Graph fixes (#317)

* Fixed plot titles

* Missing bands

lectures/time_series_models/additive_functionals.md

@@ -566,7 +566,8 @@ function plot_martingales(amf, T, npaths = 25)
               plot_martingale_paths(T, mpath_mult[(li + 1):ui, :],
                                     mbounds_mult[(LI + 1):UI, :], horline = 1))
         plot!(mart_figs[ii + 1],
-              title = L"Martingale components for many paths of $y_{ii + 1}$")
+              title = L"Martingale components for many paths of $y_{ii + 1}$",
+              titlefontsize = 12)
     end
 
     return mart_figs
@@ -594,7 +595,8 @@ function plot_given_paths(T, ypath, mpath, spath, tpath, mbounds, sbounds;
     end
     plot!(plots[1], seriestype = :hline, [horline], color = :black,
           linestyle = :dash, label = "")
-    plot!(plots[1], title = "One Path of All Variables", legend = :topleft)
+    plot!(plots[1], title = "One Path of All Variables", legend = :topleft,
+          titlefontsize = 12)    
 
     # plot martingale component
     plot!(plots[2], trange, mpath[1, :], color = :magenta, label = "")
@@ -605,7 +607,8 @@ function plot_given_paths(T, ypath, mpath, spath, tpath, mbounds, sbounds;
           label = "")
     plot!(plots[2], seriestype = :hline, [horline], color = :black,
           linestyle = :dash, label = "")
-    plot!(plots[2], title = "Martingale Components for Many Paths")
+    plot!(plots[2], title = "Martingale Components for Many Paths",
+          titlefontsize = 12)
 
     # plot stationary component
     plot!(plots[3], spath[1, :], color = :green, label = "")
@@ -616,15 +619,17 @@ function plot_given_paths(T, ypath, mpath, spath, tpath, mbounds, sbounds;
           label = "")
     plot!(plots[3], seriestype = :hline, [horline], color = :black,
           linestyle = :dash, label = "")
-    plot!(plots[3], title = "Stationary Components for Many Paths")
+    plot!(plots[3], title = "Stationary Components for Many Paths",
+          titlefontsize = 12)
 
     # plot trend component
     if show_trend == true
         plot!(plots[4], Matrix(tpath'), color = :red, label = "")
     end
     plot!(plots[4], seriestype = :hline, [horline], color = :black,
           linestyle = :dash, label = "")
-    plot!(plots[4], title = "Trend Components for Many Paths")
+    plot!(plots[4], title = "Trend Components for Many Paths",
+          titlefontsize = 12)
 
     return plots
 end
@@ -640,7 +645,8 @@ function plot_martingale_paths(T, mpath, mbounds;
     # plot martingale component
     ub = mbounds[2, :]
     lb = mbounds[1, :]
-    #plot!(plt, lb, fillrange = ub, alpha = 0.25, color = :magenta, label = "")
+    
+    plot!(plt, ub, fillrange = lb, alpha = 0.25, color = :magenta, label = "")
     plot!(plt, seriestype = :hline, [horline], color = :black,
           linestyle = :dash, label = "")
     plot!(plt, trange, Matrix(mpath'), linewidth = 0.25, color = :black,
@@ -657,7 +663,7 @@ For now, we just plot $y_t$ and $x_t$, postponing until later a description of e
 ---
 tags: [remove-cell]
 ---
-Random.seed!(42);
+Random.seed!(43);
 ```
 
 ```{code-cell} julia
@@ -685,16 +691,16 @@ x, y = simulate(amf.lss, T)
 plt_1 = plot()
 plt_2 = plot()
 plots = [plt_1, plt_2]
-# plots = plot(layout = (2, 1))
 
 plot!(plots[1], 1:T, y[amf.nx + 1, :], color = :black, lw = 2, label = "")
-plot!(plots[1], title = L"A particular path of $y_t$")
+plot!(plots[1], title = L"A particular path of $y_t$",
+          titlefontsize = 12)
 plot!(plots[2], 1:T, y[1, :], color = :green, lw = 2, label = "")
 plot!(plots[2], seriestype = :hline, [0], color = :black, lw = 2,
       linestyle = :dashdot, label = "")
-plot!(plots[2], title = L"Associated path of $x_t$")
-# plot(plots)
-plot(plots[1], plots[2], layout = (2, 1), size = (700, 500))
+plot!(plots[2], title = L"Associated path of $x_t$",
+          titlefontsize = 12)
+plot(plots[1], plots[2], layout = (2, 1), size = (700, 600))
 ```
 
 ```{code-cell} julia
@@ -933,12 +939,6 @@ $\widetilde M_t$ of the multiplicative decomposition has a peculiar property.
 
 The following simulation of many paths of $\widetilde M_t$ illustrates this property
 
-```{code-cell} julia
----
-tags: [remove-cell]
----
-Random.seed!(10021987);
-```
 
 ```{code-cell} julia
 plt = plot_martingales(amf, 12000)

lectures/time_series_models/multiplicative_functionals.md

@@ -422,7 +422,8 @@ Random.seed!(42);
 
 ```{code-cell} julia
 # Create the second (wrong) alternative model
-amf2 = AMF_LSS_VAR(A = 0.9, B = 1.0, D = 0.55, F = 0.25) # parameters for theta_1 closer to theta_0
+# parameters for theta_1 closer to theta_0
+amf2 = AMF_LSS_VAR(A = 0.9, B = 1.0, D = 0.55, F = 0.25)
 
 # Get likelihood from each path x^{i}, y^{i}
 LLit2 = simulate_likelihood(amf2, Xit, Yit)
@@ -604,10 +605,10 @@ amc, mmc = simulate_martingale_components(amf_2, 1_000, 5_000)
 amcT = amc[:, end]
 mmcT = mmc[:, end]
 
-println("The (min, mean, max) of additive Martingale component in period T is")
+println("The (min, mean, max) of additive Martingale component in period T:")
 println("\t ($(minimum(amcT)), $(mean(amcT)), $(maximum(amcT)))")
 
-println("The (min, mean, max) of multiplicative Martingale component in period T is")
+println("The (min, mean, max) of multiplicative Martingale component in period T:")
 println("\t ($(minimum(mmcT)), $(mean(mmcT)), $(maximum(mmcT)))")
 ```
 
@@ -708,13 +709,11 @@ dens_to_plot = [Mtilde_t_density(amf_2, t, xmin = 1e-8, xmax = 6.0)
 ldens_to_plot = [logMtilde_t_density(amf_2, t, xmin = -10.0, xmax = 10.0)
                  for t in times_to_plot]
 
-# plot_title = "Densities of M_t^tilda" is required, however, plot_title is not yet
-# supported in Plots
 plots = plot(layout = (3, 2), size = (600, 800))
 
 for (it, dens_t) in enumerate(dens_to_plot)
     x, pdf = dens_t
-    plot!(plots[it], title = "Density for time (time_to_plot[it])",
+    plot!(plots[it], title = "Density for time $(times_to_plot[it])",
           titlefontsize = 10)
     plot!(plots[it], pdf, fillrange = 0, label = "")
 end