How can I model the autocorrelation of objective variables under the situation where we can't observe any actual objective variable in the test phase

I'm trying to model the relationship between the declared value from a subject and stimulus. For example, modeling a relationship between the subject's happiness and strength of stimulus so that we can predict the subject's sadness from stimuli. (The Happiness are five scale ratings, stimuli are continuous value)

Emotions like happiness are obviously autocorrelated and I think modeling these autocorrelations might help the model make a better prediction. However, we can only observe happiness (actual value) in the training phase and not in the evaluation phase. So we can't use any actual objective variables in the past to predict the current value. And unfortunately, the stimulus is not enough good estimator of objective variables so far.

What can I do to model the autocorrelation in situations like above?

In the training phase, we have:

y_1, y_2, ..., y_T

X_1, X_2, ...., X_T

where corr(y_k, y_{k+1}) = 0.7

In the test phase, we only have:

X_1, X_2, ...., X_N

and need to predict

y_1, y_2, ..., y_N