Trend {s2dv}

Compute the trend

Description

Compute the linear trend or any degree of polynomial regression along the forecast time. It returns the regression coefficients (including the intercept) and the detrended array. The confidence intervals and p-value are also provided if needed.
The confidence interval relies on the student-T distribution, and the p-value is calculated by ANOVA.

Usage

Trend(
  data,
  time_dim = "ftime",
  interval = 1,
  polydeg = 1,
  alpha = 0.05,
  conf = TRUE,
  pval = TRUE,
  sign = FALSE,
  ncores = NULL
)

Arguments

data

An numeric array including the dimension along which the trend is computed.

time_dim

A character string indicating the dimension along which to compute the trend. The default value is 'ftime'.

interval

A positive numeric indicating the unit length between two points along 'time_dim' dimension. The default value is 1.

polydeg

A positive integer indicating the degree of polynomial regression. The default value is 1.

alpha

A numeric indicating the significance level for the statistical significance test. The default value is 0.05.

conf

A logical value indicating whether to retrieve the confidence intervals or not. The default value is TRUE.

pval

A logical value indicating whether to compute the p-value or not. The default value is TRUE.

sign

A logical value indicating whether to retrieve the statistical significance based on 'alpha'. The default value is FALSE.

ncores

An integer indicating the number of cores to use for parallel computation. The default value is NULL.

Value

A list containing:

$trend

A numeric array with the first dimension 'stats', followed by the same dimensions as parameter 'data' except the 'time_dim' dimension. The length of the 'stats' dimension should be polydeg + 1, containing the regression coefficients from the lowest order (i.e., intercept) to the highest degree.

$conf.lower

A numeric array with the first dimension 'stats', followed by the same dimensions as parameter 'data' except the 'time_dim' dimension. The length of the 'stats' dimension should be polydeg + 1, containing the lower limit of the (1-alpha)% confidence interval for all the regression coefficients with the same order as $trend. Only present conf = TRUE.

$conf.upper

A numeric array with the first dimension 'stats', followed by the same dimensions as parameter 'data' except the 'time_dim' dimension. The length of the 'stats' dimension should be polydeg + 1, containing the upper limit of the (1-alpha)% confidence interval for all the regression coefficients with the same order as $trend. Only present conf = TRUE.

$p.val

A numeric array of p-value calculated by anova(). The first dimension 'stats' is 1, followed by the same dimensions as parameter 'data' except the 'time_dim' dimension. Only present if pval = TRUE.

$sign

The statistical significance. Only present if sign = TRUE.

$detrended

A numeric array with the same dimensions as paramter 'data', containing the detrended values along the 'time_dim' dimension.

Examples

# Load sample data as in Load() example:
example(Load)
months_between_startdates <- 60
trend <- Trend(sampleData$obs, polydeg = 2, interval = months_between_startdates)