Load the Data and Estimate a Model.

加载数据集Data_Airline。

load('Data_Airline.mat'); y = log(Data); T = length(y); Mdl = arima('持续的',0,'D',1,'Seasonality',12,。。。'MALags',1,'SMALags',12); EstMdl = estimate(Mdl,y);

ARIMA(0,1,1) Model Seasonally Integrated with Seasonal MA(12) (Gaussian Distribution): Value StandardError TStatistic PValue _________ _____________ __________ __________ Constant 0 0 NaN NaN MA{1} -0.37716 0.066794 -5.6466 1.6364e-08 SMA{12} -0.57238 0.085439 -6.6992 2.0952e-11 Variance 0.0012634 0.00012395 10.193 2.1406e-24

res = infer(EstMdl,y);

Simulate Airline Passenger Counts.

Use the fitted model to simulate 25 realizations of airline passenger counts over a 60-month (5-year) horizon. Use the observed series and inferred residuals as presample data.

rng（'默认') Ysim =模拟(EstMdl 60'NumPaths',25,'Y0'，是的，'E0'res);mn = (Ysim意思,2); figure plot(y,'k') hold在情节（t+1：t+60，ysim，'Color',[.85,.85,.85]); h = plot(T+1:T+60,mn,'k--','LineWidth',2); xlim([0,T+60]) title('Simulated Airline Passenger Counts') legend(h,'Simulation Mean','地点','NorthWest') holdoff

The simulated forecasts show growth and seasonal periodicity similar to the observed series.

Estimate the Probability of a Future Event.

Use simulations to estimate the probability that log airline passenger counts will meet or exceed the value 7 sometime during the next 5 years. Calculate the Monte Carlo error associated with the estimated probability.

rngdefaultYsim = simulate(EstMdl,60,'NumPaths',1000,'Y0'，是的，'E0'res);g7 = sum(Ysim >= 7) > 0; phat = mean(g7)

phat = 0.3910

err = sqrt(phat*(1-phat)/1000)

err = 0.0154

在未来5年内，（日志）航空公司乘客的数量将大约有39％的可能性。估计值的蒙特卡洛标准误差约为0.02。

Plot the Distribution of Passengers at a Future Time.

Use the simulations to plot the distribution of (log) airline passenger counts 60 months into the future.

figure histogram(Ysim(60,:),10) title('Distribution of Passenger Counts in 60 months')