Phillips–Perron Unit Root Test

Applies the Phillips–Perron (PP) test to check for a unit root in annual maximum series data. The null hypothesis assumes the time series contains a unit root (also known as a stochastic trend). The alternative hypothesis is that the time series is trend-stationary with a deterministic linear trend.

Usage

eda_pp_test(data, alpha = 0.05)

Arguments

data

Numeric vector of observed annual maximum series values. Must be strictly positive, finite, and not missing.

alpha

Numeric scalar in \([0.01, 0.1]\). The significance level for confidence intervals or hypothesis tests. Default is 0.05.

Value

A list containing the test results, including:

• data: The data argument.

• alpha: The significance level as specified in the alpha argument.

• null_hypothesis: A string describing the null hypothesis.

• alternative_hypothesis: A string describing the alternative hypothesis.

• statistic: The PP test statistic.

• p_value: Reported p-value from the test. See the details for more information.

• reject: If TRUE, the null hypothesis was rejected at significance alpha.

Details

The implementation of this test is based on the aTSA package, which interpolates p-values from the table of critical values presented in Fuller W. A. (1996). The critical values are only available for \(\alpha \geq 0.01\). Therefore, a reported p-value of 0.01 indicates that \(p \leq 0.01\).

References

Fuller, W. A. (1976). Introduction to Statistical Time Series. New York: John Wiley and Sons

Phillips, P. C. B.; Perron, P. (1988). Testing for a Unit Root in Time Series Regression. Biometrika, 75 (2): 335-346

See also

eda_kpss_test()

Examples

data <- rnorm(n = 100, mean = 100, sd = 10)
eda_pp_test(data)
#> $data
#>   [1] 105.76548 116.35644 105.87302  91.87373 100.21493 102.16915 106.43384
#>   [8]  90.75542 112.09305 115.66475 106.29210  93.57340 109.91148 123.90197
#>  [15] 111.88599 107.95127 112.67272  96.37174  90.85030 109.63619 110.11232
#>  [22] 103.51880  85.45366  96.87146 101.49090  85.91269 110.95705  89.93695
#>  [29] 100.82613  97.13996 101.50056  91.73811  93.37605 103.32282 115.90949
#>  [36] 105.40615  78.21858 100.81197  92.78968  83.66820 113.59610 107.43217
#>  [43] 105.51555  95.14892 110.21334 103.11580 103.84172  97.51773  89.01770
#>  [50]  98.42764  95.09492  90.94731  91.61404 102.31428  98.29435 112.32145
#>  [57]  85.10743  95.72899  91.82995  84.94320  93.22315  86.30266  94.42601
#>  [64]  92.61220 102.89779 106.08334 108.82450 109.42153  95.22151 100.84429
#>  [71]  88.10724 107.37773 100.58236  94.05796 118.65775 102.38358  96.12942
#>  [78]  89.13372  89.66338  82.05767  86.20263 100.00840 113.10889 104.46057
#>  [85]  96.14615  91.31060  99.45665 117.31574  85.14095  93.78140 108.40636
#>  [92] 106.62350  89.15688 107.41433  98.99308 103.05388 113.90169  98.43064
#>  [99] 102.31027 106.38974
#> 
#> $alpha
#> [1] 0.05
#> 
#> $null_hypothesis
#> [1] "The time series has a unit root (stochastic trend)."
#> 
#> $alternative_hypothesis
#> [1] "The time series is trend-stationary."
#> 
#> $statistic
#> [1] -83.75394
#> 
#> $p_value
#> [1] 0.01
#> 
#> $reject
#> [1] TRUE
#>