factor analyses and time-lagged regressions

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


Only Factor 1 should be consideredOnly Factor 1 should be considered

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Most variables well explained, except XRXMost variables well explained, except XRX

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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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DELL lagged 1, but coefficient reduced => OVBDELL lagged 1, but coefficient reduced => OVB

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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


Factors 1, 2, and 3 can be considered…Factors 1, 2, and 3 can be considered…

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……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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HPQ and TXN lagged 5HPQ and TXN lagged 5

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DELL lagged 1 (coefficient virtually the same!)DELL lagged 1 (coefficient virtually the same!)

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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


Factors 1, 2, and 3 can be considered…Factors 1, 2, and 3 can be considered…

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……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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HPQ and TXN lagged 5HPQ and TXN lagged 5

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DELL lagged 1 (coefficient virtually the same!)DELL lagged 1 (coefficient virtually the same!)

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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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factor analyses and time-lagged regressions

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