In [2]:
!pip install tensorflow==2
Collecting tensorflow==2
Downloading https://files.pythonhosted.org/packages/46/0f/7bd55361168bb32796b360ad15a25de6966c9c1beb58a8e30c01c8279862/tensorflow-2.0.0-cp36-cp36m-manylinux2010_x86_64.whl (86.3MB)
|████████████████████████████████| 86.3MB 117kB/s
Requirement already satisfied: keras-applications>=1.0.8 in /usr/local/lib/python3.6/dist-packages (from tensorflow==2) (1.0.8)
Collecting tensorboard<2.1.0,>=2.0.0
Downloading https://files.pythonhosted.org/packages/d3/9e/a48cd34dd7b672ffc227b566f7d16d63c62c58b542d54efa45848c395dd4/tensorboard-2.0.1-py3-none-any.whl (3.8MB)
|████████████████████████████████| 3.8MB 29.8MB/s
Collecting tensorflow-estimator<2.1.0,>=2.0.0
Downloading https://files.pythonhosted.org/packages/fc/08/8b927337b7019c374719145d1dceba21a8bb909b93b1ad6f8fb7d22c1ca1/tensorflow_estimator-2.0.1-py2.py3-none-any.whl (449kB)
|████████████████████████████████| 450kB 41.2MB/s
Requirement already satisfied: astor>=0.6.0 in /usr/local/lib/python3.6/dist-packages (from tensorflow==2) (0.8.0)
Requirement already satisfied: six>=1.10.0 in /usr/local/lib/python3.6/dist-packages (from tensorflow==2) (1.12.0)
Requirement already satisfied: protobuf>=3.6.1 in /usr/local/lib/python3.6/dist-packages (from tensorflow==2) (3.10.0)
Requirement already satisfied: termcolor>=1.1.0 in /usr/local/lib/python3.6/dist-packages (from tensorflow==2) (1.1.0)
Requirement already satisfied: absl-py>=0.7.0 in /usr/local/lib/python3.6/dist-packages (from tensorflow==2) (0.8.1)
Requirement already satisfied: numpy<2.0,>=1.16.0 in /usr/local/lib/python3.6/dist-packages (from tensorflow==2) (1.17.3)
Requirement already satisfied: opt-einsum>=2.3.2 in /usr/local/lib/python3.6/dist-packages (from tensorflow==2) (3.1.0)
Requirement already satisfied: gast==0.2.2 in /usr/local/lib/python3.6/dist-packages (from tensorflow==2) (0.2.2)
Requirement already satisfied: google-pasta>=0.1.6 in /usr/local/lib/python3.6/dist-packages (from tensorflow==2) (0.1.7)
Requirement already satisfied: keras-preprocessing>=1.0.5 in /usr/local/lib/python3.6/dist-packages (from tensorflow==2) (1.1.0)
Requirement already satisfied: grpcio>=1.8.6 in /usr/local/lib/python3.6/dist-packages (from tensorflow==2) (1.15.0)
Requirement already satisfied: wheel>=0.26 in /usr/local/lib/python3.6/dist-packages (from tensorflow==2) (0.33.6)
Requirement already satisfied: wrapt>=1.11.1 in /usr/local/lib/python3.6/dist-packages (from tensorflow==2) (1.11.2)
Requirement already satisfied: h5py in /usr/local/lib/python3.6/dist-packages (from keras-applications>=1.0.8->tensorflow==2) (2.8.0)
Requirement already satisfied: werkzeug>=0.11.15 in /usr/local/lib/python3.6/dist-packages (from tensorboard<2.1.0,>=2.0.0->tensorflow==2) (0.16.0)
Collecting google-auth<2,>=1.6.3
Downloading https://files.pythonhosted.org/packages/c5/9b/ed0516cc1f7609fb0217e3057ff4f0f9f3e3ce79a369c6af4a6c5ca25664/google_auth-1.6.3-py2.py3-none-any.whl (73kB)
|████████████████████████████████| 81kB 9.9MB/s
Requirement already satisfied: markdown>=2.6.8 in /usr/local/lib/python3.6/dist-packages (from tensorboard<2.1.0,>=2.0.0->tensorflow==2) (3.1.1)
Requirement already satisfied: google-auth-oauthlib<0.5,>=0.4.1 in /usr/local/lib/python3.6/dist-packages (from tensorboard<2.1.0,>=2.0.0->tensorflow==2) (0.4.1)
Requirement already satisfied: setuptools>=41.0.0 in /usr/local/lib/python3.6/dist-packages (from tensorboard<2.1.0,>=2.0.0->tensorflow==2) (41.4.0)
Requirement already satisfied: pyasn1-modules>=0.2.1 in /usr/local/lib/python3.6/dist-packages (from google-auth<2,>=1.6.3->tensorboard<2.1.0,>=2.0.0->tensorflow==2) (0.2.7)
Requirement already satisfied: rsa>=3.1.4 in /usr/local/lib/python3.6/dist-packages (from google-auth<2,>=1.6.3->tensorboard<2.1.0,>=2.0.0->tensorflow==2) (4.0)
Requirement already satisfied: cachetools>=2.0.0 in /usr/local/lib/python3.6/dist-packages (from google-auth<2,>=1.6.3->tensorboard<2.1.0,>=2.0.0->tensorflow==2) (3.1.1)
Requirement already satisfied: requests-oauthlib>=0.7.0 in /usr/local/lib/python3.6/dist-packages (from google-auth-oauthlib<0.5,>=0.4.1->tensorboard<2.1.0,>=2.0.0->tensorflow==2) (1.2.0)
Requirement already satisfied: pyasn1<0.5.0,>=0.4.6 in /usr/local/lib/python3.6/dist-packages (from pyasn1-modules>=0.2.1->google-auth<2,>=1.6.3->tensorboard<2.1.0,>=2.0.0->tensorflow==2) (0.4.7)
Requirement already satisfied: oauthlib>=3.0.0 in /usr/local/lib/python3.6/dist-packages (from requests-oauthlib>=0.7.0->google-auth-oauthlib<0.5,>=0.4.1->tensorboard<2.1.0,>=2.0.0->tensorflow==2) (3.1.0)
Requirement already satisfied: requests>=2.0.0 in /usr/local/lib/python3.6/dist-packages (from requests-oauthlib>=0.7.0->google-auth-oauthlib<0.5,>=0.4.1->tensorboard<2.1.0,>=2.0.0->tensorflow==2) (2.21.0)
Requirement already satisfied: urllib3<1.25,>=1.21.1 in /usr/local/lib/python3.6/dist-packages (from requests>=2.0.0->requests-oauthlib>=0.7.0->google-auth-oauthlib<0.5,>=0.4.1->tensorboard<2.1.0,>=2.0.0->tensorflow==2) (1.24.3)
Requirement already satisfied: chardet<3.1.0,>=3.0.2 in /usr/local/lib/python3.6/dist-packages (from requests>=2.0.0->requests-oauthlib>=0.7.0->google-auth-oauthlib<0.5,>=0.4.1->tensorboard<2.1.0,>=2.0.0->tensorflow==2) (3.0.4)
Requirement already satisfied: idna<2.9,>=2.5 in /usr/local/lib/python3.6/dist-packages (from requests>=2.0.0->requests-oauthlib>=0.7.0->google-auth-oauthlib<0.5,>=0.4.1->tensorboard<2.1.0,>=2.0.0->tensorflow==2) (2.8)
Requirement already satisfied: certifi>=2017.4.17 in /usr/local/lib/python3.6/dist-packages (from requests>=2.0.0->requests-oauthlib>=0.7.0->google-auth-oauthlib<0.5,>=0.4.1->tensorboard<2.1.0,>=2.0.0->tensorflow==2) (2019.9.11)
ERROR: tensorboard 2.0.1 has requirement grpcio>=1.24.3, but you'll have grpcio 1.15.0 which is incompatible.
ERROR: google-colab 1.0.0 has requirement google-auth~=1.4.0, but you'll have google-auth 1.6.3 which is incompatible.
Installing collected packages: google-auth, tensorboard, tensorflow-estimator, tensorflow
Found existing installation: google-auth 1.4.2
Uninstalling google-auth-1.4.2:
Successfully uninstalled google-auth-1.4.2
Found existing installation: tensorboard 1.15.0
Uninstalling tensorboard-1.15.0:
Successfully uninstalled tensorboard-1.15.0
Found existing installation: tensorflow-estimator 1.15.1
Uninstalling tensorflow-estimator-1.15.1:
Successfully uninstalled tensorflow-estimator-1.15.1
Found existing installation: tensorflow 1.15.0
Uninstalling tensorflow-1.15.0:
Successfully uninstalled tensorflow-1.15.0
Successfully installed google-auth-1.6.3 tensorboard-2.0.1 tensorflow-2.0.0 tensorflow-estimator-2.0.1
In [1]:
import tensorflow as tf
print(tf.__version__)
2.0.0
The next code block will set up the time series with seasonality, trend and a bit of noise.
In [2]:
import numpy as np
import matplotlib.pyplot as plt
import tensorflow as tf
from tensorflow import keras
def plot_series(time, series, format="-", start=0, end=None):
plt.plot(time[start:end], series[start:end], format)
plt.xlabel("Time")
plt.ylabel("Value")
plt.grid(True)
def trend(time, slope=0):
return slope * time
def seasonal_pattern(season_time):
"""Just an arbitrary pattern, you can change it if you wish"""
return np.where(season_time < 0.4,
np.cos(season_time * 2 * np.pi),
1 / np.exp(3 * season_time))
def seasonality(time, period, amplitude=1, phase=0):
"""Repeats the same pattern at each period"""
season_time = ((time + phase) % period) / period
return amplitude * seasonal_pattern(season_time)
def noise(time, noise_level=1, seed=None):
rnd = np.random.RandomState(seed)
return rnd.randn(len(time)) * noise_level
time = np.arange(4 * 365 + 1, dtype="float32")
baseline = 10
series = trend(time, 0.1)
baseline = 10
amplitude = 40
slope = 0.05
noise_level = 5
# Create the series
series = baseline + trend(time, slope) + seasonality(time, period=365, amplitude=amplitude)
# Update with noise
series += noise(time, noise_level, seed=42)
plt.figure(figsize=(10, 6))
plot_series(time, series)
plt.show()
Now that we have the time series, let's split it so we can start forecasting
In [3]:
split_time = 1000
time_train = time[:split_time]
x_train = series[:split_time]
time_valid = time[split_time:]
x_valid = series[split_time:]
plt.figure(figsize=(10, 6))
plot_series(time_train, x_train)
plt.show()
plt.figure(figsize=(10, 6))
plot_series(time_valid, x_valid)
plt.show()
Naive Forecast¶
In [0]:
naive_forecast = series[split_time - 1:-1]
In [5]:
plt.figure(figsize=(10, 6))
plot_series(time_valid, x_valid)
plot_series(time_valid, naive_forecast)
Let's zoom in on the start of the validation period:
In [6]:
plt.figure(figsize=(10, 6))
plot_series(time_valid, x_valid, start=0, end=150)
plot_series(time_valid, naive_forecast, start=1, end=151)
You can see that the naive forecast lags 1 step behind the time series.
Now let's compute the mean squared error and the mean absolute error between the forecasts and the predictions in the validation period:
In [7]:
print(keras.metrics.mean_squared_error(x_valid, naive_forecast).numpy())
print(keras.metrics.mean_absolute_error(x_valid, naive_forecast).numpy())
61.827538 5.937908
That's our baseline, now let's try a moving average:
In [0]:
def moving_average_forecast(series, window_size):
"""Forecasts the mean of the last few values.
If window_size=1, then this is equivalent to naive forecast"""
forecast = []
for time in range(len(series) - window_size):
forecast.append(series[time:time + window_size].mean())
return np.array(forecast)
In [9]:
moving_avg = moving_average_forecast(series, 30)[split_time - 30:]
plt.figure(figsize=(10, 6))
plot_series(time_valid, x_valid)
plot_series(time_valid, moving_avg)
In [10]:
print(keras.metrics.mean_squared_error(x_valid, moving_avg).numpy())
print(keras.metrics.mean_absolute_error(x_valid, moving_avg).numpy())
106.674576 7.142419
That's worse than naive forecast! The moving average does not anticipate trend or seasonality, so let's try to remove them by using differencing. Since the seasonality period is 365 days, we will subtract the value at time t – 365 from the value at time t.
In [11]:
diff_series = (series[365:] - series[:-365])
diff_time = time[365:]
plt.figure(figsize=(10, 6))
plot_series(diff_time, diff_series)
plt.show()
Great, the trend and seasonality seem to be gone, so now we can use the moving average:
In [12]:
diff_moving_avg = moving_average_forecast(diff_series, 50)[split_time - 365 - 50:]
plt.figure(figsize=(10, 6))
plot_series(time_valid, diff_series[split_time - 365:])
plot_series(time_valid, diff_moving_avg)
plt.show()
Now let's bring back the trend and seasonality by adding the past values from t – 365:
In [13]:
diff_moving_avg_plus_past = series[split_time - 365:-365] + diff_moving_avg
plt.figure(figsize=(10, 6))
plot_series(time_valid, x_valid)
plot_series(time_valid, diff_moving_avg_plus_past)
plt.show()
In [14]:
print(keras.metrics.mean_squared_error(x_valid, diff_moving_avg_plus_past).numpy())
print(keras.metrics.mean_absolute_error(x_valid, diff_moving_avg_plus_past).numpy())
52.97366 5.839311
Better than naive forecast, good. However the forecasts look a bit too random, because we're just adding past values, which were noisy. Let's use a moving averaging on past values to remove some of the noise:
In [15]:
diff_moving_avg_plus_smooth_past = moving_average_forecast(series[split_time - 370:-360], 10) + diff_moving_avg
plt.figure(figsize=(10, 6))
plot_series(time_valid, x_valid)
plot_series(time_valid, diff_moving_avg_plus_smooth_past)
plt.show()
In [16]:
print(keras.metrics.mean_squared_error(x_valid, diff_moving_avg_plus_smooth_past).numpy())
print(keras.metrics.mean_absolute_error(x_valid, diff_moving_avg_plus_smooth_past).numpy())
33.45226 4.569442
In [0]: