For each training example, we want to train the network to predict a value x_t , given a sequence of lags . The ideal number of lags is a hyperparameter, so some experimentation is in order.

Structuring the input in this way is a requirement of the BPTT algorithm, as we have previously talked about. We will use the following code to train the dataset:

def lag_dataframe(data, lags=1):
    df = pd.DataFrame(data)
    columns = [df.shift(i) for i in range(lags, 0, -1)]
    columns.append(df)
    df = pd.concat(columns, axis=1)
    df.fillna(0, inplace=True)

    cols = df.columns.tolist()
    for i, col in enumerate(cols):
        if i == 0:
            cols[i] = "x"
        else:
            cols[i] = "x-" + str(i)

    cols[-1] = "y"
    df.columns = cols
    return df

As an example, if we were to call lag_dataframe with lags = 3, we would expect a dataset returned with x_t-1, x_t-2, and x_t-3. I find it very difficult to understand lag code like this, so if you do too, you aren't alone. I recommend running it and building some familiarity with the operation.