I'm looking to reproduce a diagram using the tikz package from a paper in JASA: Moodie et al 2009 104(485):155-65. This is the figure:

The nodes and arrows don't seem too difficult to generate. But I'm stumped on how to put a timescale axis, and space the nodes so that they align with it. So, to make this question relevant to a more general audience, how does one put an x-axis on the bottom of a tikz diagram, and align the nodes with elements on the axis?
Here's a starting example for time-points 0 and 1:
\begin{tikzpicture}[line width=0.05cm]
\node [circle,draw] (h1) at (0,2) {$h$};
\node [circle,draw] (h2) at (2,2) {$h$};
\node [circle,draw] (b1) at (1.5,4) {$b$};
\begin{scope}[line width=.1cm,shorten >= 5pt, shorten <= 5pt]
\draw[->] (h1) -- (h2);
\draw[->] (h1) -- (b1);
\draw[->] (b1) -- (h2);
\end{scope}
\draw[help lines] (0,0) grid (5,5) ;
\end{tikzpicture}
I'm looking for what I can add to this code to get the time-axis (lines, tick marks, numbers, and title).


grid. Or you could fake the timescale as nodesbelowthe lower nodes. – papabravo Feb 14 '14 at 14:39