Announcement

Collapse
No announcement yet.
X
  • Filter
  • Time
  • Show
Clear All
new posts

  • Forecast interval for ARIMA forecast

    I am conducting ARIMA time series modelling to compute an ex-post-forecast of a monthly time series (April 2011 - Jan 2018). In Nov 2016 a shock occured to the series whose effect I am examining. So, April 2011 to Oct 2016 is my estimation window and for the Nov 2016 to Jan 2018 period I want to conduct a dynamic ARIMA forecast. I already identified an ARIMA(2,1,1) model to be the adequate one for the data and I obtained the point estimates for the post-Nov-2016 period. These is the data and the forecasts:


    clear
    input double month float(lnVol_PPIs f_lnVol_PPIs)
    615 1.1249295 1.1249295 <-- up to month 681 (Oct 2016) the actual and predicted values are identical
    616 1.166271 1.166271
    617 .9516579 .9516579
    618 1.0919234 1.0919234
    619 -.3856625 -.3856625
    620 .8671005 .8671005
    621 .7975072 .7975072
    622 -.54472715 -.54472715
    623 1.1249295 1.1249295
    624 1.160021 1.160021
    625 1.0952734 1.0952734
    626 1.286474 1.286474
    627 1.280934 1.280934
    628 1.3110318 1.3110318
    629 1.1819606 1.1819606
    630 1.3202232 1.3202232
    631 1.4038192 1.4038192
    632 1.6331544 1.6331544
    633 1.7406234 1.7406234
    634 1.821972 1.821972
    635 1.9712994 1.9712994
    636 1.8995472 1.8995472
    637 1.9919738 1.9919738
    638 2.3373456 2.3373456
    639 2.1610427 2.1610427
    640 2.218116 2.218116
    641 2.2013965 2.2013965
    642 2.311545 2.311545
    643 2.388037 2.388037
    644 2.3799787 2.3799787
    645 2.3379292 2.3379292
    646 2.2669249 2.2669249
    647 2.3780813 2.3780813
    648 2.599741 2.599741
    649 2.646884 2.646884
    650 2.807714 2.807714
    651 2.755314 2.755314
    652 2.7880056 2.7880056
    653 2.8084755 2.8084755
    654 2.929057 2.929057
    655 2.9959056 2.9959056
    656 3.1286116 3.1286116
    657 3.4365644 3.4365644
    658 3.272572 3.272572
    659 3.366606 3.366606
    660 3.511317 3.511317
    661 3.4115534 3.4115534
    662 3.990921 3.990921
    663 4.3089423 4.3089423
    664 3.84833 3.84833
    665 4.015055 4.015055
    666 4.1671867 4.1671867
    667 3.969315 3.969315
    668 4.0606074 4.0606074
    669 4.1242795 4.1242795
    670 4.137712 4.137712
    671 4.2293158 4.2293158
    672 4.178202 4.178202
    673 4.180052 4.180052
    674 4.2773986 4.2773986
    675 4.238445 4.238445
    676 4.261927 4.261927
    677 4.3435493 4.3435493
    678 4.3547974 4.3547974
    679 4.5672884 4.5672884
    680 4.575478 4.575478
    681 4.843437 4.843437
    682 5.131805 4.916778 <-- here my forecast is starting, actual and forecasted values differ
    683 5.564866 4.809718
    684 5.689668 5.061981
    685 5.634844 4.993319
    686 5.835081 5.073544
    687 5.864288 5.191876
    688 5.627923 5.159405
    689 5.543809 5.287757
    690 5.599319 5.321162
    691 5.565058 5.360728
    692 5.481844 5.458627
    693 5.501973 5.479792
    694 5.464526 5.555726
    695 5.767844 5.616961
    696 5.889433 5.65839
    end
    format %tmMon_CCYY month



    Currently, I am struggeling with estimating the forecast intervals that reflect the forecast errors of my point predictions. As the forecast error is an increasing function of the forecast distance, the forecast intervals should widen over time. Modeling the ARIMA(2,1,1) in SPSS (that computes the confidence intervalsautomatically), this is indeed the case:
    Click image for larger version

Name:	SPSS intervals.jpg
Views:	1
Size:	126.2 KB
ID:	1445929





    Unfortunately, I do not know how to reproduce these intervals in Stata. I tried it in two ways:

    1) Using predict function in Stata, predicting the MSE:

    preserve
    drop if month > 681
    arima lnVol_PPIs, arima (2,1,1)
    restore
    predict volpred_dyn, y dynamic(682)
    predict MSE_dyn, mse dynamic(682)
    gen upper_dyn = volpred_dyn + 1.96 * sqrt(MSE_dyn)
    gen lower_dyn = volpred_dyn - 1.96 * sqrt(MSE_dyn

    This delivers:
    Click image for larger version

Name:	Stata intervals dynamic MSE.jpg
Views:	1
Size:	61.7 KB
ID:	1445930



    So, just the confidence interval for November 2016 is correctly specified. The intervals for predictions further away are too narrow.


    2) Using simulation with forecast function:

    preserve
    drop if month > 681
    arima lnVol_PPIs, arima (2,1,1)
    restore
    estimates store ARIMA211
    forecast create PPImodel, replace
    forecast estimates ARIMA211, name(DlnVol_PPIs)
    forecast identity lnVol_PPIs = DlnVol_PPIs + L.lnVol_PPIs
    forecast solve, simulate(betas, statistic(stddev, prefix(sd_))) begin(682)

    This delivers:
    Click image for larger version

Name:	Stata intervals forecast simulation.jpg
Views:	1
Size:	61.6 KB
ID:	1445931



    Obviously, the confidence intervals now are considerably too small, especially in the beginning.

    Do you have any suggestion how to obtain the correctly specified forecast intervals after ARIMA modeling in Stata? I did a lot of research, but did not find any solution. So I am thankful for any hint.


    Last edited by Doro Drees; 25 May 2018, 12:28.
Working...
X