Forecasting multiple hours with lag variable - XGBoost or GBM

Question

I have an hourly time series data like this:

df.head()

 y  v1  v2 v3 v4 v5 v6
20  1   29 3  4  0  2020
23  1   24 2  3  1  2020
29  0   17 5  6  2  2020
35  0   15 5  6  3  2020

I'm using XGBoost or GBM to predict $y$ for the next day (24 hours). Since methods like GBM or XGBoost don't take into account trends or patterns of time series, I added variables like year, hour, month, etc.. to the data. Since it doesn't take the last value into account I also created a lag variable ($x$) for $y$:

df.head()

 y  v1  v2 v3 v4 v5 v6   x
20  1   29 3  4  0  2020 
23  1   24 2  3  1  2020 20
29  0   17 5  6  2  2020 23
35  0   15 5  6  3  2020 29

Since I'm only predicting one variable ($y$) by using as input the other variables, how will my second, third, etc.. hour have in account the lag value? My pipeline is something similar to this:

import numpy as np
df_train = df
X1=df_train[['v1','v2','v3','v4','v5','v6','x']
y1=df_train['y']
from sklearn.model_selection import train_test_split
X_train, y_train =X1, y1
X_test=df_test[['v1','v2','v3','v4','v5','v6','x']
regressor=XGBRegressor()
regressor.fit(X_train,y_train)
regressor.predict(X_test)

However, I cannot give $x$ as input to predict the next 24 hours because I don't have values of x for the next 24 hours because they always depend on the last day. Is it possible for the model to predict, for example, hour 5 using the value $x$ of the predicted $y$ value at hour 4?

Edit: And if it is not possible to use predictions at time $t$ to be a lag feature for the prediction at time $t+1$, how can I overcome this issue? Can I simply predict both $x$ and $y$?

Answer 1

There are several options available, and in the end it is probably an empricial questions what works best (at least I am not aware of one best approach):

1. Predicting $Y_{t+2}$ based on the available $X_t$ (without forecasting covariates)
2. Forecasting e.g. $X_{t+2}$ and using that forecast to predict $Y_{t+2}$
3. Forecasting e.g. $Y_{t+1}$ to predict in turn $Y_{t+2}$

Next there is of course the question how many models you plan to use to forecast the next day (24 hours). One model for all 24 hours, 24 different models or somewhat in between?

This is in some way a hyperparameter here which you can optimize.