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Elliott-Rothenberg-Stock GLS-detrended ADF (DF-GLS)

Source: R/erstst.R
Erstst.Rd

Formula: local-to-unity GLS detrending at abar = 1 + cbar / T with cbar = -7 (mean case) or cbar = -13.5 (trend case). Quasi-difference both the series and the deterministic terms,


  ytil_1 = y_1,  ytil_t = y_t - abar y_{t-1}
  ztil_1 = z_1,  ztil_t = z_t - abar z_{t-1}

regress ytil on ztil to get psi, form y^d = y - z psi, and run the ADF regression without deterministic terms, dy^d_t = rho y^d_{t-1} + sum_j c_j dy^d_{t-j} + e_t. The DF-GLS statistic is the t-ratio on rho.

Usage

Erstst(x, lags = 1, trend = FALSE)

Arguments

x

Series.

lags

Number of lagged first differences p (>= 0).

trend

Detrend against (1, t) rather than the constant alone.

Value

List with estimate, statistic, rho, se, abar, lags, nobs, n, method.

References

Elliott, Rothenberg & Stock (1996), Econometrica 64(4):813-836, doi:10.2307/2171846.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Erstst(V)
#> $estimate
#> [1] 0.0127576
#> 
#> $statistic
#> [1] 0.0127576
#> 
#> $rho
#> [1] 8.293459e-19
#> 
#> $se
#> [1] 6.5008e-17
#> 
#> $abar
#> [1] 0.125
#> 
#> $lags
#> [1] 1
#> 
#> $nobs
#> [1] 6
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "Elliott-Rothenberg-Stock GLS-detrended ADF"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"