Quantile RNN

數據預處理

import numpy as np
from toolz.curried import *


@curry
def clean_nan(dataset, how='any'):
    return dataset.dropna(how=how)


@curry
def lagger(dataset, n_lags, price_columns):
    df = reduce(
        lambda df, lag: df.assign(**{col + str(lag): dataset[[col]].shift(-lag).values for col in price_columns}),
        range(1, n_lags + 1),
        dataset[price_columns])

    result = df.assign(**{col: dataset[col] for col in dataset.drop(price_columns, axis=1).columns})
    return result[sorted(result.columns)]


@curry
def diff_log_pricer(dataset, price_columns, date_column):
    """
    Takes the first difference of the logs of temporal data

    Parameters
    ----------
    dataset : pandas.DataFrame
        A Pandas' DataFrame with a Date Column and one or many price column.
        The price column must be of numerical time and not contain nones

    price_columns : list of str
        A list with the names of the price columns

    date_column : str
        The name of the date column. The column must be of type datetime.

    Returns
    ----------
    new_df : pandas.DataFrame
        A df like DataFrame with the price column replaced by the log difference in time.
        The first row will contain NaNs due to first diferentiation.
    """

    # Sorting the dataframe
    sort_fn = lambda df: df.sort_values(by=date_column)

    # Applying log to each value
    log_fn = lambda df: df.assign(**{col: np.log(df[col]) for col in price_columns})

    # Calculating the difference
    diff_fn = lambda df: df.assign(
        **{col: 100 * (df[col] - df[col].shift(1)) for col in price_columns}).reset_index(drop=True)

    return compose(diff_fn, log_fn, sort_fn)(dataset)


@curry
def time_split_dataset(df, train_start_date, train_end_date, holdout_end_date, date_col):
    """
    Splits temporal data into a training and testing datasets such that
    all training data comes before the testings set.

    Parameters
    ----------
    df : pandas.DataFrame
        A Pandas' DataFrame with an Identifier Column and a Date Column.
        The model will be trained to predict the target column
        from the features.

    train_start_date : str
        A date string representing a the starting time of the training data.
        It should be in the same format as the Date Column in `dataset`.
        Inclusive in the train set

    train_end_date : str
        A date string representing a the ending time of the training data.
        This will also be used as the start date of the holdout period.
        It should be in the same format as the Date Column in `dataset`.
        Inclusive in the train set. Exclusive in the test set.

    holdout_end_date : str
        A date string representing a the ending time of the holdout data.
        It should be in the same format as the Date Column in `dataset`.
        Inclusive in the test set.

    date_col : str
        The name of the Date column of `dataset`.


    Returns
    ----------
    train_set : pandas.DataFrame
        The in ID sample and in time training set.

    test_set : pandas.DataFrame
        The out of time testing set.
    """

    train_set = df.copy()[
        (df[date_col] >= train_start_date) & (df[date_col] <= train_end_date)]

    test_set = df.copy()[
        (df[date_col] > train_end_date) & (df[date_col] <= holdout_end_date)]

    return train_set, test_set

pipline

@curry
def pipeline(dataset, learners):
    return pipe(learners,
                reversed,
                reduce(comp))(dataset)

evaluation

@curry
def quantile_loss_evaluator(df, predict_col, target_col, tau):
    y_true = df[[target_col]].values
    y_hat = df[[predict_col]].values
    return np.mean((tau - (y_true < y_hat)) * (y_true - y_hat))

@curry
def proportion_of_hits_evaluator(df, predict_col, target_col):
    y_true = df[[target_col]].values
    y_hat = df[[predict_col]].values
    return np.mean(y_hat > y_true)

model

# coding=utf-8

import tensorflow as tf
from tensorflow.keras.models import Sequential
from tensorflow.keras.layers import Dense, LSTM
from tensorflow.keras.optimizers import Adam


def qrnn_learner(dataset, price_cols, target_col, prediction_col="prediction",
                 tau=0.05, neurons=20, lr=1e-4, batch_size=512, epochs=5):
    def to_3D(dataset):
        all_p_columns = pipe(dataset.columns,
                             filter(lambda col: reduce(lambda acc, p_col: acc or col.find(p_col) >= 0,
                                                       price_cols, False)),
                             filter(lambda col: col != target_col),
                             list)

        def p(new_data):
            return new_data[all_p_columns].values.reshape(-1,
                                                          int(len(all_p_columns) / len(price_cols)),
                                                          len(price_cols))

        return p, p(dataset)

    def quantile_loss(y_true, y_pred):
        ro = tau - tf.cast(tf.greater(y_pred, y_true), tf.float32)
        return tf.reduce_mean(ro * (y_true - y_pred))

    _3Dnator, x_train = to_3D(dataset)
    y_train = dataset[[target_col]].values
    n_samples, timesteps, n_vars = x_train.shape

    # build model
    model = Sequential()
    model.add(LSTM(neurons, input_shape=(timesteps, n_vars)))
    model.add(Dense(1, activation=None))
    opt = Adam(lr=lr)
    model.compile(loss=quantile_loss, optimizer=opt)

    # train model
    model.fit(x_train, y_train, batch_size=batch_size, epochs=epochs, verbose=0)

    def p(new_dataset):
        x_new = _3Dnator(new_dataset)
        return new_dataset.assign(**{prediction_col: model.predict(x_new)})

    return p, p(dataset)

example

from matplotlib import pyplot as plt
plt.style.use("ggplot")

tau = 0.95
N_LAGS=14
PRICE_COLS = ["Adjusted Close"]

data  = pd.read_csv('SP500.csv', usecols=['Adjusted Close', 'Date'])
data.head()

differ_learner = diff_log_pricer(price_columns=PRICE_COLS, date_column="Date")
lagger_learner = lagger(n_lags=N_LAGS, price_columns=PRICE_COLS)
na_clearn_learner = clean_nan(how="any")

pipe_learner = pipeline(learners=[differ_learner, lagger_learner, na_clearn_learner])
processed_data = pipe_learner(data)

splitter = time_split_dataset(train_start_date="1960-01-01", train_end_date="2010-01-01", holdout_end_date="2016-01-01", date_col="Date")
train, test = splitter(processed_data)
train.head()

var_estimator, train_pred = qrnn_learner(train, price_cols=PRICE_COLS, target_col="Adjusted Close14", epochs=10, lr=1e-3, tau= tau)
test_pred = var_estimator(test)

quantile_eval_fn = quantile_loss_evaluator(predict_col="prediction",
                                           target_col="Adjusted Close14",
                                           tau= tau)

hits_eval_fn = proportion_of_hits_evaluator(predict_col="prediction",
                                                target_col="Adjusted Close14")
print("Quantile loss on train %f and test %f sets" % tuple(map(quantile_eval_fn, [train_pred, test_pred])))
print("Number of hits on train %f and test %f sets" % tuple(map(hits_eval_fn, [train_pred, test_pred])))
"""
Quantile loss on train 0.094278 and test 0.091880 sets
Number of hits on train 0.941602 and test 0.940397 sets
"""

plt.figure(figsize=(20, 6))
plt.plot(test_pred["Date"], test_pred["prediction"])
plt.plot(test_pred["Date"], test_pred["Adjusted Close14"])