Assignment #9 (demo). Time series analysis

Assignment #9 (demo). Time series analysis#

mlcourse.ai – Open Machine Learning Course

Author: Mariya Mansurova, Analyst & developer in Yandex.Metrics team. Translated by Ivan Zakharov, ML enthusiast. This material is subject to the terms and conditions of the Creative Commons CC BY-NC-SA 4.0 license. Free use is permitted for any non-commercial purpose.

Same assignment as a Kaggle Notebook + solution.

In this assignment, we are using Prophet and ARIMA to analyze the number of views for a Wikipedia page on Machine Learning.

Fill cells marked with “Your code here” and submit your answers to the questions through the web form.

import os
import warnings

warnings.filterwarnings("ignore")
import numpy as np
import pandas as pd
import requests
from plotly import __version__
from plotly import graph_objs as go
from plotly.offline import download_plotlyjs, init_notebook_mode, iplot, plot
from IPython.display import display, IFrame

print(__version__)  # need 1.9.0 or greater
init_notebook_mode(connected=True)

5.22.0

def plotly_df(df, title="", width=800, height=500):
    """Visualize all the dataframe columns as line plots."""
    common_kw = dict(x=df.index, mode="lines")
    data = [go.Scatter(y=df[c], name=c, **common_kw) for c in df.columns]
    layout = dict(title=title)
    fig = dict(data=data, layout=layout)

    # in a Jupyter Notebook, the following should work
    #iplot(fig, show_link=False)

    # in a Jupyter Book, we save a plot offline and then render it with IFrame
    plot_path = f"../../_static/plotly_htmls/{title}.html".replace(" ", "_")
    plot(fig, filename=plot_path, show_link=False, auto_open=False);
    display(IFrame(plot_path, width=width, height=height))

Data preparation#

# for Jupyter-book, we copy data from GitHub, locally, to save Internet traffic,
# you can specify the data/ folder from the root of your cloned
# https://github.com/Yorko/mlcourse.ai repo, to save Internet traffic
DATA_PATH = "https://raw.githubusercontent.com/Yorko/mlcourse.ai/main/data/"

df = pd.read_csv(DATA_PATH + "wiki_machine_learning.csv", sep=" ")
df = df[df["count"] != 0]
df.head()
date count lang page rank month title
81 2015-01-01 1414 en Machine_learning 8708 201501 Machine_learning
80 2015-01-02 1920 en Machine_learning 8708 201501 Machine_learning
79 2015-01-03 1338 en Machine_learning 8708 201501 Machine_learning
78 2015-01-04 1404 en Machine_learning 8708 201501 Machine_learning
77 2015-01-05 2264 en Machine_learning 8708 201501 Machine_learning 
df.shape

(383, 7)

Predicting with FB Prophet#

We will train at first 5 months and predict the number of trips for June.

df.date = pd.to_datetime(df.date)

plotly_df(df=df.set_index("date")[["count"]], title="assign9_plot")

from prophet import Prophet

---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In[8], line 1
----> 1 from prophet import Prophet

File ~/Library/Caches/pypoetry/virtualenvs/mlcourse-ai-czBTtoES-py3.12/lib/python3.12/site-packages/prophet/__init__.py:7
      1 # Copyright (c) 2017-present, Facebook, Inc.
      2 # All rights reserved.
      3 #
      4 # This source code is licensed under the BSD-style license found in the
      5 # LICENSE file in the root directory of this source tree. An additional grant
      6 # of patent rights can be found in the PATENTS file in the same directory.
----> 7 from prophet.forecaster import Prophet
      9 from pathlib import Path
     10 about = {}

File ~/Library/Caches/pypoetry/virtualenvs/mlcourse-ai-czBTtoES-py3.12/lib/python3.12/site-packages/prophet/forecaster.py:28
     25 logger.setLevel(logging.INFO)
     26 NANOSECONDS_TO_SECONDS = 1000 * 1000 * 1000
---> 28 class Prophet(object):
     29     """Prophet forecaster.
     30 
     31     Parameters
   (...)
     79     holidays_mode: 'additive' or 'multiplicative'. Defaults to seasonality_mode.
     80     """
     82     def __init__(
     83             self,
     84             growth='linear',
   (...)
    101             holidays_mode=None,
    102     ):

File ~/Library/Caches/pypoetry/virtualenvs/mlcourse-ai-czBTtoES-py3.12/lib/python3.12/site-packages/prophet/forecaster.py:459, in Prophet()
    451     else:
    452         self.changepoints_t = np.array([0])  # dummy changepoint
    454 @staticmethod
    455 def fourier_series(
    456     dates: pd.Series,
    457     period: Union[int, float],
    458     series_order: int,
--> 459 ) -> NDArray[np.float_]:
    460     """Provides Fourier series components with the specified frequency
    461     and order.
    462 
   (...)
    471     Matrix with seasonality features.
    472     """
    473     if not (series_order >= 1):

File ~/Library/Caches/pypoetry/virtualenvs/mlcourse-ai-czBTtoES-py3.12/lib/python3.12/site-packages/numpy/__init__.py:397, in __getattr__(attr)
    394     raise AttributeError(__former_attrs__[attr])
    396 if attr in __expired_attributes__:
--> 397     raise AttributeError(
    398         f"`np.{attr}` was removed in the NumPy 2.0 release. "
    399         f"{__expired_attributes__[attr]}"
    400     )
    402 if attr == "chararray":
    403     warnings.warn(
    404         "`np.chararray` is deprecated and will be removed from "
    405         "the main namespace in the future. Use an array with a string "
    406         "or bytes dtype instead.", DeprecationWarning, stacklevel=2)

AttributeError: `np.float_` was removed in the NumPy 2.0 release. Use `np.float64` instead.

predictions = 30

df = df[["date", "count"]]
df.columns = ["ds", "y"]
df.tail()

Question 1: What is the prediction of the number of views of the wiki page on January 20? Round to the nearest integer.

  • 4947

  • 3426

  • 5229

  • 2744

# You code here (read-only in a JupyterBook, pls run jupyter-notebook to edit)

Estimate the quality of the prediction with the last 30 points.

# You code here (read-only in a JupyterBook, pls run jupyter-notebook to edit)

Question 2: What is MAPE equal to?

  • 34.5

  • 42.42

  • 5.39

  • 65.91

# You code here (read-only in a JupyterBook, pls run jupyter-notebook to edit)

Question 3: What is MAE equal to?

  • 355

  • 4007

  • 600

  • 903

# You code here (read-only in a JupyterBook, pls run jupyter-notebook to edit)

Predicting with ARIMA#

%matplotlib inline
import matplotlib.pyplot as plt
import statsmodels.api as sm
from scipy import stats

plt.rcParams["figure.figsize"] = (15, 10)

Question 4: Let’s verify the stationarity of the series using the Dickey-Fuller test. Is the series stationary? What is the p-value?

  • Series is stationary, p_value = 0.107

  • Series is not stationary, p_value = 0.107

  • Series is stationary, p_value = 0.001

  • Series is not stationary, p_value = 0.001

# You code here (read-only in a JupyterBook, pls run jupyter-notebook to edit)

Next, we turn to the construction of the SARIMAX model (sm.tsa.statespace.SARIMAX).
Question 5: What parameters are the best for the model according to the AIC criterion?

  • D = 1, d = 0, Q = 0, q = 2, P = 3, p = 1

  • D = 2, d = 1, Q = 1, q = 2, P = 3, p = 1

  • D = 1, d = 1, Q = 1, q = 2, P = 3, p = 1

  • D = 0, d = 0, Q = 0, q = 2, P = 3, p = 1

# You code here (read-only in a JupyterBook, pls run jupyter-notebook to edit)
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