Time Series Prediction using Recurrent Neural Networks

1. Auto Regressive Model

• X(t) = a₁X(t - 1) + a₂X(t - 2) + a₃X(t - 3) + U(t)
• where U(t) ~ Uniform(0, 0.1)

2. Moving Average Model

• X(t) = U(t) + a₁U(t - 1) + a₂U(t - 2) + a₃U(t - 3) + a₄U(t - 4) + a₅U(t - 5)
• where U(t) ~ Norm(0, 1)

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Non-Recurrent Model

• Modeling sequence as a function that maps term index to the term value.
• The model observes a set of 2500 terms from the sequence and predicts the next 500.
• A simple one-layer perceptron with d hidden layers is used as the model.

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