R/ts.stationary.test.R

In TimeSeries.OBeu: Time Series Analysis 'OpenBudgets.eu'

#' @title 
#' Stationarity testing
#'  
#' @description
#' This functions tests the stationarity of the input time series data.
#' 
#' @usage ts.stationary.test(tsdata)
#' 
#' @param tsdata The input univariate time series data
#' 
#' @details 
#' This function tests the deterministic and stochastic trend of the input time series data. This function uses ACF and PACF functions 
#' from forecast package, Phillips Perron test, Augmented Dickey Fuller (ADF) test, Kwiatkowski Phillips Schmidt Shin (KPSS) test,
#' from tseries package and Mann Kendall test for Monotonic Trend Cox Stuart trend test from trend package.
#' 
#' Phillips Perron test tests the null hypothesis of whether a unit root is present in a time series sample, 
#' against a stationary alternative. The truncation lag parameter is set to trunc(4*(n/100)^0.25), 
#' where n the length of the in input time series data
#'
#' Augmented Dickey Fuller (ADF) test, tests the null hypothesis of whether a unit root is present in a time series sample.
#' The truncation lag parameter is set to trunc((n-1)^(1/3))), where n the length of the input time series data
#'
#' Kwiatkowski Phillips Schmidt Shin (KPSS) test, tests a null hypothesis that an observable time series is stationary
#' around a deterministic trend (i.e. trend stationary) against the alternative of a unit root. 
#' The truncation lag parameter is set to trunc(3*sqrt(n)/13), where n the length of the input time series data
#'
#' The non parametric Mann Kendall test is used to detect monotonic trends. The null hypothesis, H0, is that the data 
#' come from a population with independent realizations and are identically distributed. 
#' The alternative hypothesis, HA, is that the data follow a monotonic trend.
#'
#' The Cox Stuart test is a modified sign test. The null hypothesis, H0, is that the input time series assumed to be independent
#' against the fact that there is a time dependent trend (monotonic trend).
#'
#' @return 
#' A string indicating if the time series is stationary or non stationary for internal use in ts.analysis.
#'
#' @author Kleanthis Koupidis, Charalampos Bratsas
#' 
#' @references tseries, trend
#' 
#' @seealso \code{\link{ts.analysis}}, \code{\link[forecast]{Acf}}, \code{\link{Pacf}}, \code{\link[tseries]{pp.test}},
#' \code{\link[tseries]{adf.test}}, \code{\link[tseries]{kpss.test}}, \code{\link[trend]{mk.test}}, \code{\link[trend]{cs.test}}
#' 
#' 
#' @examples
#' ts.stationary.test(Athens_approved_ts)
#' 
#' @rdname ts.stationary.test
#' @export
#' 

ts.stationary.test <- function(tsdata) {
  
  #ACF
  acF <- forecast::Acf(tsdata, plot = FALSE)
  acftest <- ifelse(all(acF$acf[2:length(acF$lag)] < 1.96/sqrt(length(tsdata))) &&
                      all(acF$acf[2:length(acF$lag)] > -1.96/sqrt(length(tsdata))),
                    "Stationary",
                    "Non Stationary")
  #PACF
  pacF <- forecast::Pacf(tsdata, plot = FALSE)
  pacftest <- ifelse(all(pacF$acf[2:length(pacF$lag)] < 1.96/sqrt(length(tsdata))) &&
                       all(pacF$acf[2:length(pacF$lag)] > -1.96/sqrt(length(tsdata))),
                     "Stationary",
                     "Non Stationary")
  
  acf_pacf <- c(acftest, pacftest)
  
  # Phillips Perron test
  if (length(tsdata) > 4) {
    pptest <- tseries::pp.test(tsdata, alternative = "stationary")
  } else {
    pptest <- NULL
  }
  # Augmented Dickey Fuller (ADF) test
  if (length(tsdata) < 7) {
    adftest <- tseries::adf.test(tsdata, alternative = "stationary", k = 0)
  } else {
    adftest <- tseries::adf.test(tsdata, alternative = "stationary")
  }
  
  # Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test
  kpsstest <- tseries::kpss.test(tsdata)
  
  # Mann Kendall Test For Monotonic Trend
  mktest <- trend::mk.test(tsdata)
  
  # Cox and Stuart trend test
  cstest <- trend::cs.test(tsdata)
  
  ## Summary of Tests Results
  test_hypo <- data.frame("p_value" = c(pptest$p.value, 
                                        adftest$p.value, 
                                        kpsstest$p.value,
                                        mktest$p.value,
                                        cstest$p.value))
  
  rownames(test_hypo) <- c("Phillips Perron test",
                           "Augmented Dickey Fuller test",
                           "Kwiatkowski Phillips Schmidt Shin test",
                           "Mann Kendall Test",
                           "Cox Stuart test")
  
  test_hypo$result <- ifelse(test_hypo$p_value > 0.05,
                             "Non Stationary",
                             "Stationary")
  
  #Fix the Kpss Result
  test_hypo$result[3] <- ifelse(kpsstest$p.value < 0.05, 
                                "Non Stationary", 
                                "Stationary")
  tests <- test_hypo$result
  
  #Add acf,pacf results
  tests[6] <- acf_pacf[1]
  tests[7] <- acf_pacf[2]
  
  # Most test show that the tsdata is (see check_stat result):
  occurences <- max(table(tests))
  check_stat <- names(which(table(tests) == occurences))
  
  return(check_stat)
}