\begin{thebibliography}{35}
% BibTex style file: imsart-nameyear.bst, 2017-11-03
% Default style options (sort=1,type=nameyear).
% Used options (sort=1,type=nameyear).

\bibitem[\protect\citeauthoryear{Bai and Silverstein}{2010}]{bai2010spectral}
\begin{bbook}[author]
\bauthor{\bsnm{Bai},~\bfnm{Zhidong}\binits{Z.}} \AND
  \bauthor{\bsnm{Silverstein},~\bfnm{Jack~W}\binits{J.~W.}}
(\byear{2010}).
\btitle{Spectral analysis of large dimensional random matrices}
\bvolume{20}.
\bpublisher{Springer}.
\end{bbook}
\endbibitem

\bibitem[\protect\citeauthoryear{Benaych-Georges and
  Knowles}{2016}]{benaych2016lectures}
\begin{barticle}[author]
\bauthor{\bsnm{Benaych-Georges},~\bfnm{Florent}\binits{F.}} \AND
  \bauthor{\bsnm{Knowles},~\bfnm{Antti}\binits{A.}}
(\byear{2016}).
\btitle{Lectures on the local semicircle law for Wigner matrices}.
\bjournal{arXiv preprint arXiv:1601.04055}.
\end{barticle}
\endbibitem

\bibitem[\protect\citeauthoryear{B{\"o}hm and von
  Sachs}{2009}]{bohm2009shrinkage}
\begin{barticle}[author]
\bauthor{\bsnm{B{\"o}hm},~\bfnm{Hilmar}\binits{H.}} \AND
  \bauthor{\bparticle{von} \bsnm{Sachs},~\bfnm{Rainer}\binits{R.}}
(\byear{2009}).
\btitle{Shrinkage estimation in the frequency domain of multivariate time
  series}.
\bjournal{Journal of Multivariate Analysis}
\bvolume{100}
\bpages{913--935}.
\end{barticle}
\endbibitem

\bibitem[\protect\citeauthoryear{Brillinger}{1981}]{brillinger1981time}
\begin{bbook}[author]
\bauthor{\bsnm{Brillinger},~\bfnm{David~R}\binits{D.~R.}}
(\byear{1981}).
\btitle{Time series: data analysis and theory}
\bvolume{36}.
\bpublisher{Siam}.
\end{bbook}
\endbibitem

\bibitem[\protect\citeauthoryear{Capitaine, Donati-Martin and
  Féral}{2009}]{capitainedonatiferal2009annprob}
\begin{barticle}[author]
\bauthor{\bsnm{Capitaine},~\bfnm{Mireille}\binits{M.}},
  \bauthor{\bsnm{Donati-Martin},~\bfnm{Catherine}\binits{C.}} \AND
  \bauthor{\bsnm{Féral},~\bfnm{Delphine}\binits{D.}}
(\byear{2009}).
\btitle{The largest eigenvalue of finite rank deformation of large Wigner
  matrices}.
\bjournal{Ann.Probab.}
\bvolume{37}
\bpages{1-47}.
\end{barticle}
\endbibitem

\bibitem[\protect\citeauthoryear{Chen and Liu}{2018}]{chenliu2018}
\begin{barticle}[author]
\bauthor{\bsnm{Chen},~\bfnm{Xi}\binits{X.}} \AND
  \bauthor{\bsnm{Liu},~\bfnm{Weidung}\binits{W.}}
(\byear{2018}).
\btitle{Testing independence with high-dimensional correlated samples}.
\bjournal{Ann. Stat.}
\bvolume{46(2)}
\bpages{866--895}.
\end{barticle}
\endbibitem

\bibitem[\protect\citeauthoryear{Dette and
  D{\"o}rnemann}{2020}]{dette2020likelihood}
\begin{barticle}[author]
\bauthor{\bsnm{Dette},~\bfnm{Holger}\binits{H.}} \AND
  \bauthor{\bsnm{D{\"o}rnemann},~\bfnm{Nina}\binits{N.}}
(\byear{2020}).
\btitle{Likelihood ratio tests for many groups in high dimensions}.
\bjournal{Journal of Multivariate Analysis}
\bpages{104605}.
\end{barticle}
\endbibitem

\bibitem[\protect\citeauthoryear{Duchesne and Roy}{2003}]{duchesne2003robust}
\begin{barticle}[author]
\bauthor{\bsnm{Duchesne},~\bfnm{Pierre}\binits{P.}} \AND
  \bauthor{\bsnm{Roy},~\bfnm{Roch}\binits{R.}}
(\byear{2003}).
\btitle{Robust tests for independence of two time series}.
\bjournal{Statistica Sinica}
\bpages{827--852}.
\end{barticle}
\endbibitem

\bibitem[\protect\citeauthoryear{Dyn'kin}{1972}]{dyn1972operator}
\begin{barticle}[author]
\bauthor{\bsnm{Dyn'kin},~\bfnm{Evsey~Mordukhovich}\binits{E.~M.}}
(\byear{1972}).
\btitle{An operator calculus based on the Cauchy--Green formula}.
\bjournal{Zapiski Nauchnykh Seminarov POMI}
\bvolume{30}
\bpages{33--39}.
\end{barticle}
\endbibitem

\bibitem[\protect\citeauthoryear{Eichler}{2007}]{eichler2007frequency}
\begin{barticle}[author]
\bauthor{\bsnm{Eichler},~\bfnm{Michael}\binits{M.}}
(\byear{2007}).
\btitle{A frequency-domain based test for non-correlation between stationary
  time series}.
\bjournal{Metrika}
\bvolume{65}
\bpages{133--157}.
\end{barticle}
\endbibitem

\bibitem[\protect\citeauthoryear{Eichler}{2008}]{eichler2008testing}
\begin{barticle}[author]
\bauthor{\bsnm{Eichler},~\bfnm{Michael}\binits{M.}}
(\byear{2008}).
\btitle{Testing nonparametric and semiparametric hypotheses in vector
  stationary processes}.
\bjournal{Journal of Multivariate Analysis}
\bvolume{99}
\bpages{968--1009}.
\end{barticle}
\endbibitem

\bibitem[\protect\citeauthoryear{El~Himdi, Roy and
  Duchesne}{2003}]{elhimdiduchesneroy2003}
\begin{barticle}[author]
\bauthor{\bsnm{El~Himdi},~\bfnm{Khalid}\binits{K.}},
  \bauthor{\bsnm{Roy},~\bfnm{Roch}\binits{R.}} \AND
  \bauthor{\bsnm{Duchesne},~\bfnm{Pierre}\binits{P.}}
(\byear{2003}).
\btitle{Tests for non-norrelation of two multivariate time series: A
  nonparametric approach}.
\bjournal{Lecture Notes-Monograph Series, vol. 42}
\bpages{397--416}.
\end{barticle}
\endbibitem

\bibitem[\protect\citeauthoryear{Erdos, Knowles and
  Yau}{2013}]{erdHos2013averaging}
\begin{binproceedings}[author]
\bauthor{\bsnm{Erdos},~\bfnm{L{\'a}szl{\'o}}\binits{L.}},
  \bauthor{\bsnm{Knowles},~\bfnm{Antti}\binits{A.}} \AND
  \bauthor{\bsnm{Yau},~\bfnm{Horng-Tzer}\binits{H.-T.}}
(\byear{2013}).
\btitle{Averaging fluctuations in resolvents of random band matrices}.
In \bbooktitle{Annales Henri Poincar{\'e}}
\bvolume{14}
\bpages{1837--1926}.
\bpublisher{Springer}.
\end{binproceedings}
\endbibitem

\bibitem[\protect\citeauthoryear{Haagerup and
  Thorbjornsen}{2003}]{haagerup2003random}
\begin{barticle}[author]
\bauthor{\bsnm{Haagerup},~\bfnm{Uffe}\binits{U.}} \AND
  \bauthor{\bsnm{Thorbjornsen},~\bfnm{Steen}\binits{S.}}
(\byear{2003}).
\btitle{Random matrices with complex Gaussian entries}.
\bjournal{Expositiones Mathematicae}
\bvolume{21}
\bpages{293--337}.
\end{barticle}
\endbibitem

\bibitem[\protect\citeauthoryear{Hachem, Loubaton and
  Najim}{2007}]{hachemloubatonnajim2007detequiv}
\begin{barticle}[author]
\bauthor{\bsnm{Hachem},~\bfnm{Walid}\binits{W.}},
  \bauthor{\bsnm{Loubaton},~\bfnm{Philippe}\binits{P.}} \AND
  \bauthor{\bsnm{Najim},~\bfnm{Jamal}\binits{J.}}
(\byear{2007}).
\btitle{Deterministic equivalents for certain functionals of large random
  matrices}.
\bjournal{The Annals of Applied Probability}
\bvolume{17}
\bpages{875--930}.
\end{barticle}
\endbibitem

\bibitem[\protect\citeauthoryear{Hachem
  et~al.}{2008}]{hachemkhorunzhyloubatonnajimpastur2008newapproach}
\begin{barticle}[author]
\bauthor{\bsnm{Hachem},~\bfnm{Walid}\binits{W.}},
  \bauthor{\bsnm{Kohrunzhiy},~\bfnm{Oleksiy}\binits{O.}},
  \bauthor{\bsnm{Loubaton},~\bfnm{Philippe}\binits{P.}},
  \bauthor{\bsnm{Najim},~\bfnm{Jamal}\binits{J.}} \AND
  \bauthor{\bsnm{Pastur},~\bfnm{Leonid}\binits{L.}}
(\byear{2008}).
\btitle{A New Approach for Capacity Analysis of Large Dimensional Multi-Antenna
  Channels}.
\bjournal{IEEE Transactions on Information Theory}
\bvolume{54}
\bpages{3987--4003}.
\end{barticle}
\endbibitem

\bibitem[\protect\citeauthoryear{Haugh}{1976}]{haugh1976checking}
\begin{barticle}[author]
\bauthor{\bsnm{Haugh},~\bfnm{Larry~D}\binits{L.~D.}}
(\byear{1976}).
\btitle{Checking the independence of two covariance-stationary time series: a
  univariate residual cross-correlation approach}.
\bjournal{Journal of the American Statistical Association}
\bvolume{71}
\bpages{378--385}.
\end{barticle}
\endbibitem

\bibitem[\protect\citeauthoryear{Helffer and
  Sjostrand}{1989}]{helffer1989equation}
\begin{bincollection}[author]
\bauthor{\bsnm{Helffer},~\bfnm{Bernard}\binits{B.}} \AND
  \bauthor{\bsnm{Sjostrand},~\bfnm{J}\binits{J.}}
(\byear{1989}).
\btitle{Equation de Schr{\"o}dinger avec champ magn{\'e}tique et {\'e}quation
  de Harper}.
In \bbooktitle{Schr{\"o}dinger operators}
\bpages{118--197}.
\bpublisher{Springer}.
\end{bincollection}
\endbibitem

\bibitem[\protect\citeauthoryear{Himdi and Roy}{1997}]{himdi1997tests}
\begin{barticle}[author]
\bauthor{\bsnm{Himdi},~\bfnm{Khalid~El}\binits{K.~E.}} \AND
  \bauthor{\bsnm{Roy},~\bfnm{Roch}\binits{R.}}
(\byear{1997}).
\btitle{Tests for noncorrelation of two multivariate ARMA time series}.
\bjournal{Canadian Journal of Statistics}
\bvolume{25}
\bpages{233--256}.
\end{barticle}
\endbibitem

\bibitem[\protect\citeauthoryear{Hong}{1996}]{hong1996testing}
\begin{barticle}[author]
\bauthor{\bsnm{Hong},~\bfnm{Yongmiao}\binits{Y.}}
(\byear{1996}).
\btitle{Testing for independence between two covariance stationary time
  series}.
\bjournal{Biometrika}
\bvolume{83}
\bpages{615--625}.
\end{barticle}
\endbibitem

\bibitem[\protect\citeauthoryear{Jiang}{2004a}]{jiang2004}
\begin{barticle}[author]
\bauthor{\bsnm{Jiang},~\bfnm{Tiefeng}\binits{T.}}
(\byear{2004}a).
\btitle{The limiting distributions of eigenvalues of sample correlation
  matrices}.
\bjournal{Sankhya: The Indian Journal of Statistics}
\bvolume{66}
\bpages{35--48}.
\end{barticle}
\endbibitem

\bibitem[\protect\citeauthoryear{Jiang}{2004b}]{jiangmaxcorr2004}
\begin{barticle}[author]
\bauthor{\bsnm{Jiang},~\bfnm{Tiefeng}\binits{T.}}
(\byear{2004}b).
\btitle{The asymptotic distributions of the largest entries of sample
  correlation matrices}.
\bjournal{Ann. Appl. Probab.}
\bvolume{14(2)}
\bpages{865--880}.
\end{barticle}
\endbibitem

\bibitem[\protect\citeauthoryear{Jiang and Yang}{2013}]{jiangyang2013}
\begin{barticle}[author]
\bauthor{\bsnm{Jiang},~\bfnm{Tiefeng}\binits{T.}} \AND
  \bauthor{\bsnm{Yang},~\bfnm{Fan}\binits{F.}}
(\byear{2013}).
\btitle{Central limit theorems for classical likelihood ratio tests for
  high-dimensional distributions}.
\bjournal{Ann. of Stats.}
\bvolume{41}
\bpages{2029--2074}.
\end{barticle}
\endbibitem

\bibitem[\protect\citeauthoryear{Koch and Yang}{1986}]{koch1986method}
\begin{barticle}[author]
\bauthor{\bsnm{Koch},~\bfnm{Paul~D}\binits{P.~D.}} \AND
  \bauthor{\bsnm{Yang},~\bfnm{Shie-Shien}\binits{S.-S.}}
(\byear{1986}).
\btitle{A method for testing the independence of two time series that accounts
  for a potential pattern in the cross-correlation function}.
\bjournal{Journal of the American Statistical Association}
\bvolume{81}
\bpages{533--544}.
\end{barticle}
\endbibitem

\bibitem[\protect\citeauthoryear{Li and Hui}{1994}]{li1994robust}
\begin{barticle}[author]
\bauthor{\bsnm{Li},~\bfnm{WK}\binits{W.}} \AND
  \bauthor{\bsnm{Hui},~\bfnm{YV}\binits{Y.}}
(\byear{1994}).
\btitle{Robust residual cross correlation tests for lagged relations in time
  series}.
\bjournal{Journal of Statistical Computation and Simulation}
\bvolume{49}
\bpages{103--109}.
\end{barticle}
\endbibitem

\bibitem[\protect\citeauthoryear{Loubaton}{2016}]{loubaton2016jotp}
\begin{barticle}[author]
\bauthor{\bsnm{Loubaton},~\bfnm{Philippe}\binits{P.}}
(\byear{2016}).
\btitle{On the almost sure location of the singular values of certain Gaussian
  block-Hankel large random matrices}.
\bjournal{J. Theor. Prob.}
\bvolume{4}
\bpages{1339-1443}.
\end{barticle}
\endbibitem

\bibitem[\protect\citeauthoryear{Loubaton, Rosuel and
  Vallet}{2021}]{loubatonrosuelvallet2021jmva}
\begin{barticle}[author]
\bauthor{\bsnm{Loubaton},~\bfnm{Philippe}\binits{P.}},
  \bauthor{\bsnm{Rosuel},~\bfnm{Alexis}\binits{A.}} \AND
  \bauthor{\bsnm{Vallet},~\bfnm{Pascal}\binits{P.}}
(\byear{2021}).
\btitle{On the asymptotic distribution of the maximum sample spectral coherence
  of Gaussian time series in the high dimensional regime}.
\bnote{Preprint arXiv:2107.02891}.
\end{barticle}
\endbibitem

\bibitem[\protect\citeauthoryear{Mestre and
  Vallet}{2017}]{mestre2017correlation}
\begin{barticle}[author]
\bauthor{\bsnm{Mestre},~\bfnm{Xavier}\binits{X.}} \AND
  \bauthor{\bsnm{Vallet},~\bfnm{Pascal}\binits{P.}}
(\byear{2017}).
\btitle{Correlation tests and linear spectral statistics of the sample
  correlation matrix}.
\bjournal{IEEE Transactions on Information Theory}
\bvolume{63}
\bpages{4585--4618}.
\end{barticle}
\endbibitem

\bibitem[\protect\citeauthoryear{Pan, Jiti and
  Yanrong}{2014}]{pangaoyang2014jasa}
\begin{barticle}[author]
\bauthor{\bsnm{Pan},~\bfnm{Guangming}\binits{G.}},
  \bauthor{\bsnm{Jiti},~\bfnm{Gao}\binits{G.}} \AND
  \bauthor{\bsnm{Yanrong},~\bfnm{Yang}\binits{Y.}}
(\byear{2014}).
\btitle{Testing independence among a large numbers of high-dimensional random
  vectors}.
\bjournal{J. Amer. Stat. Assoc.}
\bvolume{109}
\bpages{600-612}.
\end{barticle}
\endbibitem

\bibitem[\protect\citeauthoryear{Pastur and
  Shcherbina}{2011}]{pasturshcherbina2011}
\begin{bbook}[author]
\bauthor{\bsnm{Pastur},~\bfnm{L}\binits{L.}} \AND
  \bauthor{\bsnm{Shcherbina},~\bfnm{M}\binits{M.}}
(\byear{2011}).
\btitle{Eigenvalue Distribution of Large Random Matrices}.
\bpublisher{Mathematical Surveys and Monographs, AMS}.
\end{bbook}
\endbibitem

\bibitem[\protect\citeauthoryear{Rosuel
  et~al.}{2021}]{rosuelvalletloubatonmestre2021ieeesp}
\begin{barticle}[author]
\bauthor{\bsnm{Rosuel},~\bfnm{Alexis}\binits{A.}},
  \bauthor{\bsnm{Vallet},~\bfnm{Pascal}\binits{P.}},
  \bauthor{\bsnm{Loubaton},~\bfnm{Philippe}\binits{P.}} \AND
  \bauthor{\bsnm{Mestre},~\bfnm{Xavier}\binits{X.}}
(\byear{2021}).
\btitle{On the detection of low-rank signal in the presence of spatially
  uncorrelated noise: a frequency domain approach}.
\bnote{Preprint . arXiv:2106.12815}.
\end{barticle}
\endbibitem

\bibitem[\protect\citeauthoryear{Rudelson et~al.}{2013}]{rudelson2013hanson}
\begin{barticle}[author]
\bauthor{\bsnm{Rudelson},~\bfnm{Mark}\binits{M.}},
  \bauthor{\bsnm{Vershynin},~\bfnm{Roman}\binits{R.}} \betal{et~al.}
(\byear{2013}).
\btitle{Hanson-Wright inequality and sub-gaussian concentration}.
\bjournal{Electronic Communications in Probability}
\bvolume{18}.
\end{barticle}
\endbibitem

\bibitem[\protect\citeauthoryear{Taniguchi, Puri and
  Kondo}{1996}]{taniguchi1996nonparametric}
\begin{barticle}[author]
\bauthor{\bsnm{Taniguchi},~\bfnm{Masanobu}\binits{M.}},
  \bauthor{\bsnm{Puri},~\bfnm{Madan~L}\binits{M.~L.}} \AND
  \bauthor{\bsnm{Kondo},~\bfnm{Masao}\binits{M.}}
(\byear{1996}).
\btitle{Nonparametric approach for non-Gaussian vector stationary processes}.
\bjournal{Journal of Multivariate Analysis}
\bvolume{56}
\bpages{259--283}.
\end{barticle}
\endbibitem

\bibitem[\protect\citeauthoryear{Tao}{2011}]{tao2011topics}
\begin{barticle}[author]
\bauthor{\bsnm{Tao},~\bfnm{Terence}\binits{T.}}
(\byear{2011}).
\btitle{Topics in random matrix theory}.
\bjournal{Graduate Studies in Mathematics}
\bvolume{132}.
\end{barticle}
\endbibitem

\bibitem[\protect\citeauthoryear{Wahba}{1971}]{wahba1971some}
\begin{barticle}[author]
\bauthor{\bsnm{Wahba},~\bfnm{Grace}\binits{G.}}
(\byear{1971}).
\btitle{Some tests of independence for stationary multivariate time series}.
\bjournal{Journal of the Royal Statistical Society: Series B (Methodological)}
\bvolume{33}
\bpages{153--166}.
\end{barticle}
\endbibitem

\end{thebibliography}
