Factor Analyses and Time-Lagged Regressions ECON 201FS Factor Analyses and Time-Lagged Regressions Zed Lamba 3/26/08
Tech Stocks in S&P 100 (besides MSFT) ECON 201FS Tech Stocks in S&P 100 (besides MSFT) AAPL – Apple, ignored due to lack of trustworthy data CSCO – Cisco Systems DELL – Dell EMC – EMC Corporation (data storage, competes with IBM, HP, etc.) GOOG – ignored for now due to limited data HPQ – HP IBM – IBM INTC – Intel ORCL – Oracle TXN – Texas Instruments XRX – Xerox
Realized Variance Daily Realized Variance, where rt,j = log return ECON 201FS Realized Variance Daily Realized Variance, where rt,j = log return M = # returns/day
Realized Variance Summary Statistics (Mean, Corr with MSFT) ECON 201FS Realized Variance Summary 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
Only Factor 1 should be considered ECON 201FS Factor Analysis I Only Factor 1 should be considered
Most variables well explained, except XRX ECON 201FS Factor Analysis II Most variables well explained, except XRX
Time-Lagged Regressions I ECON 201FS Time-Lagged Regressions I
Time-Lagged Regressions IIa ECON 201FS Time-Lagged Regressions IIa DELL lagged 1
Time-Lagged Regressions IIb ECON 201FS Time-Lagged Regressions IIb INTC, ORCL, and TXN lagged 1; ORCL lagged 22
Time-Lagged Regressions IIIa ECON 201FS Time-Lagged Regressions IIIa DELL lagged 1, but coefficient reduced => OVB
Time-Lagged Regressions IIIb ECON 201FS Time-Lagged Regressions IIIb INTC and MSFT lagged 1; MSFT lagged 5; more OVB
ECON 201FS Bipower Variation
BV Summary Statistics (Mean, Corr with MSFT) ECON 201FS BV Summary Statistics (Mean, Corr with MSFT) 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 considered ECON 201FS Factor Analysis I Only Factor 1 should be considered
Most variables well explained, except XRX ECON 201FS Factor Analysis II Most variables well explained, except XRX
Time-Lagged Regressions I ECON 201FS Time-Lagged Regressions I
Time-Lagged Regressions IIa ECON 201FS Time-Lagged Regressions IIa DELL lagged 1
Time-Lagged Regressions IIb ECON 201FS Time-Lagged Regressions IIb INTC and ORCL lagged 1; HPQ lagged 5; ORCL lagged 22
Time-Lagged Regressions IIIa ECON 201FS Time-Lagged Regressions IIIa DELL lagged 1, but coefficient reduced => OVB
Time-Lagged Regressions IIIb ECON 201FS Time-Lagged Regressions IIIb INTC and MSFT lagged 1; MSFT lagged 5; more OVB
Tri-Power Max Test Statistics ECON 201FS Tri-Power Max Test Statistics Tri-Power Quarticity: Estimator of: Useful Constants: Test Statistic:
Summary Statistics (Mean, Corr with MSFT) ECON 201FS Summary Statistics (Mean, Corr with MSFT) 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… ECON 201FS Factor Analysis I Factors 1, 2, and 3 can be considered…
…or not – no variable is well-explained (or even close to it) ECON 201FS Factor Analysis II …or not – no variable is well-explained (or even close to it)
Time-Lagged Regressions I ECON 201FS Time-Lagged Regressions I
Time-Lagged Regressions IIa ECON 201FS Time-Lagged Regressions IIa DELL lagged 1
Time-Lagged Regressions IIb ECON 201FS Time-Lagged Regressions IIb HPQ and TXN lagged 5
Time-Lagged Regressions IIIa ECON 201FS Time-Lagged Regressions IIIa DELL lagged 1 (coefficient virtually the same!)
Time-Lagged Regressions IIIb ECON 201FS Time-Lagged Regressions IIIb HPQ and TXN lagged 5 (coefficients again virtually the same!)
Quad-Power Max Test Statistics ECON 201FS Quad-Power Max Test Statistics Quad-Power Quarticity: Estimator of: Useful Constants: Test Statistic:
Summary Statistics (Mean, Corr with MSFT) ECON 201FS Summary Statistics (Mean, Corr with MSFT) 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… ECON 201FS Factor Analysis I Factors 1, 2, and 3 can be considered…
…or not – no variable is well-explained (or even close to it) ECON 201FS Factor Analysis II …or not – no variable is well-explained (or even close to it)
Time-Lagged Regressions I ECON 201FS Time-Lagged Regressions I
Time-Lagged Regressions IIa ECON 201FS Time-Lagged Regressions IIa DELL lagged 1
Time-Lagged Regressions IIb ECON 201FS Time-Lagged Regressions IIb HPQ and TXN lagged 5
Time-Lagged Regressions IIIa ECON 201FS Time-Lagged Regressions IIIa DELL lagged 1 (coefficient virtually the same!)
Time-Lagged Regressions IIIb ECON 201FS Time-Lagged Regressions IIIb HPQ lagged 5; MSFT lagged 22 (coefficients virtually the same!)
Extensions Also do time-lagged regressions with HAR-RV type models ECON 201FS Extensions Also do time-lagged regressions with HAR-RV type models Now incorporate GOOG and see whether it matches trends established so far Have concrete estimates for suspected OVB