updating airline example in docs

LAMPSPUC · Jul 27, 2019 · e91d91c · e91d91c
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diff --git a/docs/src/assets/logap_components.png b/docs/src/assets/logap_components.png
diff --git a/docs/src/assets/logap_forecast.png b/docs/src/assets/logap_forecast.png
diff --git a/docs/src/assets/seasonalairpassengers.png b/docs/src/assets/seasonalairpassengers.png
diff --git a/docs/src/assets/simulationlogofairpassengers.png b/docs/src/assets/simulationlogofairpassengers.png
diff --git a/docs/src/assets/trendairpassengers.png b/docs/src/assets/trendairpassengers.png
diff --git a/docs/src/examples.md b/docs/src/examples.md
@@ -18,51 +18,41 @@ p1 = plot(AP[:Date], logAP, label = "AirPassengers timeseries", size = (1000, 50
 
 ![Log of Air Passengers time series](./assets/logofairpassengers.png)
 
-Estimating a `StateSpaceModel` gives us the trend and seasonal components of the time series.
+First we need to specify a state-space model. In this case, we'll utilize the basic structural model.
 
 ```julia
-# Define its seasonality 
-s = 12
+# Create structural model with seasonality of 12 months
+model = structural(logAP, 12)
+```
 
-# Estimate a StateSpace Structure
-ss = statespace(logAP, s)
+Estimating the model gives us the trend and seasonal components of the time series.
 
-# Analyze its decomposition in seasonal and trend
-p2 = plot(AP[:Date], ss.state.seasonal, label = "AirPassengers seasonal", size = (1000, 500))
-p3 = plot(AP[:Date], ss.state.trend, label = "AirPassengers trend", size = (1000, 500))
+```julia
+# Estimate a StateSpace structure
+ss = statespace(model)
+
+# Analyze its decomposition in trend and seasonal
+p2 = plot(AP[:Date], [ss.smoother.alpha[:, 1] ss.smoother.alpha[:, 3]], layout = (2, 1),
+            label = ["Trend component" "Seasonal component"], legend = :topleft)
 ```
 
-![Log of Air Passengers trend component](./assets/trendairpassengers.png)
-![Log of Air Passengers seasonal component](./assets/seasonalairpassengers.png)
+![Trend and seasonal components for log of Air Passengers](./assets/logap_components.png)
 
-We can also generate future scenarios for this time series through Monte Carlo simulation. In this example, we simulate 100 scenarios for up to five years (60 time periods) ahead.
+We can also forecast this time series. In this example, we will forecast 24 months ahead.
 
 ```julia
-# Simulate 100 scenarios, 60 steps ahead
-num_scenarios = 100
-num_steps_ahead = 60
-simulation = simulate(ss, num_steps_ahead, num_scenarios)
+# Forecast 24 months ahead
+N = 24
+pred, dist = forecast(ss, N)
 
-# Define simulation dates
+# Define forecasting dates
 firstdate = AP[:Date][end] + Month(1)
-newdates = collect(firstdate:Month(1):firstdate + Month(num_steps_ahead - 1))
-
-# Evaluating the mean of the forecast and its quantiles
-simulation_mean = mean(simulation, dims = 3)[1, :, :]
-
-n = length(logAP)
-nmonths = length(simulation[1, :, 1])
-simulation_q05 = zeros(nmonths)
-simulation_q95 = zeros(nmonths)
-for t = 1:nmonths
-    simulation_q05[t] = quantile(simulation[1, t, :], 0.05)
-    simulation_q95[t] = quantile(simulation[1, t, :], 0.95)
-end
+newdates = collect(firstdate:Month(1):firstdate + Month(N - 1))
 
-plot!(p1, newdates, [simulation_q05, simulation_mean, simulation_q95], labels = ["5% quantile", "mean", "95% quantile"])
+p3 = plot!(p1, newdates, pred, label = "Forecast")
 ```
 
-![Log of Air Passengers simulation](./assets/simulationlogofairpassengers.png)
+![Forecast for log of Air Passengers](./assets/logap_forecast.png)
 
 
 ## Vehicle tracking