What are the differences in implementation of ARIMA models (estimate and forecast) in R2015b vs R2017a

Hello,

What is the difference between the implementation of the estimate and forecast for ARIMA models in MATLAB R2015b and R2017a?

1. I use the same initial data:

Y = [3238.85771666667;495692.242477273;620127.784434784;805698.931308334;832196.957949276;1081468.10228572;1006897.26552381;766067.854362746;1003777.34977500;1351877.69538334;1409466.77578788;1586375.07296297;1436406.19039474;1450211.28306522;1493506.59720455;1756110.45665873;1531985.99165217;1486898.11119167;1476536.53156818;1147942.85200981;1154699.67890834;1562813.44030834;1702504.30705303;1531763.51470176;2141511.85906141;1794537.08138406;2290941.48489683;2158768.33656061;2052875.33455797;2530067.84966667;2591242.44766667;2086263.50453334;2356404.12841229;2774383.93994445;3184444.18581819;3340204.13019445;3425985.99122223;3379796.49488406;3339218.35409525;3945938.97741667;3952469.32532576;3911466.08617500;4490404.00303624;3356351.15163334;4782200.66358334;4599126.17056350;5797454.39915874;5240208.50205264;4556966.53039684;4148571.04911906;4631018.07771740;5344881.55400001;5749479.25874604;5279529.74444445]

2. Create model ARIMA:

model = arima(  'ARLags',   [] ,...
                'D',        0, ...
                'MALags',   1 ,...
                'SARLags',  12 ,...
                'Seasonality',  12 ,...
                'SMALags',  12 ,...
                'Distribution', 'Gaussian');

3. Fit created model:

fit = estimate(model, Y, 'Display', 'off');

4. Make forecast of the trained model in R2017a or in R2015b (horizon = 21):

Yf = forecast(fit, 21, 'Y0', Y);

The same steps in MATLAB R2015B and R2017a give a different result (the results of the script are shown in the figure):

Can anybody tells me the difference between the implementation of the estimate and the forecast for ARIMA models in MATLAB R2015b and R2017a?

Tha same problem exists with state-space models (SSM).

Thank you!

Answer 1

[Hang Qian]

Hi Jonas, ARIMA model is estimated by maximum likelihood, which requires numeric maximization using the Optimization Toolbox. There could be some upgrade there. Check the maximized log likelihood. Is the value larger in R2017a?