I have data indexed from 0 to 54. Using 6 principal components that explains 99% variation of data I was not expecting the error function to exhibit such a clear shape? By error function from following formula that is: $$ y_t(x) = \hat{\mu}(x) + \sum_{k=1}^{10} \hat{\phi}_k(x) \hat{\beta}_{k,t} + \epsilon_t(x) $$
Where $$\hat{\phi}_k(x)$$ are principal component vectors and $$\hat{\beta}_{k,t}$$ are respective scores.
To my understanding, If I conduct PCA that can explain 99% of the data, then any functional curve in my data can be reconstructed using principal component vectors and scores. This is in fact not the case in my analysis and I believe it is coming from the fact that the error function itself is a curve or perhaps a principal component vector of higher K than 10? Why is this happening? Increasing K to 20 even can not get rid of this shape in the error.