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analysis.py
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analysis.py
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"""
Analysis of Sales data
Dataset
-------
The given dataset contains monthly total sales of a company for the period 2013-2016.
Objectives
---------
1. To analyse the sales data and understand the performance of the company.
2. Find patterns and construct a model to forecast future sales.
"""
from time_series import TimeSeries
# Imports for data visualization
import matplotlib.pyplot as plt
from pandas.plotting import register_matplotlib_converters
from matplotlib.dates import DateFormatter
from matplotlib import dates as mpld
# Seasonal Decompose
from statsmodels.tsa.seasonal import seasonal_decompose
# Holt-Winters or Triple Exponential Smoothing model
from statsmodels.tsa.holtwinters import ExponentialSmoothing
register_matplotlib_converters()
ts = TimeSeries('dataset/monthly_sales.csv', train_size=0.8)
print("Sales Data\n")
print(ts.data.describe())
print("\nHead and Tail of the time series\n")
print(ts.data.head(5).iloc[:, 1:])
print(ts.data.tail(5).iloc[:, 1:])
# Plot of raw time series data
plt.plot(ts.data.index, ts.data.sales)
plt.gcf().autofmt_xdate()
date_format = mpld.DateFormatter('%Y-%m')
plt.gca().xaxis.set_major_formatter(date_format)
plt.title("Sales Data Analysis (2013-2016)")
plt.xlabel("Time")
plt.ylabel("Sales")
"""
Seasonal Decompose of the time series
-------------------------------------
Seasonal decompose is a method used to decompose the components of a time series into the following:
- Level - average value in the series.
- Trend - increasing or decreasing value in the series.
- Seasonality - repeating short-term cycle in the series.
- Noise - random variation in the series.
The analysis of the components individually provide better insights for model selection.
"""
result_add = seasonal_decompose(
ts.data.iloc[:, 1], period=12, model='additive')
result_add.plot()
plt.gcf().autofmt_xdate()
date_format = mpld.DateFormatter('%y-%m')
plt.gca().xaxis.set_major_formatter(date_format)
result_mul = seasonal_decompose(
ts.data.iloc[:, 1], period=12, model='multiplicative')
result_mul.plot()
plt.gcf().autofmt_xdate()
date_format = mpld.DateFormatter('%y-%m')
plt.gca().xaxis.set_major_formatter(date_format)
plt.show()
"""
Observations from Seasonal Decompose
------------------------------------
1. The time series seems to roughly have a constant seasonality but has an overall **increasing trend**.
2. A slightly decreasing trend is observed till 2014-07 after that an increasing trend is observed.
Model Selection
---------------
From the above observations we can evidently conclude that **Holt-Winter additive model** would
be an appropriate choice as there is a constant seasonality component along with an increasing trend.
"""
# Scaling down the data by a factor of 1000
ts.set_scale(1000)
# Training the model
model = ExponentialSmoothing(ts.train, trend='additive',
seasonal='additive', seasonal_periods=12).fit(damping_slope=1)
plt.plot(ts.train.index, ts.train, label="Train")
plt.plot(ts.test.index, ts.test, label="Actual")
# Create a 5 year forecast
plt.plot(model.forecast(60), label="Forecast")
plt.legend(['Train', 'Actual', 'Forecast'])
plt.gcf().autofmt_xdate()
date_format = mpld.DateFormatter('%Y-%m')
plt.gca().xaxis.set_major_formatter(date_format)
plt.title("Sales Data Analysis (2013-2016)")
plt.xlabel("Time")
plt.ylabel("Sales (x1000)")
plt.show()
"""
Validation of the model
-----------------------
Let's do a brief comparison between the additive and the multiplicative models.
"""
ts = TimeSeries('dataset/monthly_sales.csv', train_size=0.8)
# Additive model
model_add = ExponentialSmoothing(
ts.data.iloc[:, 1], trend='additive', seasonal='additive', seasonal_periods=12, damped=True).fit(damping_slope=0.98)
prediction = model_add.predict(
start=ts.data.iloc[:, 1].index[0], end=ts.data.iloc[:, 1].index[-1])
plt.plot(ts.data.iloc[:, 1].index, ts.data.iloc[:, 1], label="Train")
plt.plot(ts.data.iloc[:, 1].index, prediction, label="Model")
plt.plot(model_add.forecast(60))
plt.legend(['Actual', 'Model', 'Forecast'])
plt.gcf().autofmt_xdate()
date_format = mpld.DateFormatter('%Y-%m')
plt.gca().xaxis.set_major_formatter(date_format)
plt.title("Sales Data Analysis (2013-2016)")
plt.xlabel("Time")
plt.ylabel("Sales")
plt.show()
# Multiplicative model
model_mul = ExponentialSmoothing(
ts.data.iloc[:, 1], trend='additive', seasonal='multiplicative', seasonal_periods=12, damped=True).fit()
prediction = model_mul.predict(
start=ts.data.iloc[:, 1].index[0], end=ts.data.iloc[:, 1].index[-1])
plt.plot(ts.data.iloc[:, 1].index, ts.data.iloc[:, 1], label="Train")
plt.plot(ts.data.iloc[:, 1].index, prediction, label="Model")
plt.plot(model_mul.forecast(60))
plt.legend(['Actual', 'Model', 'Forecast'])
plt.gcf().autofmt_xdate()
date_format = mpld.DateFormatter('%Y-%m')
plt.gca().xaxis.set_major_formatter(date_format)
plt.title("Sales Data Analysis (2013-2016)")
plt.xlabel("Time")
plt.ylabel("Sales")
plt.show()
print(model_add.summary())
print(model_mul.summary())
"""
Conclusion of the analysis
--------------------------
From the model summary obtained it is clear that the sum of squared errors (SSE) for
the additive model (5088109579.122) < the SSE for the multiplicative(5235252441.242) model.
Hence the initial assumption that seasonality is roughly constant and therefore choosing
additive model was appropriate.
Note: The forecast made using multiplicative model seems to be unrealistic since the
variance between the high and low on an average is 100000 which is somewhat unexpected in
real world sales compared to 63000 incase of additive model.
"""