Business Case - Price Forecasting - Autoregressive Integrated Moving Average Model (ARIMA)

Case Introduction

• Working at HIRC Inc., a real estate company, I had a hands-on experience in coordinating with the construction department to conduct a predictive analysis in price of the raw construction materials. By building an ARIMA model, the time series forecasting model, I successfully helped the construction department to generate better purchasing decisions and to reduce purchasing cost by 12%.


• This example shows a whole process of building an ARIMA model in python to predict the purchasing price of concrete, a construction material. Raw data used in the model is sample data.

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Data and Model Design

Import Libraries

libraries: pandas, matplotlib, scikit-learn, statsmodels

import pandas as pd
import matplotlib.pyplot as plt
from datetime import datetime
from sklearn.model_selection import train_test_split
from statsmodels.tsa.arima.model import ARIMA

Data Visualization and Descriptive Analysis

# define a function to transfer the type of 'Month' from string to date
def dateparse(x):
    return datetime.strptime(x, '%Y-%m')

# import data from csv
price = pd.read_csv('arima-sample-data-csv.csv', index_col=[0], parse_dates=[0], date_parser=dateparse)
price.head(10)

	Price
Month
2019-01-01	270
2019-02-01	150
2019-03-01	182
2019-04-01	120
2019-05-01	177
2019-06-01	165
2019-07-01	250
2019-08-01	244
2019-09-01	194
2019-10-01	133

# draw a graph using matplot function
def test_stationarity(data):
    #Determing statistical properties
    mean = data.rolling(window=12).mean()
    std = data.rolling(window=12).std()

    #Plot rolling statistics:
    original = plt.plot(data, label='Original')
    mean = plt.plot(mean, color='red', label='Rolling Mean')
    std = plt.plot(std, color='black', label = 'Rolling Std')
    plt.legend(loc='best')
    plt.ylabel('Purchase Price', fontsize=11)
    plt.title('Concrete Purchase Price 2019-2021')
    plt.xticks(fontsize=8)
    plt.show(block=False)

test_stationarity(price)

Results from Data Visualization

From the line chart above describing the relationship between months and purchasing price, we find that the data is in a nonstationary condition that its means, variances, and covariances change over time. Therefore, we need to transform nonstationary data into stationary data with a differencing method.

The nonstationary might be caused by:

Seasonality – during each quarter, we can see that there is a peak purchasing price.

Trend - the rolling means keep growing over the whole time period.

Differencing Method

# differencing the non stationary to stationary data
# by integrating of order 1
price_diff = price.diff(periods=1)
price_diff.plot()
plt.ylabel('Purchase Price after Differencing', fontsize=11)
plt.title('Concrete Purchase Price after Differencing 2019-2021')
leg = plt.legend(loc='upper left')
plt.show()   
# After differencing, the mean and other statistical properties return to constant
# Therefore, the parameter d in the ARIMA model should be 1

Training and Testing Sets

# split the testing and training data (80%=train, 20%=test, random state=10)
x = price.values
x_train, x_test = train_test_split(x, test_size=0.2, random_state=10)

ARIMA Model

# pick the ARIMA model with lowest AIC - choose the parameter p, d, q
import itertools
import warnings
warnings.filterwarnings('ignore')
p = range(10, 13)
q = range(0, 2)
d = range(1,2)
pdq = list(itertools.product(p, d, q))
smallest_aic = 10000
result_pdq = 0
for parameter in pdq:
    try:
        model_arima = ARIMA(x_train, order=parameter)
        model_arima_fit = model_arima.fit()
        if model_arima_fit.aic < smallest_aic:
            smallest_aic = model_arima_fit.aic
            result_pdq = parameter
    except:
        pass
print('These are parameters p,d,q with the lowest AIC:{}.'.format(result_pdq))

These are parameters p,d,q with the lowest AIC:(11, 1, 1).

# draw a graph with most fitted ARIMA model
model_arima = ARIMA(x_train, order=result_pdq)
model_arima_fit = model_arima.fit()
x_pred = model_arima_fit.forecast(steps=10)
plt.xlabel('Next Ten Time Periods', fontsize=11)
plt.ylabel('Price', fontsize=11)
plt.title('Price Forecasting for Next Ten Time Periods')
plt.plot(x_test, label='Actual Price')
plt.plot(x_pred, label='Predicted Price', color='red')
plt.ylim(0, 1000)
leg = plt.legend(loc='lower left')
plt.show()

# the summary of the most fitted ARIMA model 
print('Function Related Information')
print('AIC Number with Most Fitted ARIMA Model', model_arima_fit.aic)
print('-------------------------------------------------------------')
print('Predicted Price for the Next Ten Time Period', x_pred)

Function Related Information
AIC Number with Most Fitted ARIMA Model 338.47178354139584
-------------------------------------------------------------
Predicted Price for the Next Ten Time Period [357.03912331 539.09632475 320.97851364 369.61425201 265.9263721
 152.21175181 426.33373751 359.75924127 363.63837398 431.91655858]

Conclusion

We can predict the overall trend of the purchasing price for now. However, we still need more data to train the model and improve the accuracy of prediction for the model.