A common example of generating synthetic sequence data uses $T = 1000$ time steps. At each step $t$, the observed value is computed as $x_t = \sin(0.01 \cdot t) + \epsilon_t$, where $\epsilon_t$ is noise drawn from a standard normal distribution and scaled to have a standard deviation of 0.2. The sinusoidal signal provides a smooth, periodic ground truth, while the additive noise makes the prediction nontrivial. To construct training data assuming a $\tau$-th order Markov condition with $\tau = 4$, the sequence is converted into overlapping windows. This yields $T - \tau = 996$ total examples. The first 600 examples, which cover approximately one full period of the sine function, are used for training, and the remainder are reserved for evaluation.