# 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 (a one-dimensional array of cells (e.g., rows or columns)).
X
is the second data series (a 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 the 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 (i.e., two-sides) test, so the computed p-value should be compared with half of the significance level ($\alpha$).

## 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.