Any-mean-model + GARCH(1, 1) for probabilistic stock forecasting

In this blog post, we will explore the combination of any model with GARCH(1,1) for probabilistic stock forecasting. This approach allows us to capture both the conditional mean and conditional variance of stock returns. We will demonstrate the implementation using Python and the ahead package.

Ref: https://en.wikipedia.org/wiki/Autoregressive_conditional_heteroskedasticity

See also:

• https://thierrymoudiki.github.io/blog/2025/06/21/r/python/beyond-garch-statistical
• https://thierrymoudiki.github.io/blog/2025/06/03/python/beyond-garch-python
• https://thierrymoudiki.github.io/blog/2025/06/02/r/beyond-garch

install.packages("pak")pak::pak("fpp2")devtools::install_github("Techtonique/ahead")pak::pak("fGarch")(res <- ahead::agnosticgarchf(fpp2::goog200,                           FUN=forecast::auto.arima, h=20))    Point Forecast    Lo 95    Hi 95201       532.1750 518.1879 546.1621202       532.8717 518.8757 546.8678203       533.5684 519.5635 547.5734204       534.2652 520.2513 548.2790205       534.9619 520.9391 548.9847206       535.6586 521.6269 549.6903207       536.3553 522.3148 550.3959208       537.0521 523.0026 551.1015209       537.7488 523.6905 551.8071210       538.4455 524.3783 552.5127211       539.1422 525.0662 553.2183212       539.8390 525.7540 553.9239213       540.5357 526.4419 554.6295214       541.2324 527.1298 555.3351215       541.9291 527.8176 556.0407216       542.6259 528.5055 556.7462217       543.3226 529.1934 557.4518218       544.0193 529.8813 558.1573219       544.7160 530.5692 558.8629220       545.4128 531.2571 559.5684ggplot2::autoplot(res)

(res <- ahead::agnosticgarchf(fpp2::goog200,                           FUN=forecast::thetaf, h=20))    Point Forecast    Lo 95    Hi 95201       531.4982 518.2318 544.7646202       531.7610 516.1991 547.3230203       532.0238 514.1041 549.9436204       532.2867 511.9078 552.6655205       532.5495 509.5788 555.5201206       532.8123 507.0890 558.5356207       533.0751 504.4117 561.7384208       533.3379 501.5205 565.1553209       533.6007 498.3883 568.8131210       533.8635 494.9868 572.7402211       534.1263 491.2863 576.9663212       534.3891 487.2548 581.5234213       534.6519 482.8584 586.4454214       534.9147 478.0601 591.7693215       535.1775 472.8202 597.5348216       535.4403 467.0955 603.7851217       535.7031 460.8392 610.5670218       535.9659 454.0004 617.9315219       536.2288 446.5235 625.9340220       536.4916 438.3483 634.6349ggplot2::autoplot(res)

(res <- ahead::agnosticgarchf(fpp2::goog200,                           FUN=ahead::ridge2f, h=20))    Point Forecast    Lo 95    Hi 95201       532.1740 519.4742 544.8737202       532.9003 517.9900 547.8106203       533.6547 516.8217 550.4877204       534.4346 515.8770 552.9921205       535.2377 515.1028 555.3726206       536.0622 514.4648 557.6596207       536.9062 513.9392 559.8731208       537.7679 513.5087 562.0272209       538.6460 513.1598 564.1321210       539.5390 512.8824 566.1956211       540.4458 512.6679 568.2236212       541.3651 512.5096 570.2207213       542.2961 512.4018 572.1905214       543.2378 512.3395 574.1361215       544.1894 512.3188 576.0601216       545.1501 512.3359 577.9643217       546.1193 512.3879 579.8506218       547.0963 512.4721 581.7205219       548.0805 512.5859 583.5751220       549.0716 512.7274 585.4158ggplot2::autoplot(res)

(res <- ahead::agnosticgarchf(fpp2::goog200,                           FUN=ahead::loessf, h=20))    Point Forecast    Lo 95    Hi 95201       544.3276 520.1558 568.4994202       548.2888 523.7199 572.8578203       552.0027 527.0698 576.9356204       554.1810 528.9140 579.4481205       556.8539 531.2797 582.4282206       560.3601 534.5032 586.2171207       561.5067 535.3893 587.6240208       565.6928 539.3353 592.0502209       567.2796 540.7006 593.8586210       570.1362 543.3525 596.9198211       574.0123 547.0395 600.9850212       578.5510 551.4034 605.6986213       580.8285 553.5191 608.1379214       584.2104 556.7512 611.6695215       587.9165 560.3187 615.5144216       591.1329 563.4066 618.8593217       594.0383 566.1929 621.8837218       595.6430 567.6872 623.5988219       602.2172 574.1590 630.2754220       604.7474 576.5943 632.9006ggplot2::autoplot(res)

As we can see from the plots, combining any model with GARCH(1,1) provides a comprehensive view of both the expected stock prices and the associated uncertainty. This method is particularly useful for financial forecasting, where volatility plays a significant role.