  We present a method of extrapolating the spectroscopic behavior of Type Ia
supernovae (SNe Ia) in the near-infrared (NIR) wavelength regime up to 2.30
$\mu$m using optical spectroscopy. Such a process is useful for accurately
estimating K-corrections and other photometric quantities of SNe Ia in the NIR.
Principal component analysis is performed on data consisting of Carnegie
Supernova Project I & II optical and near-infrared FIRE spectra to produce
models capable of making these extrapolations. This method differs from
previous spectral template methods by not parameterizing models strictly by
photometric light-curve properties of SNe Ia, allowing for more flexibility of
the resulting extrapolated NIR flux. A difference of around -3.1% to -2.7% in
the total integrated NIR flux between these extrapolations and the observations
is seen here for most test cases including Branch core-normal and
shallow-silicon subtypes. However, larger deviations from the observation are
found for other tests, likely due to the limited high-velocity and broad-line
SNe Ia in the training sample. Maximum-light principal components are shown to
allow for spectroscopic predictions of the color-stretch light-curve parameter,
$s_{BV}$, within approximately $\pm$0.1 units of the value measured with
photometry. We also show these results compare well with NIR templates,
although in most cases the templates are marginally more fitting to
observations, illustrating a need for more concurrent optical+NIR spectroscopic
observations to truly understand the diversity of SNe Ia in the NIR.
