Description Usage Arguments Details Value References Examples
This function computes the Hidalgo-Seo statistic for a change in mean model.
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dat |
The data vector |
estimate |
Set to |
corr |
If |
get_all_vals |
If |
custom_var |
Can be a vector the same length as |
use_kernel_var |
Set to |
kernel |
If character, the identifier of the kernel function as used in
cointReg (see |
bandwidth |
If character, the identifier for how to compute the
bandwidth as defined in cointReg (see
|
For a data set x_t with n observations, the test statistic is
\max_{1 ≤q s ≤q n - 1} (\mathcal{LM}(s) - B_n)/A_n
where \hat{u}_t = x_t - \bar{x} (\bar{x} is the sample mean), a_n = (2 \log \log n)^{1/2}, b_n = a_n^2 - \frac{1}{2} \log \log \log n - \log Γ (1/2), A_n = b_n / a_n^2, B_n = b_n^2/a_n^2, \hat{Δ} = \hat{σ}^2 = n^{-1} ∑_{t = 1}^{n} \hat{u}_t^2, and \mathcal{LM}(s) = n (n - s)^{-1} s^{-1} \hat{Δ}^{-1} ≤ft( ∑_{t = 1}^{s} \hat{u}_t\right)^2.
If corr
is FALSE
, then the residuals are assumed to be
uncorrelated. Otherwise, the residuals are assumed to be correlated and
\hat{Δ} = \hat{γ}(0) + 2 ∑_{j = 1}^{\lfloor √{n}
\rfloor} (1 - \frac{j}{√{n}}) \hat{γ}(j) with \hat{γ}(j)
= \frac{1}{n}∑_{t = 1}^{n - j} \hat{u}_t \hat{u}_{t + j}.
This statistic was presented in \insertCitehidalgoseo13CPAT.
If both estimate
and get_all_vals
are FALSE
, the
value of the test statistic; otherwise, a list that contains the test
statistic and the other values requested (if both are TRUE
,
the test statistic is in the first position and the estimated change
point in the second)
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