26 26
\newcommand\Pone{P_{t|t-1}}

27 27
\newcommand\diag{\textrm{diag}}

28 28
\newcommand\ep{\textrm{elem\_prod}}

29
\newcommand\admbversion{11.1}

29 30

30 31
\makeindex

31 32

......
35 36
  \smalltitlepart{An Introduction to}

36 37
  \largetitlepart{AD MODEL BUILDER}

37 38
  \smalltitlepart{for Use in Nonlinear Modeling and Statistics}

38
  \vspace{3ex}\textsf{\textit{Version 11.1~~(2013-05-01)}}\vspace{3ex}

39
  \vspace{3ex}\textsf{\textit{Version \admbversion~~(2013-05-01)\\[3pt]

40
      Revised manual~~(2013-06-24)}}\vspace{3ex}

39 41
}

40 42
\author{\textsf{\textit{David Fournier}}}

41 43
\manualname{AD Model Builder}

......
44 46

45 47
~\vfill

46 48
\noindent ADMB Foundation, Honolulu.\\\\

47
\noindent This is the manual for AD Model Builder (ADMB) version 10.0.\\\\

49
\noindent This is the manual for AD Model Builder (ADMB) version

50
\admbversion.\\\\

48 51
\noindent Copyright \copyright\ 1993, 1994, 1996, 2000, 2001, 2004, 2007, 2008,

49
2011 David Fournier\\\\

52
2011, 2013 David Fournier\\\\

50 53
\noindent The latest edition of the manual is available at:\\

51
\url{http://admb-project.org/documentation/manuals/admb-user-manuals}

54
\url{http://admb-project.org/documentation/manuals}

52 55

53 56
\tableofcontents

54 57

......
163 166
render the estimation of parameters in such nonlinear models more tractable. The

164 167
\ADMS package is intended to organize these techniques in such a way that they

165 168
are easy to employ (where possible, employing them in a way that the user does

166
not need to be aware of them), so that investigating nonlinear statistical models

167
becomes---so far as possible---as simple as for linear statistical models.

169
not need to be aware of them), so that investigating nonlinear statistical

170
models becomes---so far as possible---as simple as for linear statistical

171
models.

168 172

169 173
\section{Installing the software}

170 174

......
3052 3056
$\infty$ for this example). The integer argument \texttt{nsteps} determines how

3053 3057
accurate the integration will be. Higher values of \texttt{nsteps} will be more

3054 3058
accurate, but greatly increase the amount of time necessary to fit the model.

3055
The basic strategy is to use a moderate value for \texttt{nsteps}, such as~6, and

3056
then to increase this value to see if the parameter estimates change much.

3059
The basic strategy is to use a moderate value for \texttt{nsteps}, such as~6,

3060
and then to increase this value to see if the parameter estimates change much.

3057 3061
\begin{lstlisting}

3058 3062
  FUNCTION dvariable h(const dvariable& z)

3059 3063
\end{lstlisting}

......
3423 3427
default behavior of \ADM\ is to read in initial parameter values for the

3424 3428
parameters from a \texttt{PAR} file, if it finds one. Otherwise, they are given

3425 3429
default values consistent with their type. The quantity~\texttt{f} is a vector

3426
of four coefficients for the autoregressive process. \texttt{Pcoff} is a $2\times  3427 2$ matrix used to parameterize the transition matrix \texttt{P} for the Markov

3428
process. Its values are restricted to lie between~$0.01$ and~$0.99$.

3430
of four coefficients for the autoregressive process. \texttt{Pcoff} is a

3431
$2\times 2$ matrix used to parameterize the transition matrix \texttt{P} for the

3432
Markov process. Its values are restricted to lie between~$0.01$ and~$0.99$.

3429 3433
\texttt{smult} is a number used to parameterize \texttt{sigma} and \texttt{var}

3430 3434
(which is the variance) as a multiple of the mean-squared residuals. This

3431 3435
reparameterization undimensionalizes the calculation and is a good technique to

......
3616 3620
interest. The matrix~\texttt{z} is calculated using a transformed matrix,

3617 3621
because \ADM\ deals with vector rows better than columns. The probability

3618 3622
distribution for the states in period~1, \texttt{qb1}, is set equal to the

3619
unconditional distribution for a Markov process in terms of its transition matrix

3620
\texttt{P}, as discussed in~\cite{hamilton1994}. The transition matrix is used

3621
to compute the probability distribution of the states in periods $(2,1)$,

3623
unconditional distribution for a Markov process in terms of its transition

3624
matrix \texttt{P}, as discussed in~\cite{hamilton1994}. The transition matrix is

3625
used to compute the probability distribution of the states in periods $(2,1)$,

3622 3626
$(3,2,1)$, $(4,3,2,1)$, and finally, $(5,4,3,2,1)$. For the last quintuplet,

3623 3627
this is the probability distribution before observing~\texttt{y(5)}. The

3624 3628
quantities \texttt{eps} in the code correspond to the possible realized values


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