XCFTest - Cross-Correlation Test

Calculates the test stats, p-value or critical value of the correlation test.

Syntax

XCFTest(Y, X, K, Rho, Method, Return_type, Alpha)

Y is the first data series (one dimensional array of cells (e.g. rows or columns)).

X is the second data series (one dimensional array of cells (e.g. rows or columns)).

K is the lag order (e.g. 0=no lag, 1=1st lag, etc.) to use with second time series input (X). If missing, the default lag order of zero (i.e. no-lag) is assumed.

Rho is the hypothetical (assumed) correlation factor. If missing, the default value of zero is assumed.

Method is the desired correlation coefficient (1=Pearson (default), 2=Spearman, 3= Kendall). If missing, a Pearson coefficient is assumed.

Method Description
1 Pearson
2 Spearman
3 Kendall

Return_type is a switch to select the return output (1 = P-Value (default), 2 = Test Stats, 3 = Critical Value).

Method Description
1 P-Value
2 Test Statistics (e.g. Z-score)
3 Critical Value

Alpha is the statistical significance or confidence level (i.e. alpha). If missing or omitted, an alpha value of 5% is assumed.

Remarks

1. The XCF test performs the following test:
2. The XCF test hypothesis: $$H_{o}: \rho_{x,y}=0$$ $$H_{1}: \rho_{x,y} \neq 0$$ Where:
• $H_{o}$ is the null hypothesis ($\hat\rho$ is not different from zero)
• $H_{1}$ is the alternate hypothesis ($\hat\rho$ is statistically significant)
• $\rho_{x,y}$ is the correlation factor between population X and Y
3. The time series is homogeneous or equally spaced.
4. The significance level (i.e. alpha) is only needed for calculating the test critical value.
5. The time series may include missing values (e.g. #N/A) at either end.
6. This is a two-tails (sides) test, so the computed p-value should be compared with half of the significance level ($\alpha$).

Examples

Example 1:

A B C
1 Date Series1 Series2
2 1/1/2008 #N/A -2.61
3 1/2/2008 -2.83 -0.28
4 1/3/2008 -0.95 -0.90
5 1/4/2008 -0.88 -1.72
6 1/5/2008 1.21 1.92
7 1/6/2008 -1.67 -0.17
8 1/7/2008 0.83 -0.04
9 1/8/2008 -0.27 1.63
10 1/9/2008 1.36 -0.12
11 1/10/2008 -0.34 0.14
12 1/11/2008 0.48 -1.96
13 1/12/2008 -2.83 1.30
14 1/13/2008 -0.95 -2.51
15 1/14/2008 -0.88 -0.93
16 1/15/2008 1.21 0.39
17 1/16/2008 -1.67 -0.06
18 1/17/2008 -2.99 -1.29
19 1/18/2008 1.24 1.41
20 1/19/2008 0.64 2.37

Formula Description (Result)
=XCFTest(\$B\$2:\$B\$20,\$C\$2:\$C\$20,1,1) =XCFTest for P-Value (0.100)
=XCFTest(\$B\$2:\$B\$20,\$C\$2:\$C\$20,1,2) XCFTest for Test Statistics (1.335)
=XCFTest(\$B\$2:\$B\$20,\$C\$2:\$C\$20,1,3) XCFTest for Critical Value (2.120)

References

• Jarque, Carlos M.; Anil K. Bera (1980). "Efficient tests for normality, homoscedasticity and serial independence of regression residuals". Economics Letters 6 (3): 255-259.
• Ljung, G. M. and Box, G. E. P., "On a measure of lack of fit in time series models." Biometrika 65 (1978): 297-303
• Enders, W., "Applied econometric time series", John Wiley & Sons, 1995, p. 86-87
• Shapiro, S. S. and Wilk, M. B. (1965). "An analysis of variance test for normality (complete samples)", Biometrika, 52, 3 and 4, pages 591-611