVB
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Tri-Power Max Test StatisticsTri-Power Max Test Statistics
Tri-Power Quarticity:Tri-Power Quarticity:
Estimator of: Estimator of: Useful Constants:Useful Constants:
Test Statistic: Test Statistic:
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Summary Statistics (Mean, Corr Summary Statistics (Mean, Corr with MSFT)with MSFT)
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MSFT 0.6232, 1.000
CSCO 0.6250, 0.0601
DELL 0.6942, -0.0001
IBM 0.5492, 0.0749
HPQ 0.7931, 0.0333
EMC 0.6957, 0.0222
INTC 0.5670, 0.0361
ORCL 0.8586, 0.0534
TXN 0.6435, 0.0076
XRX 1.1594, -0.0013
Factor Analysis IFactor Analysis I
Factors 1, 2, and 3 can be considered…Factors 1, 2, and 3 can be considered…
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Factor Analysis IIFactor Analysis II
……or not – no variable is well-explained (or even close to it)or not – no variable is well-explained (or even close to it)
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Time-Lagged Regressions ITime-Lagged Regressions I
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Time-Lagged Regressions IIaTime-Lagged Regressions IIa
DELL lagged 1DELL lagged 1
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Time-Lagged Regressions IIbTime-Lagged Regressions IIb
HPQ and TXN lagged 5HPQ and TXN lagged 5
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Time-Lagged Regressions IIIaTime-Lagged Regressions IIIa
DELL lagged 1 (coefficient virtually the same!)DELL lagged 1 (coefficient virtually the same!)
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Time-Lagged Regressions IIIbTime-Lagged Regressions IIIb
HPQ and TXN lagged 5 (coefficients again virtually the same!)HPQ and TXN lagged 5 (coefficients again virtually the same!)
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Quad-Power Max Test StatisticsQuad-Power Max Test Statistics
Quad-Power Quarticity:Quad-Power Quarticity:
Estimator of: Estimator of: Useful Constants: Useful Constants:
Test Statistic: Test Statistic:
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Summary Statistics (Mean, Corr Summary Statistics (Mean, Corr with MSFT)with MSFT)
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MSFT 0.6492, 1.000
CSCO 0.6507, 0.0650
DELL 0.7282, 0.0003
IBM 0.5741, 0.0790
HPQ 0.8383, 0.0387
EMC 0.7451, 0.0264
INTC 0.5879, 0.0356
ORCL 0.9080, 0.0564
TXN 0.6776, 0.0122
XRX 1.2466, -0.0025
Factor Analysis IFactor Analysis I
Factors 1, 2, and 3 can be considered…Factors 1, 2, and 3 can be considered…
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Factor Analysis IIFactor Analysis II
……or not – no variable is well-explained (or even close to it)or not – no variable is well-explained (or even close to it)
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Time-Lagged Regressions ITime-Lagged Regressions I
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Time-Lagged Regressions IIaTime-Lagged Regressions IIa
DELL lagged 1DELL lagged 1
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Time-Lagged Regressions IIbTime-Lagged Regressions IIb
HPQ and TXN lagged 5HPQ and TXN lagged 5
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Time-Lagged Regressions IIIaTime-Lagged Regressions IIIa
DELL lagged 1 (coefficient virtually the same!)DELL lagged 1 (coefficient virtually the same!)
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Time-Lagged Regressions IIIbTime-Lagged Regressions IIIb
HPQ lagged 5; MSFT lagged 22 (coefficients virtually the same!)HPQ lagged 5; MSFT lagged 22 (coefficients virtually the same!)
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ExtensionsExtensions
Also do time-lagged regressions with Also do time-lagged regressions with HAR-RV type modelsHAR-RV type models
Now incorporate GOOG and see whether Now incorporate GOOG and see whether it matches trends established so farit matches trends established so far
Have concrete estimates for suspected Have concrete estimates for suspected OVBOVB
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