Tests whether the benchmark model encompasses the alternative model, using the ENC-NEW statistic of Clark and McCracken (2001). Under the null, the benchmark forecast encompasses the alternative (no additional information in the alternative).
Value
A list with class "enc_new" containing:
- statistic
The ENC-NEW test statistic.
- n
Number of observations.
Details
The ENC-NEW statistic is: $$\text{ENC-NEW} = n \cdot \frac{\bar{c}}{\text{MSFE}_2}$$ where \(\bar{c} = n^{-1} \sum (e_{1,t}^2 - e_{2,t} e_{1,t})\) and \(\text{MSFE}_2 = n^{-1} \sum e_{2,t}^2\).
Critical values are non-standard and depend on the estimation setup. See Clark and McCracken (2001, Table 2) for asymptotic critical values.
References
Clark, T.E. and McCracken, M.W. (2001). Tests of Equal Forecast Accuracy and Encompassing for Nested Models. Journal of Econometrics, 105(1), 85-110.
Examples
set.seed(42)
e1 <- rnorm(100)
e2 <- rnorm(100, sd = 0.9)
enc_new(e1, e2)
#>
#> ╭────────────────────────────────────────────────────╮
#> │ ENC-NEW Encompassing Test │
#> │ (Clark and McCracken, 2001) │
#> ├────────────────────────────────────────────────────┤
#> │ H0: Benchmark encompasses the alternative │
#> │ H1: Alternative adds predictive content │
#> ├┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┤
#> │ Test Results: │
#> │ ENC-NEW statistic: 158.8083 │
#> ├┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┤
#> │ Details: │
#> │ Observations (n): 100 │
#> │ Note: Critical values are non-standard. │
#> │ See Clark & McCracken (2001, Table 2). │
#> ╰────────────────────────────────────────────────────╯
#>