statioVAR (version 0.1.3)

detrender: Within-unit linear detrending for multilevel VAR analysis

Description

Remove unit-specific linear trends from panel data to approximate stationarity, preparing inputs for multilevel Vector Autoregressive (VAR) modeling (among others). For each unit (subject) and each selected variable, a linear regression of the variable on the time index is tested at significance level alpha; if the slope is significant, the fitted trend is subtracted and the mean of the unit is re-added, to produce detrended series while preserving between-unit information.

Caution: models with lagged outcomes and per-unit intercepts (fixed or random) are prone to Nickell-type bias when there are fewer than 10 time points (T) per unit; detrending does not remove it. T >= 10 is recommended (Nickell, 1981; Judson & Owen, 1999). For VAR(1) with an intercept and linear trend, a minimum of K + 4 time points per unit (where K is the number of detrended series) is required to maintain positive residual degrees of freedom (Lütkepohl, 2005).

Usage

detrender(
  df,
  id_var,
  time_var,
  vars_to_detrend,
  alpha = 0.05,
  min_obs = 3
)

Value

A named list with:

df

Tibble. The original dataset with additional detrended columns.

n_units

Integer. Number of unique units (subjects) processed.

total_trends

Integer. Total number of individual trends removed across all variables.

summary

Tibble. Number of removed linear trends per variable, with columns variable and removed_trends.

Arguments

df

Data frame or tibble (long format).

id_var

Character string. Unit (subject) identifier column (required).

time_var

Character string. Numeric time index column (required).

vars_to_detrend

Character vector. Column names to detrend within each unit (subject) (required).

alpha

Numeric in (0,1). Significance threshold for retaining a non-zero time slope (default: 0.05).

min_obs

Integer >2. Minimum observations per unit-variable to attempt detrending (default: 3).

References

Judson, R. A., & Owen, A. L. (1999). Estimating dynamic panel data models: a guide for macroeconomists. Economics letters, 65(1), 9-15. tools:::Rd_expr_doi("10.1016/s0165-1765(99)00130-5")

Lütkepohl, H. (2005). New Introduction to Multiple Time Series Analysis. Springer Berlin Heidelberg. tools:::Rd_expr_doi("10.1007/978-3-540-27752-1")

Nickell, S. (1981). Biases in dynamic models with fixed effects. Econometrica: Journal of the econometric society, 1417-1426. tools:::Rd_expr_doi("10.2307/1911408")

Examples

df_example <- data.frame(
id = rep(1:2, each = 5),
time = rep(1:5, 2),
x = rep(1:5, 2) + rnorm(10)
)
res <- statioVAR::detrender(
df = df_example,
id_var = "id",
time_var = "time",
vars_to_detrend = "x",
alpha = 0.05,
min_obs = 3
)
res$df[7:9,]
res$n_units
res$total_trends
res$summary