Introduction to ARIMA models

ARIMA Models in Python

James Fulton

Climate informatics researcher

Non-stationary time series recap

Forecast of differenced time series

Reconstructing original time series after differencing

diff_forecast = results.get_forecast(steps=10).predicted_mean

from numpy import cumsum

mean_forecast = cumsum(diff_forecast)

Reconstructing original time series after differencing

diff_forecast = results.get_forecast(steps=10).predicted_mean

from numpy import cumsum

mean_forecast = cumsum(diff_forecast) + df.iloc[-1,0]

Reconstructing original time series after differencing

The ARIMA model

Take the difference
Fit ARMA model
Integrate forecast

Can we avoid doing so much work?

Yes!

ARIMA - Autoregressive Integrated Moving Average

Using the ARIMA model

from statsmodels.tsa.arima.model import ARIMA

model = ARIMA(df, order=(p,d,q))

p - number of autoregressive lags
d - order of differencing
q - number of moving average lags

ARIMA$(p,0,q)$ = ARMA$(p,q)$

Using the ARIMA model

# Create model
model = ARIMA(df, order=(2,1,1))

# Fit model
model.fit()

# Make forecast
mean_forecast = results.get_forecast(steps=10).predicted_mean

Using the ARIMA model

# Make forecast
mean_forecast = results.get_forecast(steps=steps).predicted_mean

Picking the difference order

adf = adfuller(df.iloc[:,0])
print('ADF Statistic:', adf[0])
print('p-value:', adf[1])

ADF Statistic: -2.674
p-value: 0.0784

adf = adfuller(df.diff().dropna().iloc[:,0])
print('ADF Statistic:', adf[0])
print('p-value:', adf[1])

ADF Statistic: -4.978
p-value: 2.44e-05

Picking the difference order

model = ARIMA(df, order=(p,1,q))

Let's practice!

ARIMA Models in Python