PCA_VAR - Calculations using a subset of Principal Components

Returns an array of cells for the i-th principal component (or residuals).

Syntax

PCA_VAR (X, Mask, Standardize, Number, Number of PC, Return)

X

is the independent variables data matrix, such that each column represents one variable.

Mask

is the boolean array to select a subset of the input variables in X. If missing, all variables in X are included.

Standardize

is a flag or switch to standardize the input variables prior to the analysis (i.e., standardize = 1 (default), subtract mean = 2)).

Value	Standardize
1	Standardize (subtract mean and divide by standard deviation) (default).
2	Subtract mean (subtract mean).

Number

is the input variable number.

Number of PC

is the number of principal components (PC) to include. If missing or zero, all components will be used.

Return

is a switch to select the return output (1 = Final communality (default), 2 = Loading/weights, 3 = Fitted values, 4 = Residuals).

Value	Return
1	Final communality (default).
2	Loading or weights for factors.
3	Fitted input variable (from PCs).
4	Residuals.

Remarks

1. The underlying model is described here.
2. The PCA_VAR function must be entered as an array formula (for return-types other than 1) in a range that has the rows as the number of variables (return-type = 2) or the number of observations (return-type > 2).
3. The sample data may include missing values.
4. Each column in the input matrix corresponds to a separate variable.
5. Each row in the input matrix corresponds to an observation.
6. Observations (i.e., rows) with missing values are removed.
7. The PC_VAR function is available starting with version 1.60 APACHE.

Files Examples

Related Links

• Wikipedia - Principal component analysis.
• Wikipedia - Regression analysis.
• Wikipedia - Ordinary least squares.

References

• J. Edward Jackson; A User's Guide to Principal Components; Wiley-Interscience; (Sep 10, 2003), ISBN: 471471348.
• I.T. Jolliffe; Principal Component Analysis; Springer; 2nd Edition(Oct 01, 2002), ISBN: 0387954422.
• John Y. Campbell, Andrew W. Lo, A. Craig MacKinlay, Andrew Y. Lo; The Econometrics of Financial Markets; Princeton University Press; 2nd edition(Dec 09, 1996), ISBN: 691043019.
• Hamilton, J.D.; Time Series Analysis, Princeton University Press (1994), ISBN 0-691-04289-6.
• Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0-471-690740.