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\begin{document}
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\title{Online Supplementary Material for: \vspace{0.5cm} \\ Cointegrating Polynomial Regressions: Fully Modified OLS Estimation and
Inference \vspace{0.5cm} \\ published in \\ {\em Econometric
Theory} {\bf Vol.} (year), pages}
\author{Martin Wagner
\\
{\small Faculty of Statistics} \\
{\small  Technical University Dortmund} \\
{\small Dortmund, Germany} \\
{\small \&}\\
{\small  Institute for Advanced Studies} \\
{\small Vienna, Austria} \\
{\small \&}\\
{\small Bank of Slovenia} \\
{\small Ljubljana, Slovenia}
 \and Seung Hyun Hong
\\
{\small Korea Institute of Public Finance} \\
{\small Seoul, Korea} }
\date{}
 \maketitle


\newpage

\section*{Online Appendix B: Modified Bonferroni Bound Tests, the Minimum Volatility Rule and Critical Values for the CS Test}

By construction tests based on the Bonferroni bound are
conservative and are known to be particularly conservative when
the individual test statistics that are combined are highly
correlated \citeaffixed{Ho86}{see}. In the literature several less
conservative modified Bonferroni bound type test procedures have
been presented, e.g., in \citeasnoun{Ho88}, \citeasnoun{Si86} or
\citeasnoun{Ro90}. Denote the test statistics ordered in magnitude
by $CT_b^{(1)}\ge \cdots \ge CT_b^{(M)}$. The modification of
\citeasnoun{Ho88} amounts to rejecting the null hypothesis if at
least one of the test statistics $CT_b^{(j)} \ge c_{\alpha^H(j)}$,
with $\alpha^H(j) = \frac{j}{C_M}\frac{\alpha}{M}$ and $C_M = 1 +
1/2 + \cdots + 1/M$. The modification of \citeasnoun{Si86} is very
similar and almost coincides with the procedure of
\citeasnoun{Ho88} with the only difference being that the
additional adjustment factor $C_M$ is not included, i.e.,
$\alpha^S(j) = j\frac{\alpha}{M}$. A further modification of the
computation of the levels used in the sequential test procedure
has been proposed in \citeasnoun{Ro90}. For this modification the
levels $\alpha^R(j)$ are computed recursively via $\alpha^R(M) =
\alpha$, $\alpha^R(M-1) = \frac{\alpha}{2}$ and for $k=3,\ldots,M$
they are computed as
%
\begin{eqnarray*}
\alpha^R(M-k+1) = \frac{1}{k}\left[\sum_{j=1}^{k-1} \alpha^j
-\sum_{j=1}^{k-1}\binom{k}{j}(\alpha^R(M-j))^{k-j} \right].
\end{eqnarray*}
%
The null hypothesis is rejected if all test statistics $CT_b^{(j)}
\ge c_{\alpha^R(j)}$.


The block length selection for the sub-sampling is based on the
{\em minimum volatility} rule proposed by
\citeasnoun[p.~1297]{RoWo01}. To be precise, we choose $b_{\min} =
0.5T^{1/2}$ and $b_{\max} = 2.5T^{1/2}$. For all
$b\in[b_{\min}+2,b_{\max}-2]$ we compute the mean $m$ and standard
deviation $sd$ of the test statistics over the five neighboring
block sizes, i.e., for a block size $b^*$, we use the test
statistics $CT_{b}$ for $b=b^*-2,b^*-1,b^*,b^*+1,b^*+2$ to compute
the mean and standard deviation of $CT_{b}$ as a function of $b$.
The optimal block length is then given by the value $b_{opt} \in
[b_{\min}+2,b_{\max}-2]$ that minimizes, again over five five
neighboring values of $b$, the change of the empirical
distribution in terms of the first two moments. Hence we choose
the block length to minimize $mv_{b_i} =
std(m_{b_i-2},m_{b_i-1},m_{b_i},m_{b_i+1},m_{b_i+2}) +
std(sd_{b_i-2},sd_{b_i-1},sd_{b_i},sd_{b_i+1},sd_{b_i+2})$, with
$std(\cdot)$ denoting the standard deviation. The $M_{opt} =
\lfloor T/b_{opt}\rfloor$ sub-sample test statistics can then be
used in conjunction with any of the Bonferroni type procedures.

{\tt MATLAB} code that implements the described test procedures is
available from the authors upon request.

        \begin{table}[htp]
        \renewcommand{\arraystretch}{1.15}
        \begin{center}
            %\caption{
            \begin{tabular}{ccc|ccc|ccc}
            \multicolumn{9}{c}{\textbf{Table B1:}
            Critical values $c_{\frac{\alpha}{M}}$ from}\\
            \multicolumn{9}{c}{$\mP\left[\int_0^1 W(r)^2dr \ge c_{\frac{\alpha}{M}} \right]=\frac{\alpha}{M}$ for $\alpha = 5\%$ and $10\%$} \\%\vspace{0.05in}
            \multicolumn{9}{c}{} \\
            \hline\hline
            M & 5\% & 10\% & M & 5\% & 10\% & M & 5\% & 10\% \\
            \hline
            \multicolumn{9}{c}{Sum in~(27) truncated at 30}\\
            \hline
             2 &      2.135 &      1.656 &     15 &      3.588 &      3.076 &     28 &      4.034 &     3.538 \\
             3 &      2.421 &      1.934 &     16 &      3.635 &      3.121 &     29 &      4.058 &     3.563 \\
             4 &      2.627 &      2.135 &     17 &      3.680 &      3.164 &     30 &      4.081 &     3.588 \\
             5 &      2.787 &      2.292 &     18 &      3.721 &      3.203 &     31 &      4.103 &     3.612 \\
             6 &      2.917 &      2.421 &     19 &      3.760 &      3.241 &     32 &      4.124 &     3.635 \\
             7 &      3.027 &      2.531 &     20 &      3.797 &      3.276 &     33 &      4.145 &     3.658 \\
             8 &      3.121 &      2.627 &     21 &      3.832 &      3.309 &     34 &      4.165 &     3.680 \\
             9 &      3.203 &      2.711 &     22 &      3.865 &      3.340 &     35 &      4.184 &     3.700 \\
            10 &      3.276 &      2.787 &     23 &      3.897 &      3.370 &     36 &      4.202 &     3.721 \\
            11 &      3.340 &      2.855 &     24 &      3.927 &      3.398 &     37 &      4.220 &     3.741 \\
            12 &      3.398 &      2.917 &     25 &      3.955 &      3.424 &     38 &      4.237 &     3.760 \\
            13 &      3.484 &      2.974 &     26 &      3.983 &      3.484 &     39 &      4.253 &     3.779 \\
            14 &      3.538 &      3.027 &     27 &      4.009 &      3.511 &     40 &      4.269 &     3.797 \\
            \hline
            \multicolumn{9}{c}{Sum in~(27) truncated at 10}\\
            \hline
             2 &      2.135 &      1.656 &     15 &      3.582 &      3.081 &     28 &      3.997 &     3.533 \\
             3 &      2.421 &      1.934 &     16 &      3.627 &      3.128 &     29 &      4.018 &     3.558 \\
             4 &      2.626 &      2.135 &     17 &      3.669 &      3.172 &     30 &      4.038 &     3.582 \\
             5 &      2.785 &      2.292 &     18 &      3.709 &      3.214 &     31 &      4.058 &     3.605 \\
             6 &      2.912 &      2.421 &     19 &      3.746 &      3.253 &     32 &      4.076 &     3.627 \\
             7 &      3.031 &      2.531 &     20 &      3.781 &      3.291 &     33 &      4.094 &     3.649 \\
             8 &      3.128 &      2.626 &     21 &      3.813 &      3.326 &     34 &      4.111 &     3.669 \\
             9 &      3.214 &      2.710 &     22 &      3.844 &      3.360 &     35 &      4.127 &     3.689 \\
            10 &      3.291 &      2.785 &     23 &      3.873 &      3.392 &     36 &      4.143 &     3.709 \\
            11 &      3.360 &      2.852 &     24 &      3.900 &      3.422 &     37 &      4.158 &     3.728 \\
            12 &      3.422 &      2.912 &     25 &      3.926 &      3.452 &     38 &      4.172 &     3.746 \\
            13 &      3.480 &      2.977 &     26 &      3.951 &      3.480 &     39 &      4.186 &     3.763 \\
            14 &      3.533 &      3.031 &     27 &      3.974 &      3.507 &     40 &      4.199 &     3.781 \\
            \hline\hline
            \end{tabular}
            \\
            %\begin{flushleft}
            \begin{footnotesize}Note: Number~(27) refers to equation~(27) in the underlying article. \end{footnotesize}
            %\end{flushleft}
        \end{center}
        \end{table}


\newpage

\section*{Online Appendix C: Additional Simulation Results}

As mentioned in the main text, in addition to the bandwidth rules
of \citeasnoun{An91} and the simplified version of
\citeasnoun{NeWe94} we also use the bandwidths $T^{1/5}, T^{1/4},
T^{1/3}$. These are considered because of the results of
\citeasnoun[Theorems~4 and~5]{HoPh10} that show -- for the special
case of the RESET test considered in that paper -- that the
convergence behavior under the null and the divergence behavior
under the alternative depend upon the ratio of the bandwidth to
the sample size. In particular they show that in their setup
smaller bandwidths lead to slower convergence of their test
statistic under the null but to faster divergence (i.e., higher
rejection probabilities) under their alternative. In their
simulations, they, however, find only small effects of the
bandwidth to sample size ratio. To assess whether the situation is
similar in our setting, we include these bandwidths also in our
simulations. The main findings in relation to the additional
bandwidths $T^{1/5}, T^{1/4}, T^{1/3}$ are:
%
\begin{itemize}

\item The additional bandwidth choices do not have large or
systematic effects on the coefficient estimators (see Tables~C1 to
C3).

\item The null rejection probabilities are to a certain extent
influenced by bandwidth choice (see Table~C4). But also here the
effects are small and can go either way, depending upon sample
size, kernel and $\rho_1,\rho_2$ as well as null hypothesis
considered.

\item With the minimal effects on null rejection probabilities, it
is clear that size-corrected power is not strongly affected by the
bandwidth choice from the considered set. Figures~C4 to~C6 show
that there is hardly any effect at all.

\end{itemize}


Compared to the main text we include here in addition the $t$-test
results for $H_0:\beta_2 = -0.3$, i.e., we also consider the
coefficient to the square of the integrated variable $x_t^2$. Here
the findings are as expected, given the faster convergence rate of
$\hat\beta_2^+$ than of $\hat\beta_1^+$. First, over-rejections
under the null are smaller than for the other hypotheses
considered. Second, power increases faster in the difference
between null and alternative coefficient value than for the other
hypotheses.




\clearpage



% TAble bias beta 1:
\begin{center}
\begin{scriptsize}
\begin{tabular}
[c]{ccccccccccccc}%
\multicolumn{13}{c}{\textbf{Table C1:} Bias for coefficients
$\beta_{1}$ and $\beta_{2}$}\\\hline
&  &    &  &  &  &  &  &  &  &  &  & \\
\multicolumn{13}{c}{Panel A: Bias for coefficient $\beta_1$}\\
\multicolumn{13}{c}{$T=100$}\\\hline
 & & \multicolumn{5}{c}{Bartlett Kernel} &  & \multicolumn{5}{c}{QS
Kernel}\\\cline{3-7}\cline{9-13}%
$\rho_{1},\rho_{2}$ & OLS & $T^{1/5}$ & $T^{1/4}$ & $T^{1/3}$ &
AND & NW & & $T^{1/5}$ & $T^{1/4}$ & $T^{1/3}$ & AND & NW \\\hline
 0.0 & -.0013 & -.0019 & -.0019 & -.0018 & -.0019 & -.0018    &   & -.0019 & -.0018 & -.0018 & -.0019 & -.0018 \\
 0.3 &  .0167 & -.0034 & -.0039 & -.0049 & -.0050 & -.0044    &   & -.0042 & -.0047 & -.0060 & -.0057 & -.0054 \\
 0.6 &  .0743 &  .0399 &  .0409 &  .0419 &  .0404 &  .0418    &   &  .0410 &  .0425 &  .0433 &  .0411 &  .0433 \\
 0.8 &  .1952 &  .1567 &  .1597 &  .1655 &  .1657 &  .1633    &   &  .1595 &  .1639 &  .1710 &  .1655 &  .1685 \\
\hline
%&  &    &  &  &  &  &  &  &  &  &  & \\
\multicolumn{13}{c}{$T=200$}\\\hline
 & & \multicolumn{5}{c}{Bartlett Kernel} &  & \multicolumn{5}{c}{QS
Kernel}\\\cline{3-7}\cline{9-13}%
$\rho_{1},\rho_{2}$ & OLS & $T^{1/5}$ & $T^{1/4}$ & $T^{1/3}$ &
AND & NW & & $T^{1/5}$ & $T^{1/4}$ & $T^{1/3}$ & AND & NW \\\hline

 0.0 & -.0003 & -.0005 & -.0005 & -.0006 & -.0005 & -.0005 &      & -.0005 & -.0005 & -.0006 & -.0006 & -.0005 \\
 0.3 &  .0087 & -.0012 & -.0014 & -.0018 & -.0019 & -.0014 &      & -.0015 & -.0016 & -.0022 & -.0020 & -.0017 \\
 0.6 &  .0396 &  .0228 &  .0239 &  .0252 &  .0250 &  .0241 &      &  .0240 &  .0253 &  .0265 &  .0261 &  .0256 \\
 0.8 &  .1117 &  .0933 &  .0967 &  .1027 &  .1070 &  .0974 &      &  .0963 &  .1006 &  .1078 &  .1100 &  .1017 \\

\hline\hline
&  &    &  &  &  &  &  &  &  &  &  & \\
\multicolumn{13}{c}{Panel B: Bias ($\times 1000$) for coefficient $\beta_{2}$}\\
%\multicolumn{13}{c}{Data Dependent Bandwidths and Lag Lengths}\\\hline\hline
\multicolumn{13}{c}{$T=100$}\\\hline
 & & \multicolumn{5}{c}{Bartlett Kernel} &  & \multicolumn{5}{c}{QS
Kernel}\\\cline{3-7}\cline{9-13}%
$\rho_{1},\rho_{2}$ & OLS & $T^{1/5}$ & $T^{1/4}$ & $T^{1/3}$ &
AND & NW & & $T^{1/5}$ & $T^{1/4}$ & $T^{1/3}$ & AND & NW \\\hline
 0.0 & .0841 & .0895 & .0877 & .0841 & .0852 & .0860 & & .0878 & .0842 & .0810 & .0825 & .0832 \\
 0.3 & .0868 & .1162 & .1132 & .1057 & .1067 & .1096 & & .1140 & .1086 & .0996 & .1049 & .1046 \\
 0.6 & .0970 & .1611 & .1604 & .1545 & .1425 & .1583 & & .1616 & .1600 & .1505 & .1311 & .1571 \\
 0.8 & .1576 & .2340 & .2371 & .2399 & .2197 & .2400 & & .2369 & .2421 & .2433 & .2031 & .2459 \\
 \hline
%  &  &  &  &  &  &  &  &  &  &  &  & \\
\multicolumn{13}{c}{$T=200$}\\\hline
 & & \multicolumn{5}{c}{Bartlett Kernel} &  & \multicolumn{5}{c}{QS
Kernel}\\\cline{3-7}\cline{9-13}%
$\rho_{1},\rho_{2}$ & OLS & $T^{1/5}$ & $T^{1/4}$ & $T^{1/3}$ &
AND & NW & & $T^{1/5}$ & $T^{1/4}$ & $T^{1/3}$ & AND & NW \\\hline

 0.0 & -.0021 & -.0017 & -.0018 & -.0007 & -.0005 & -.0018 & &-.0023 & -.0023 & .0005 & -.0015 & -.0023 \\
 0.3 &  .0042 & -.0000 & -.0003 &  .0008 &  .0014 & -.0003 & &-.0009 & -.0013 & .0023 & -.0002 & -.0015 \\
 0.6 &  .0354 &  .0245 &  .0229 &  .0220 &  .0271 &  .0226 & & .0224 &  .0202 & .0219 &  .0255 &  .0197 \\
 0.8 &  .1356 &  .1213 &  .1173 &  .1112 &  .1150 &  .1165 & & .1176 &  .1122 & .1066 &  .1164 &  .1108 \\

\hline
\end{tabular}% Table bias beta 2:
\end{scriptsize}
\end{center}

% Table for RMSE Beta 1:
\begin{center}
\begin{scriptsize}
\begin{tabular}
[c]{ccccccccccccc}%
\multicolumn{13}{c}{\textbf{Table C2:} RMSE for coefficients
$\beta_{1}$ and $\beta_2$}\\\hline
&  &  &  &  &  &  &  &  &  &  &  & \\
\multicolumn{13}{c}{Panel A: RMSE for coefficient $\beta_1$}\\
\multicolumn{13}{c}{$T=100$}\\\hline
 & & \multicolumn{5}{c}{Bartlett Kernel} &  & \multicolumn{5}{c}{QS
Kernel}\\\cline{3-7}\cline{9-13}%
$\rho_{1},\rho_{2}$ & OLS & $T^{1/5}$ & $T^{1/4}$ & $T^{1/3}$ &
AND & NW & & $T^{1/5}$ & $T^{1/4}$ & $T^{1/3}$ & AND & NW \\\hline

 0.0 & .0670 & .0717 & .0721 & .0728 & .0727 & .0725 & & .0723 & .0729 & .0738 & .0736 & .0735 \\
 0.3 & .0938 & .0962 & .0967 & .0977 & .0977 & .0973 & & .0967 & .0975 & .0991 & .0987 & .0985 \\
 0.6 & .1725 & .1570 & .1572 & .1580 & .1589 & .1577 & & .1572 & .1579 & .1593 & .1606 & .1588 \\
 0.8 & .3285 & .3008 & .3016 & .3038 & .3063 & .3029 & & .3015 & .3032 & .3067 & .3093 & .3054 \\
\hline
%&  &  &  &  &  &  &  &  &  &  &  & \\
\multicolumn{13}{c}{$T=200$}\\\hline
 & & \multicolumn{5}{c}{Bartlett Kernel} &  & \multicolumn{5}{c}{QS
Kernel}\\\cline{3-7}\cline{9-13}%
$\rho_{1},\rho_{2}$ & OLS & $T^{1/5}$ & $T^{1/4}$ & $T^{1/3}$ &
AND & NW & & $T^{1/5}$ & $T^{1/4}$ & $T^{1/3}$ & AND & NW \\\hline

 0.0 & .0325 & .0336 & .0337 & .0339 & .0339 & .0337 & &.0337 & .0339 & .0341 & .0341 & .0339 \\
 0.3 & .0470 & .0464 & .0465 & .0468 & .0468 & .0465 & &.0465 & .0467 & .0471 & .0469 & .0468 \\
 0.6 & .0915 & .0812 & .0816 & .0821 & .0823 & .0817 & &.0816 & .0822 & .0829 & .0830 & .0823 \\
 0.8 & .1919 & .1752 & .1770 & .1806 & .1846 & .1775 & &.1769 & .1794 & .1842 & .1879 & .1801 \\
\hline\hline
&  &  &  &  &  &  &  &  &  &  &  & \\
\multicolumn{13}{c}{Panel B: RMSE for coefficient $\beta_{2}$}\\
%\multicolumn{13}{c}{Data Dependent Bandwidths and Lag Lengths}\\\hline\hline
\multicolumn{13}{c}{$T=100$}\\\hline
 & & \multicolumn{5}{c}{Bartlett Kernel} &  & \multicolumn{5}{c}{QS
Kernel}\\\cline{3-7}\cline{9-13}%
$\rho_{1},\rho_{2}$ & OLS & $T^{1/5}$ & $T^{1/4}$ & $T^{1/3}$ &
AND & NW & & $T^{1/5}$ & $T^{1/4}$ & $T^{1/3}$ & AND & NW \\\hline

 0.0 & .0056 & .0058 & .0058 & .0058 & .0058 & .0058 & &.0058 & .0058 & .0059 & .0059 & .0059 \\
 0.3 & .0075 & .0077 & .0077 & .0077 & .0077 & .0077 & &.0077 & .0077 & .0078 & .0078 & .0078 \\
 0.6 & .0119 & .0117 & .0117 & .0118 & .0119 & .0118 & &.0117 & .0118 & .0119 & .0120 & .0119 \\
 0.8 & .0192 & .0188 & .0188 & .0189 & .0193 & .0189 & &.0188 & .0189 & .0190 & .0197 & .0190 \\
\hline
%&  &  &  &  &  &  &  &  &  &  &  & \\
\multicolumn{13}{c}{$T=200$}\\\hline
 & & \multicolumn{5}{c}{Bartlett Kernel} &  & \multicolumn{5}{c}{QS
Kernel}\\\cline{3-7}\cline{9-13}%
$\rho_{1},\rho_{2}$ & OLS & $T^{1/5}$ & $T^{1/4}$ & $T^{1/3}$ &
AND & NW & & $T^{1/5}$ & $T^{1/4}$ & $T^{1/3}$ & AND & NW \\\hline

 0.0 & .0019 & .0019 & .0019 & .0019 & .0019 & .0019 & &.0019 & .0019 & .0019 & .0019 & .0019 \\
 0.3 & .0027 & .0027 & .0027 & .0027 & .0027 & .0027 & &.0027 & .0027 & .0027 & .0027 & .0027 \\
 0.6 & .0045 & .0043 & .0043 & .0043 & .0043 & .0043 & &.0043 & .0043 & .0043 & .0044 & .0043 \\
 0.8 & .0080 & .0077 & .0077 & .0078 & .0079 & .0077 & &.0077 & .0078 & .0078 & .0080 & .0078 \\

\hline
\end{tabular}% RMSE beta_2
\end{scriptsize}
\end{center}

% Table with bias and rmse for coefficient to trend:
\begin{center}
\begin{scriptsize}
\begin{tabular}
[c]{ccccccccccccc}%
\multicolumn{13}{c}{\textbf{Table C3:} Bias and RMSE for
coefficient $\delta$}\\\hline
&  &    &  &  &  &  &  &  &  &  &  & \\
\multicolumn{13}{c}{Panel A: Bias ($\times 1000$) for coefficient $\delta$}\\
\multicolumn{13}{c}{$T=100$}\\\hline
 & & \multicolumn{5}{c}{Bartlett Kernel} &  & \multicolumn{5}{c}{QS
Kernel}\\\cline{3-7}\cline{9-13}%
$\rho_{1},\rho_{2}$ & OLS & $T^{1/5}$ & $T^{1/4}$ & $T^{1/3}$ &
AND & NW & & $T^{1/5}$ & $T^{1/4}$ & $T^{1/3}$ & AND & NW \\\hline
 0.0  & -0.0220 & -0.0305 & -0.0337 & -0.0422 & -0.0443 & -0.0373 & &-0.0303 & -0.0390 & -0.0365 & -0.0398 & -0.0411 \\
 0.3  & -0.1559 & -0.0782 & -0.0818 & -0.0928 & -0.0942 & -0.0872 & &-0.0763 & -0.0878 & -0.0851 & -0.0878 & -0.0913 \\
 0.6  & -0.5040 & -0.3545 & -0.3636 & -0.3858 & -0.3984 & -0.3766 & &-0.3579 & -0.3797 & -0.3859 & -0.4121 & -0.3905 \\
 0.8  & -1.1533 & -0.9913 & -1.0030 & -1.0309 & -1.0289 & -1.0198 & &-0.9971 & -1.0246 & -1.0354 & -0.9970 & -1.0396 \\
\multicolumn{13}{c}{$T=200$}\\\hline
 & & \multicolumn{5}{c}{Bartlett Kernel} &  & \multicolumn{5}{c}{QS
Kernel}\\\cline{3-7}\cline{9-13}%
$\rho_{1},\rho_{2}$ & OLS & $T^{1/5}$ & $T^{1/4}$ & $T^{1/3}$ &
AND & NW & & $T^{1/5}$ & $T^{1/4}$ & $T^{1/3}$ & AND & NW \\\hline
 0.0 & -0.0344 & -0.0233 & -0.0220 & -0.0204 & -0.0187 & -0.0217 & &-0.0214 & -0.0208 & -0.0186 & -0.0176 & -0.0207 \\
 0.3 & -0.0635 & -0.0417 & -0.0393 & -0.0359 & -0.0335 & -0.0389 & &-0.0389 & -0.0373 & -0.0327 & -0.0318 & -0.0369 \\
 0.6 & -0.1542 & -0.1266 & -0.1249 & -0.1205 & -0.1130 & -0.1246 & &-0.1255 & -0.1246 & -0.1169 & -0.1153 & -0.1238 \\
 0.8 & -0.3683 & -0.3363 & -0.3352 & -0.3330 & -0.2998 & -0.3350 & &-0.3354 & -0.3355 & -0.3306 & -0.2866 & -0.3349 \\
\hline \hline
&  &    &  &  &  &  &  &  &  &  &  & \\
\multicolumn{13}{c}{Panel B: RMSE for coefficient $\delta$}\\
\multicolumn{13}{c}{$T=100$}\\\hline
 & & \multicolumn{5}{c}{Bartlett Kernel} &  & \multicolumn{5}{c}{QS
Kernel}\\\cline{3-7}\cline{9-13}%
$\rho_{1},\rho_{2}$ & OLS & $T^{1/5}$ & $T^{1/4}$ & $T^{1/3}$ &
AND & NW & & $T^{1/5}$ & $T^{1/4}$ & $T^{1/3}$ & AND & NW \\\hline
  0.0 & 0.0065 & 0.0067 & 0.0068 & 0.0069 & 0.0069 & 0.0069 & &0.0068 & 0.0069 & 0.0071 & 0.0071 & 0.0070 \\
  0.3 & 0.0097 & 0.0092 & 0.0093 & 0.0094 & 0.0095 & 0.0094 & &0.0093 & 0.0094 & 0.0097 & 0.0097 & 0.0096 \\
  0.6 & 0.0206 & 0.0167 & 0.0167 & 0.0167 & 0.0169 & 0.0167 & &0.0167 & 0.0167 & 0.0169 & 0.0171 & 0.0168 \\
  0.8 & 0.0438 & 0.0380 & 0.0381 & 0.0385 & 0.0389 & 0.0384 & &0.0381 & 0.0384 & 0.0390 & 0.0394 & 0.0387 \\
\multicolumn{13}{c}{$T=200$}\\\hline
 & & \multicolumn{5}{c}{Bartlett Kernel} &  & \multicolumn{5}{c}{QS
Kernel}\\\cline{3-7}\cline{9-13}%
$\rho_{1},\rho_{2}$ & OLS & $T^{1/5}$ & $T^{1/4}$ & $T^{1/3}$ &
AND & NW & & $T^{1/5}$ & $T^{1/4}$ & $T^{1/3}$ & AND & NW \\\hline
  0.0 & 0.0022 & 0.0023 & 0.0023 & 0.0023 & 0.0023 & 0.0023 & &0.0023 & 0.0023 & 0.0023 & 0.0023 & 0.0023 \\
  0.3 & 0.0034 & 0.0032 & 0.0032 & 0.0032 & 0.0032 & 0.0032 & &0.0032 & 0.0032 & 0.0033 & 0.0032 & 0.0032 \\
  0.6 & 0.0077 & 0.0062 & 0.0062 & 0.0063 & 0.0063 & 0.0062 & &0.0062 & 0.0063 & 0.0064 & 0.0064 & 0.0063 \\
  0.8 & 0.0179 & 0.0157 & 0.0159 & 0.0164 & 0.0168 & 0.0160 & &0.0159 & 0.0162 & 0.0169 & 0.0172 & 0.0163 \\
\hline
\end{tabular}% RMSE beta_2
\end{scriptsize}
\end{center}

\vspace{1cm}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%\begin{table}[ht]
\begin{center}
\begin{scriptsize}
\begin{tabular}{ccccccccccccccc}%
\multicolumn{15}{c}{{\bf Table C4:} Empirical Null Rejection
Probabilities,
0.05 Level}\\\hline%, $t$-tests for $H_0: \beta_{1} = 5$}\\
&  &  &  &  &  &  &  &  &  &  &  &  &  &   \\
\multicolumn{15}{c}{{Panel A}: $t$-tests for $H_0: \beta_{1} = 5$}\\
\multicolumn{15}{c}{$T=100$}\\\hline &  &
\multicolumn{6}{c}{Bartlett Kernel} &  & \multicolumn{6}{c}{QS
Kernel}\\\cline{3-8}\cline{10-15}%
$\rho_{1},\rho_{2}$ & OLS & HAC & $T^{1/5}$ & $T^{1/4}$ &
$T^{1/3}$ & AND & NW & & HAC & $T^{1/5}$ & $T^{1/4}$ & $T^{1/3}$ &
AND & NW \\\hline
  0.0 & .0594 & .1060 & .0754 & .0826 & .1020 & .1058 & .0932 & &.1222 & .0842 & .0972 & .1246 & .1234 & .1136 \\
  0.3 & .1542 & .1424 & .1128 & .1092 & .1138 & .1162 & .1092 & &.1462 & .1034 & .1038 & .1168 & .1164 & .1118 \\
  0.6 & .3706 & .2678 & .2146 & .1896 & .1662 & .1604 & .1716 & &.2498 & .1788 & .1604 & .1474 & .1488 & .1514 \\
  0.8 & .5876 & .4612 & .4270 & .3998 & .3622 & .3108 & .3774 & &.4286 & .3940 & .3680 & .3282 & .2984 & .3408 \\
\hline
%&  &  &  &  &  &  &  &  &  &  &  &  &  &   \\
\multicolumn{15}{c}{$T=200$}\\\hline
 & & \multicolumn{6}{c}{Bartlett Kernel} &  & \multicolumn{6}{c}{QS
Kernel}\\\cline{3-8}\cline{10-15}%
$\rho_{1},\rho_{2}$ & OLS & HAC & $T^{1/5}$ & $T^{1/4}$ &
$T^{1/3}$ & AND & NW & & HAC & $T^{1/5}$ & $T^{1/4}$ & $T^{1/3}$ &
AND & NW \\\hline
  0.0 & .0478 & .0784 & .0588 & .0634 & .0722 & .0738 & .0650 & &.0890 & .0658 & .0714 & .0862 & .0784 & .0726 \\
  0.3 & .1472 & .1100 & .0932 & .0874 & .0872 & .0878 & .0866 & &.1058 & .0818 & .0796 & .0844 & .0802 & .0790 \\
  0.6 & .3736 & .2306 & .1930 & .1710 & .1458 & .1350 & .1660 & &.2010 & .1638 & .1446 & .1278 & .1242 & .1406 \\
  0.8 & .6154 & .4410 & .4228 & .3906 & .3412 & .2930 & .3820 & &.3968 & .3880 & .3538 & .3150 & .2846 & .3446 \\
\hline\hline
&  &  &  &  &  &  &  &  &  &  &  &  &  &   \\
\multicolumn{15}{c}{{Panel B}: $t$-tests for $H_0: \beta_{2} = -0.3$}\\
%\multicolumn{13}{c}{Data Dependent Bandwidths and Lag Lengths}\\\hline\hline
\multicolumn{15}{c}{$T=100$}\\\hline & &
\multicolumn{6}{c}{Bartlett Kernel} &  & \multicolumn{6}{c}{QS
Kernel}\\\cline{3-8}\cline{10-15}%
$\rho_{1},\rho_{2}$ & OLS & HAC & $T^{1/5}$ & $T^{1/4}$ &
$T^{1/3}$ & AND & NW & & HAC & $T^{1/5}$ & $T^{1/4}$ & $T^{1/3}$ &
AND & NW \\\hline
 0.0 & .0570 & .1030 & .0686 & .0736 & .0874 & .0926 & .0822 & &.1188 & .0764 & .0848 & .1060 & .1056 & .0964 \\
 0.3 & .1424 & .1360 & .1102 & .1052 & .1070 & .1088 & .1048 & &.1352 & .1006 & .0988 & .1056 & .1064 & .1036 \\
 0.6 & .2776 & .1956 & .1772 & .1590 & .1384 & .1340 & .1466 & &.1800 & .1498 & .1314 & .1182 & .1216 & .1210 \\
 0.8 & .4202 & .2784 & .2696 & .2378 & .1970 & .1626 & .2116 & &.2462 & .2306 & .2022 & .1640 & .1552 & .1770 \\
\hline
%\hline
%&  &  &  &  &  &  &  &  &  &  &  &  &  &  \\
\multicolumn{15}{c}{$T=200$}\\\hline & &
\multicolumn{6}{c}{Bartlett Kernel} &  & \multicolumn{6}{c}{QS
Kernel}\\\cline{3-8}\cline{10-15}%
$\rho_{1},\rho_{2}$ & OLS & HAC & $T^{1/5}$ & $T^{1/4}$ &
$T^{1/3}$ & AND & NW & & HAC & $T^{1/5}$ & $T^{1/4}$ & $T^{1/3}$ &
AND & NW \\\hline
 0.0 & .0528 & .0748 & .0616 & .0674 & .0758 & .0764 & .0684 & &.0846 & .0668 & .0712 & .0846 & .0810 & .0728 \\
 0.3 & .1368 & .1000 & .0916 & .0882 & .0870 & .0872 & .0876 & &.0962 & .0822 & .0798 & .0808 & .0798 & .0796 \\
 0.6 & .2678 & .1466 & .1558 & .1364 & .1118 & .1042 & .1326 & &.1242 & .1296 & .1112 & .0952 & .0938 & .1082 \\
 0.8 & .4368 & .2438 & .2596 & .2196 & .1726 & .1320 & .2128 & &.2056 & .2170 & .1844 & .1460 & .1264 & .1790 \\
\hline\hline
&  &  &  &  &  &  &  &  &  &  &  &  &  &   \\
\multicolumn{15}{c}{{Panel C}: Wald tests for $H_0: \beta_1 = 5, \beta_{2} = -0.3$}\\
%\multicolumn{13}{c}{Data Dependent Bandwidths and Lag Lengths}\\\hline\hline
\multicolumn{15}{c}{$T=100$}\\\hline & &
\multicolumn{6}{c}{Bartlett Kernel} &  & \multicolumn{6}{c}{QS
Kernel}\\\cline{3-8}\cline{10-15}%
$\rho_{1},\rho_{2}$ & OLS & HAC & $T^{1/5}$ & $T^{1/4}$ &
$T^{1/3}$ & AND & NW & & HAC & $T^{1/5}$ & $T^{1/4}$ & $T^{1/3}$ &
AND & NW \\\hline
 0.0 & .0568 & .1348 & .0832 & .0946 & .1184 & .1238 & .1092 & &.1706 & .0972 & .1146 & .1478 & .1466 & .1352 \\
 0.3 & .2002 & .1958 & .1410 & .1382 & .1442 & .1470 & .1402 & &.2032 & .1260 & .1294 & .1476 & .1470 & .1372 \\
 0.6 & .5258 & .3878 & .3018 & .2714 & .2364 & .2226 & .2472 & &.3550 & .2556 & .2266 & .2038 & .2070 & .2120 \\
 0.8 & .8124 & .6652 & .6356 & .5982 & .5462 & .4800 & .5650 & &.6250 & .5894 & .5486 & .4978 & .4654 & .5188 \\
\hline
%&  &  &  &  &  &  &  &  &  &  &  &  &  &  \\
\multicolumn{15}{c}{$T=200$}\\\hline & &
\multicolumn{6}{c}{Bartlett Kernel} &  & \multicolumn{6}{c}{QS
Kernel}\\\cline{3-8}\cline{10-15}%
$\rho_{1},\rho_{2}$ & OLS & HAC & $T^{1/5}$ & $T^{1/4}$ &
$T^{1/3}$ & AND & NW & & HAC & $T^{1/5}$ & $T^{1/4}$ & $T^{1/3}$ &
AND & NW \\\hline
 0.0 & .0532 & .0910 & .0652 & .0726 & .0866 & .0880 & .0740 & &.1118 & .0746 & .0802 & .1044 & .0960 & .0830 \\
 0.3 & .1924 & .1426 & .1104 & .1040 & .1020 & .1034 & .1038 & &.1384 & .0968 & .0932 & .1022 & .0956 & .0922 \\
 0.6 & .5290 & .3140 & .2668 & .2318 & .1990 & .1870 & .2258 & &.2720 & .2216 & .1952 & .1718 & .1698 & .1898 \\
 0.8 & .8254 & .6228 & .6228 & .5826 & .5316 & .4602 & .5758 & &.5638 & .5782 & .5392 & .4996 & .4514 & .5348 \\
\hline
\end{tabular} % Size Wald:
\end{scriptsize}
\end{center}
%\end{table}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\begin{table}[!ht]
\begin{scriptsize}
\begin{center}
\begin{tabular}{lccccccccccccc}
\multicolumn{14}{c}{{\bf Table C5:} Raw Power of Specification
Tests,
0.05 Level, Bartlett Kernel, Newey-West}\\\hline%, $t$-tests for $H_0: \beta_{1} = 5$}\\\hline
&  &  &  &  & & &  & & & & &  \\
%\hline
 & &  \multicolumn{4}{c}{Wald}  & & \multicolumn{4}{c}{LM } & & CT & CS \\
 \cline{3-6}  \cline{8-11} \cline{13-14}
& $\rho_1,\rho_2$ & I & II & III & IV & & I & II & III & IV  & &  &  \\
\hline
\multicolumn{14}{c}{Panel A: T = 100} \\
\hline
(A) & 0.0 &  0.5048 & 0.9704 & 0.9704 & 0.3600 & & 0.3456 & 0.9590 & 0.9526 & 0.2658 & & 0.4114 & 0.0296 \\
    & 0.3 &  0.4938 & 0.9522 & 0.9502 & 0.3574 & & 0.3380 & 0.9366 & 0.9240 & 0.2608 & & 0.4044 & 0.0322 \\
    & 0.6 &  0.5258 & 0.9206 & 0.9286 & 0.3844 & & 0.3460 & 0.8860 & 0.8696 & 0.2634 & & 0.4616 & 0.0380 \\
    & 0.8 &  0.6428 & 0.8856 & 0.9268 & 0.4424 & & 0.4282 & 0.8124 & 0.8236 & 0.3034 & & 0.6262 & 0.0638 \\
(B)  & -- &  0.8128 & 0.4844 & 0.8446 & 0.5498 & & 0.7122 & 0.3536 & 0.6580 & 0.4412 & & 0.8424 & 0.1958 \\
(C)  & -- &  0.8024 & 0.4622 & 0.8232 & 0.5524 & & 0.7012 & 0.3306 & 0.6314 & 0.4374 & & 0.8422 & 0.2000 \\
\hline
\multicolumn{14}{c}{Panel B: T = 200} \\
\hline
(A) & 0.0 & 0.6314 & 1.0000 & 1.0000 & 0.4880 & & 0.5418 & 1.0000 & 0.9996 & 0.4200 & & 0.7170 & 0.2326 \\
    & 0.3 & 0.6258 & 0.9996 & 0.9992 & 0.4886 & & 0.5364 & 0.9992 & 0.9992 & 0.4178 & & 0.7110 & 0.2334 \\
    & 0.6 & 0.6408 & 0.9988 & 0.9980 & 0.4918 & & 0.5370 & 0.9968 & 0.9970 & 0.4182 & & 0.7240 & 0.2334 \\
    & 0.8 & 0.6936 & 0.9940 & 0.9952 & 0.5316 & & 0.5838 & 0.9882 & 0.9890 & 0.4384 & & 0.8056 & 0.2738 \\
(B)  & -- & 0.8728 & 0.6398 & 0.9076 & 0.6998 & & 0.8456 & 0.5782 & 0.8640 & 0.6542 & & 0.9706 & 0.7008 \\
(C)  & -- & 0.8766 & 0.6342 & 0.9086 & 0.7052 & & 0.8472 & 0.5610 & 0.8608 & 0.6526 & & 0.9760 & 0.6860 \\
\hline
\end{tabular}
%\caption{Raw Power Specification Tests}
\end{center}
\end{scriptsize}
\end{table}



% Null rejection probabilities: ANDREWS BANDWIDTH:
\begin{table}[!ht]
\begin{scriptsize}
\begin{center}
\begin{tabular}{lccccccccccccc}
\multicolumn{14}{c}{{\bf Table C6:} Empirical Null Rejection
Probabilities of Specification Tests,
0.05 Level,} \\
\multicolumn{14}{c}{Bartlett Kernel, Andrews}\\\hline%, $t$-tests for $H_0: \beta_{1} = 5$}\\\hline
&  &  &  &  & & &  & & & & &  \\
%\hline
 & &  \multicolumn{4}{c}{Wald}  & & \multicolumn{4}{c}{LM } & & CT & CS \\
 \cline{3-6}  \cline{8-11} \cline{13-14}
& $\rho_1,\rho_2$ & I & II & III & IV & & I & II & III & IV  & &  &  \\
\hline
\multicolumn{14}{c}{Panel A: T = 100} \\
\hline
(28) & 0.0 & 0.1492 & 0.2188 & 0.2340 & 0.2150 & & 0.0430 & 0.1296 & 0.0650 & 0.1400 & & 0.0658 & 0.0002 \\
     & 0.3 & 0.1880 & 0.2356 & 0.2624 & 0.2306 & & 0.0580 & 0.1364 & 0.0600 & 0.1488 & & 0.0906 & 0.0024 \\
     & 0.6 & 0.2940 & 0.2716 & 0.3478 & 0.2836 & & 0.0786 & 0.1540 & 0.0446 & 0.1860 & & 0.1462 & 0.0032 \\
     & 0.8 & 0.4984 & 0.3464 & 0.5520 & 0.3796 & & 0.0958 & 0.2202 & 0.0418 & 0.2640 & & 0.2608 & 0.0042 \\
\hline
\multicolumn{14}{c}{Panel B: T = 200} \\
\hline
(28) & 0.0 & 0.1054 & 0.1470 & 0.1500 & 0.1434 & & 0.0440 & 0.0934 & 0.0570 & 0.0990 & & 0.0594 & 0.0012 \\
     & 0.3 & 0.1320 & 0.1634 & 0.1718 & 0.1568 & & 0.0600 & 0.0992 & 0.0640 & 0.1108 & & 0.0790 & 0.0050 \\
     & 0.6 & 0.2216 & 0.2024 & 0.2748 & 0.2112 & & 0.0660 & 0.1160 & 0.0544 & 0.1346 & & 0.1282 & 0.0074 \\
     & 0.8 & 0.4270 & 0.2784 & 0.4678 & 0.2966 & & 0.0638 & 0.1506 & 0.0370 & 0.1940 & & 0.2578 & 0.0072 \\
\hline
\end{tabular}
%\caption{Null Rejections Specification Tests}
%\begin{flushleft}
\begin{footnotesize}Note: Number~(28) refers to equation~(28) in the underlying article. \end{footnotesize}
%\end{flushleft}
\end{center}
\end{scriptsize}
\end{table}


\begin{table}[!ht]
\begin{scriptsize}
\begin{center}
\begin{tabular}{lccccccccccccc}
\multicolumn{14}{c}{{\bf Table C7:} Size Corrected Power of
Specification Tests,
0.05 Level, Bartlett Kernel, Andrews}\\\hline%, $t$-tests for $H_0: \beta_{1} = 5$}\\\hline
&  &  &  &  & & &  & & & & &  \\
%\hline
 & &  \multicolumn{4}{c}{Wald}  & & \multicolumn{4}{c}{LM } & & CT & CS \\
 \cline{3-6}  \cline{8-11} \cline{13-14}
& $\rho_1,\rho_2$ & I & II & III & IV & & I & II & III & IV  & &  &  \\
\hline
\multicolumn{14}{c}{Panel A: T = 100} \\
\hline                                                                                           % Raw Power
 (A)& 0.0 & 0.3234 & 0.9364 & 0.9372 & 0.1548 & & 0.2530 & 0.9288 & 0.9326 & 0.1592 & & 0.1898 & 0.1338 \\
    & 0.3 & 0.2792 & 0.8972 & 0.8904 & 0.1422 & & 0.2018 & 0.8842 & 0.9018 & 0.1610 & & 0.1128 & 0.0840 \\
    & 0.6 & 0.1940 & 0.8120 & 0.7880 & 0.1064 & & 0.1508 & 0.7398 & 0.8238 & 0.1350 & & 0.0722 & 0.0576 \\
    & 0.8 & 0.1032 & 0.6642 & 0.5914 & 0.0668 & & 0.1236 & 0.4016 & 0.6782 & 0.0878 & & 0.0580 & 0.0548 \\
(B) & -- &  0.6486 & 0.2030 & 0.6272 & 0.2832 & & 0.3040 & 0.2528 & 0.1132 & 0.3004 & & 0.4402 & 0.2288 \\%0.1958 \\
(C) & -- &  0.6344 & 0.1764 & 0.5986 & 0.2694 & & 0.2856 & 0.2370 & 0.1014 & 0.2784 & & 0.4260 & 0.2236 \\%0.2000 \\
\hline
\multicolumn{14}{c}{Panel B: T = 200} \\
\hline
(A) & 0.0 & 0.4344 & 0.9998 & 0.9996 & 0.2332 & & 0.2570 & 0.9962 & 0.9902 & 0.2262 & & 0.2260 & 0.1266 \\
    & 0.3 & 0.3952 & 0.9982 & 0.9982 & 0.2188 & & 0.2180 & 0.9944 & 0.9872 & 0.2248 & & 0.1666 & 0.1042 \\
    & 0.6 & 0.3056 & 0.9892 & 0.9876 & 0.1718 & & 0.1950 & 0.9806 & 0.9822 & 0.1834 & & 0.0938 & 0.0772 \\
    & 0.8 & 0.1748 & 0.9492 & 0.9262 & 0.1102 & & 0.1884 & 0.8930 & 0.9584 & 0.1338 & & 0.0636 & 0.0700 \\
(B) & -- &  0.6990 & 0.2350 & 0.6846 & 0.3252 & & 0.2982 & 0.2748 & 0.1158 & 0.3468 & & 0.4580 & 0.2056 \\%0.7008  \\
(C) & -- &  0.6890 & 0.2242 & 0.6678 & 0.3066 & & 0.2828 & 0.2634 & 0.1022 & 0.3358 & & 0.4336 & 0.1786 \\%0.6860  \\
\hline
\end{tabular}
%\caption{Size Corrected Power Specification Tests: Attn-CS is not size correction!}
\end{center}
%{\small [\,Note] For the CS test procedure we report raw power, since it is not possible to perform size correction in conjunction
%with the Bonferroni inequality. A table with raw power for all of the considered tests is available in the supplementary material.}
\end{scriptsize}
\end{table}


\begin{table}[!ht]
\begin{scriptsize}
\begin{center}
\begin{tabular}{lccccccccccccc}
\multicolumn{14}{c}{{\bf Table C8:} Raw Power of Specification
Tests,
0.05 Level, Bartlett Kernel, Andrews}\\\hline%, $t$-tests for $H_0: \beta_{1} = 5$}\\\hline
&  &  &  &  & & &  & & & & &  \\
%\hline
 & &  \multicolumn{4}{c}{Wald}  & & \multicolumn{4}{c}{LM } & & CT & CS \\
 \cline{3-6}  \cline{8-11} \cline{13-14}
& $\rho_1,\rho_2$ & I & II & III & IV & & I & II & III & IV  & &  &  \\
\hline
\multicolumn{14}{c}{Panel A: T = 100} \\
\hline
(A) & 0.0 &  0.4866 & 0.9722 & 0.9706 & 0.3464 & & 0.2362 & 0.9586 & 0.9434 & 0.2748 & & 0.2362 & 0.0112 \\
    & 0.3 &  0.4764 & 0.9518 & 0.9502 & 0.3516 & & 0.2208 & 0.9362 & 0.9114 & 0.2812 & & 0.2214 & 0.0102 \\
    & 0.6 &  0.5058 & 0.9166 & 0.9230 & 0.3780 & & 0.1878 & 0.8718 & 0.8156 & 0.2928 & & 0.2504 & 0.0104 \\
    & 0.8 &  0.5960 & 0.8676 & 0.9042 & 0.4218 & & 0.1766 & 0.7744 & 0.6584 & 0.3330 & & 0.3214 & 0.0130 \\
(B)  & -- &  0.7718 & 0.4202 & 0.7998 & 0.4838 & & 0.2790 & 0.3486 & 0.1502 & 0.4240 & & 0.5066 & 0.0242 \\
(C)  & -- &  0.7592 & 0.3876 & 0.7760 & 0.4696 & & 0.2540 & 0.3318 & 0.1318 & 0.4026 & & 0.4870 & 0.0186 \\
\hline
\multicolumn{14}{c}{Panel B: T = 200} \\
\hline
(A) & 0.0 & 0.5368 & 1.0000 & 1.0000 & 0.3574 & & 0.2452 & 0.9996 & 0.9918 & 0.2948 & & 0.2790 & 0.0256 \\
    & 0.3 & 0.5286 & 0.9996 & 0.9992 & 0.3626 & & 0.2384 & 0.9990 & 0.9900 & 0.2942 & & 0.2702 & 0.0256 \\
    & 0.6 & 0.5418 & 0.9976 & 0.9974 & 0.3682 & & 0.2200 & 0.9946 & 0.9830 & 0.3032 & & 0.2814 & 0.0264 \\
    & 0.8 & 0.5812 & 0.9878 & 0.9892 & 0.3844 & & 0.2082 & 0.9714 & 0.9502 & 0.3154 & & 0.3232 & 0.0280 \\
(B)  & -- & 0.7668 & 0.3720 & 0.7878 & 0.4614 & & 0.2802 & 0.3402 & 0.1320 & 0.4292 & & 0.5158 & 0.0378 \\
(C)  & -- & 0.7542 & 0.3594 & 0.7720 & 0.4414 & & 0.2634 & 0.3272 & 0.1162 & 0.4122 & & 0.4978 & 0.0334 \\
\hline
\end{tabular}
%\caption{Raw Power Specification Tests}
\end{center}
\end{scriptsize}
\end{table}



\clearpage


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% New figure orientation:
\begin{center}
\begin{figure}
\begin{center}
\includegraphics[
natheight=9.375400in, natwidth=12.500000in, height=3.0907in,
width=4.779in]{CorrPower_beta1_T_100_ba_rho1_6_rho2_6.jpg}
%\caption{
\\
Figure C1: Size Corrected Power, $t$-test for $\beta_1$, $T=100$,
$\rho_{1}=\rho _{2}=0.6$, Bartlett Kernel
%\end{center}
%\end{figure}
%\end{center}
%
%\nopagebreak
%
%\begin{center}
%\begin{figure}
%\begin{center}

\vspace{2cm}

\includegraphics[
natheight=9.375400in, natwidth=12.500000in, height=3.0907in,
width=4.779in]{CorrPower_beta2_T_100_ba_rho1_8_rho2_8.jpg}
%\caption{
\\
Figure C2: Size Corrected Power, $t$-test for $\beta_2$, $T=100$,
$\rho_{1}=\rho _{2}=0.8$, Bartlett Kernel
\end{center}
\end{figure}
\end{center}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{center}
\begin{figure}
\begin{center}
\includegraphics[
natheight=9.375400in, natwidth=12.500000in, height=3.0907in,
width=4.779in]{CorrPower_Wald_T_100_ba_rho1_8_rho2_8.jpg}
%\caption{
\\
Figure C3: Size Corrected Power, Wald test, $T=100$,
$\rho_{1}=\rho_{2}=0.8$, Bartlett Kernel%\end{center}
%\end{figure}
%\end{center}
%
%\nopagebreak
%
%\begin{center}
%\begin{figure}
%\begin{center}

\vspace{2cm}

% New figure orientation:
\includegraphics[
natheight=9.375400in, natwidth=12.500000in, height=3.0907in,
width=4.779in]{FMBAND_CorrPower_beta1_T_100_ba_rho1_6_rho2_6.jpg}
%\caption{
\\
Figure C4: Size Corrected Power, $t$-test for $\beta_1$, $T=100$,
$\rho_{1}=\rho _{2}=0.6$, Bartlett Kernel
\end{center}
\end{figure}
\end{center}
%
%\nopagebreak
%
\begin{center}
\begin{figure}
\begin{center}

%\vspace{2cm}

\includegraphics[
natheight=9.375400in, natwidth=12.500000in, height=3.0907in,
width=4.779in]{FMBAND_CorrPower_beta2_T_100_ba_rho1_8_rho2_8.jpg}
%\caption{
\\
Figure C5: Size Corrected Power, $t$-test for $\beta_2$, $T=100$,
$\rho_{1}=\rho _{2}=0.8$, Bartlett Kernel

\vspace{2cm}

\includegraphics[
natheight=9.375400in, natwidth=12.500000in, height=3.0907in,
width=4.779in]{FMBAND_CorrPower_Wald_T_100_ba_rho1_8_rho2_8.jpg}
%\caption{
\\
Figure C6: Size Corrected Power, Wald test, $T=100$,
$\rho_{1}=\rho_{2}=0.8$, Bartlett Kernel%\end{center}
\end{center}
\end{figure}
\end{center}
%
%\nopagebreak

\begin{center}
\begin{figure}
\begin{center}

\includegraphics[
natheight=9.375400in, natwidth=12.500000in, height=3.0907in,
width=4.779in]{KernComp_CorrPower_Wald_T_100_rho1_8_rho2_8.jpg}
%\caption
\\
Figure C7: Size Corrected Power, Wald test, $T=100$,
$\rho_{1}=\rho _{2}=0.8$, Comparison of Bartlett and Quadratic
Spectral Kernels
\end{center}
\end{figure}
\end{center}



\clearpage

\newpage

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\end{document}