# An Overview of the wwntests Package In wwntests: Hypothesis Tests for Functional Time Series

### Applying the Independence Test to Data

The 'components' parameter (denoted by p above) determines how many functional principal components to use (kept in order of importance, which is determined by the proportion of the variance that each computed component explains). The 'lag' parameter (denoted by H above) determines the maximum lag to consider. We apply the independence test to our Brownian motion and FAR data.

fport_test(b, test = 'independence', components = 3, lag = 3, suppress_raw_output = TRUE)

fport_test(f, test = 'independence', components = 16, lag = 10, suppress_raw_output = TRUE)


## General Remarks

### Suppressing Output

The main hypothesis function fport_test, as well as all the individual test functions may return two forms of output. In the default configuration, when suppress_raw_output and suppress_print_output are given as FALSE, each function will first print to the console the name of the test, the null hypothesis being tested, the p-value of the test, the sample size of the functional data, and additional information that may be unique to the given test. It will then return a list containing the p-value, the value of the test statistic, and the quantile of the respective limiting distribution. Passing suppress_print_output = TRUE will cause the function to omit any output to the console. Passing suppress_raw_output = TRUE will cause the function to not return the list. At least one of these parameters must be TRUE.

## References

[1] Kokoszka P., & Rice G., & Shang H.L. (2017). Inference for the autocovariance of a functional time series under conditional heteroscedasticity. Journal of Multivariate Analysis, 162, 32-50, DOI: 10.1016/j.jmva.2017.08.004 .

[2] Characiejus V., & Rice G. (2019). A general white noise test based on kernel lag-window estimates of the spectral density operator. Econometrics and Statistics, DOI: 10.1016/j.ecosta.2019.01.003 .

[3] Gabrys R., & Kokoszka P. (2007). Portmanteau Test of Independence for Functional Observations. Journal of the American Statistical Association, 102:480, 1338-1348, DOI: 10.1198/016214507000001111 .

[4] Zhang X. (2016). White noise testing and model diagnostic checking for functional time series. Journal of Econometrics, 194, 76-95, DOI: 10.1016/j.jeconom.2016.04.004 .

[5] Chen W.W. & Deo R.S. (2004). Power transformations to induce normality and their applications. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 66, 117–130, DOI: 10.1111/j.1467-9868.2004.00435.x .

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wwntests documentation built on July 2, 2020, 2:57 a.m.