Horizon Plots in Mathematica?

I am not going to give you the whole code for this, rather some pointers on how to get there.

To get a single horizon plot, you need to apply Filling appropriately. Unfortunately, getting different filling styles on different lines in a plot is not actually well documented. Here is some test data and a plot that does it correctly.

aapl = FinancialData["AAPL", {2007, 1}];
ibm = FinancialData["IBM", {2007, 1}];
msft = FinancialData["MSFT", {2007, 1}];    
aapl1 = {#1, #2 - aapl[[1, 2]]} & @@@ aapl;    
ibm1 = {#1, #2 - ibm[[1, 2]]} & @@@ ibm;    
msft1 = {#1, #2 - msft[[1, 2]]} & @@@ msft;

DateListPlot[{msft1, ibm1}, Joined -> True, 
  Filling -> {1 -> {Bottom, Directive[Blue, Opacity[0.2]]}, 
  2 -> {Bottom, Directive[Red, Opacity[0.2]]}}, PlotStyle -> None, 
  PlotRangePadding -> 0, GridLines -> None, 
  FrameTicks -> {{Automatic, None}, {Automatic, None}}, AspectRatio -> 0.2]

A Grid full of plots is easy to code up, but to create a function that takes a grid of plots and formats them automatically according to their position in the grid (e.g. hiding ImagePadding so x-axes are hidden for all but the bottom panel), you may find my answer to a question of my own useful.

My suggestion is that you create a horizonPlotGrid master function that takes a list of data, and Maps an auxiliary function horizonPlotPanel to each one.

The horizonPlotPanel function would look something like this:

 horizonplot[data : {{_List, _?NumericQ} ..}] := 
 With[{neg = {#1, If[Negative[#2], -#2, 0]} & @@@ data, 
   pos = {#1, If[Positive[#2], #2, 0]} & @@@ data}, 
  DateListPlot[{pos, neg}, Joined -> True, 
   Filling -> {1 -> {Bottom, Directive[Blue, Opacity[0.2]]}, 
     2 -> {Bottom, Directive[Red, Opacity[0.2]]}}, PlotStyle -> None, 
   PlotRangePadding -> 0, GridLines -> None, 
   FrameTicks -> {{Automatic, None}, {Automatic, None}}, 
   AspectRatio -> 0.2]]

You could also add the ability to add custom options using OptionsPattern. See this question for more information.

Things to notice about this function:

1. The way I've used pattern matching {{_List, _?NumericQ} ..} in the function defintion to indicate that it's dated data (time series)

2. The use of With to define local constants, in this case the positive and the negative data as separate series. (There might be even better ways to do this, but this ensures that each series goes back to zero where the other series is operative.)

3. The custom Filling as shown in the other example.

To get the formatting you require, with horizontal bands as filling, I'd suggest adapting this existing answer.

A very "manual" procedure, just to help you get started:

ge = MovingAverage[FinancialData["GE", {2000}][[All, 2]], 100];
ge = ge - Min@ge - (Max@ge - Min@ge)/2;
s = Max@ge/2;
Attributes[f] = HoldAll;
f[x_, y_] := AppendTo[x, y];
Array[(l[#] = {}) &, 6];
(*for simplicity,we will work with all values>0*)
If[# > 0, f[l[1], #]; f[l[2], 0],     f[l[1], 0]; f[l[2], #]] & /@  ge;
If[# > s, f[l[3], s]; f[l[4], # - s], f[l[3], #]; f[l[4], 0]] & /@  l[1];
If[# > s, f[l[5], s]; f[l[6], # - s], f[l[5], #]; f[l[6], 0]] & /@ -l[2];

ListLinePlot[{l[3], l[4], l[5], l[6]}, 
 PlotStyle -> None, 
 Filling -> {
   1 -> {Axis, Directive[Blue, Opacity[0.2]]}, 
   2 -> {Axis, Directive[Blue, Opacity[0.4]]}, 
   3 -> {Axis, Directive[Red,  Opacity[0.2]]}, 
   4 -> {Axis, Directive[Red,  Opacity[0.4]]}}, AspectRatio -> 1/4]

Please note: The procedure above is manual on purpose, you will have to generalize it. Teaching to fish.

A Sin[x] horizon Plot:

Plot[Sin[Exp[ Sin[x]]] - .6, {x, 0, 4 Pi}, Filling -> Axis, 
 FillingStyle -> {LightRed, LightBlue}]

Plot[Sin[Exp[ Sin[x]]] - .6, {x, 0, 4 Pi}, 
 ColorFunction -> Function[{x, y}, Hue[y]], Filling -> Axis, 
 FillingStyle -> Automatic]

Show[Plot[Sin[Exp[ Sin[x]]] - .6, {x, 0, 4 Pi}, 
  ColorFunction -> Function[{x, y}, Hue[y]], Filling -> Axis, 
  FillingStyle -> Automatic], 
 Plot[(Sin[Exp[ Sin[x]]] - .6)/3, {x, 0, 4 Pi}, 
  ColorFunction -> Function[{x, y}, Hue[y/2]], Filling -> Axis, 
  FillingStyle -> Automatic]]

Show[Plot[Sin[Exp[ Sin[x]]] - .6, {x, 0, 4 Pi}, Filling -> Axis, 
  FillingStyle -> {LightRed, LightBlue}], 
 Plot[(Sin[Exp[ Sin[x]]] - .6)/3, {x, 0, 4 Pi}, Filling -> Axis, 
  FillingStyle -> {Red, Blue}]]

Plot[{Sin[Exp[ Sin[x]]] - .6, (Sin[Exp[ Sin[x]]] - .6)/3}, {x, 0, 
  4 Pi}, ColorFunction -> Function[{x, y}, Blend[{Red, Blue}, y]], 
 Filling -> Axis, FillingStyle -> Automatic]

data = Accumulate[RandomInteger[{-10, 10}, 100]];
avg = MovingAverage[data, 10];
DateListPlot[{data, Legended[avg, "moving average"]}, {{2013, 1, 1}, 
  Automatic, "Day"}, Joined -> True, 
 Filling -> {{1 -> {Axis, {Red, Blue}}}, {2 -> {Axis, {LightRed, 
       LightBlue}}}}]

Show[Plot[
  Piecewise[{{Exp[-(x + .45)^2/.005]/4, -5 < 
      x < -.3}, {-Exp[-(x + 0.15)^2/.005]/4, -.3 < x < 
      0}, {Exp[-(x - 0.15)^2/.005], 
     0 < x < 0.3}, {-Exp[-(x - 0.5)^2/.005], 
     0.35 < x < 0.65}}], {x, -1, 1}, Filling -> Axis, 
  FillingStyle -> {LightRed, LightBlue}, PlotRange -> All], 
 Plot[Piecewise[{{Exp[-(x + .45)^2/.005]/4, -5 < 
       x < -.3}, {-Exp[-(x + 0.15)^2/.005]/4, -.3 < x < 
       0}, {Exp[-(x - 0.15)^2/.005], 
      0 < x < 0.3}, {-Exp[-(x - 0.5)^2/.005], 0.35 < x < 0.65}}]/
   3, {x, -1, 1}, Filling -> Axis, FillingStyle -> {Red, Blue}, 
  PlotRange -> All]]

Plot[Sin[x], {x, 0, 2 Pi}, Filling -> 0.3, 
 FillingStyle -> {Red, Blue}]

Plot[{Piecewise[{{Abs@Sin[x], 0 < x < [Pi]}}], 
  Piecewise[{{Abs@Sin[x], [Pi] < x < 2 [Pi]}}]}, {x, 0, 2 Pi}, 
 Filling -> Axis, FillingStyle -> {{1 -> Red}, {2 -> Blue}}]

And other combinations.