I can decompose the timeseries data using this way -
from statsmodels.tsa.seasonal import seasonal_decompose
decomposition = seasonal_decompose(ts)
trend = decomposition.trend
seasonal = decomposition.seasonal
residual = decomposition.resid
My question is how to covert this residual value to original value. So that I can use them for predicting future value.
I tried to add original trend and seasonality back but doesn't work well. So when I am comparing the predicted result with original result, I just used predicted result with residual.
efrom statsmodels.tsa.seasonal import seasonal_decompose
# trend, seasonality are separated out from data, and we can model the residuals
decomposition = seasonal_decompose(ts_log)
trend = decomposition.trend
seasonal = decomposition.seasonal
residual = decomposition.resid
# AR model
model = ARIMA(ts_log, order=(2, 1, 0))
results_AR = model.fit(disp=-1)
plt.figure(figsize=(20,10))
plt.plot(ts_log_decompose)
plt.plot(results_AR.fittedvalues, color='red')
result = (results_AR.fittedvalues-ts_log_decompose)**2
result.dropna(inplace=True)
plt.title('Decompose RSS: %.4f'% sum(result))
plt.show()
I tried AR, MA, ARIMA models and found AR model had lowest RSS. So now, I am doing forecasting with AR model.
predictions_AR = pd.Series(results_AR.fittedvalues, copy=True)
print predictions_AR.head()
plt.figure(figsize=(20,10))
plt.plot(series, color='red')
plt.plot(predictions_ARIMA, color='green')
result = (predictions_AR-residual)**2
result.dropna(inplace=True)
plt.title('RMSE: %.4f'% np.sqrt(sum(result)/len(series)))
plt.show()
It works well:
If you want to check all my code: https://github.com/hanhanwu/Hanhan_Data_Science_Practice/blob/master/sequencial_analysis/try_LSTM.ipynb
Just Scroll Down to decompose method
If you're doing an additive model, you just add up the trend, seasonal, and residual components, to get back to the original values. The end result is your original data, so there's not a lot of value in backing into it. The residual is what is left of your original data after taking into account the trend and seasonal effects. It's like linear regression, where the predicted value plus the residual returns your actual outcome for the dependent variable.
