Exponential Smoothing predicts all null values

Question

I have written a program that should forecast the value using exponential smoothing. I have got data for 6 months (from April to September). Based on these 6 months, I want to forecast for the next 6 months (i.e., from October to March).

Here is my code:

import pandas as pd
import matplotlib.pyplot as plt
import numpy as np
from statsmodels.tsa.holtwinters import ExponentialSmoothing

d = {'Month':['April','May','June','July','August','September'],'Value':[2.868,7.205,13.349,20.115,22.769,23.981]}
df = pd.DataFrame(data=d)

model = ExponentialSmoothing(df['Value'],trend='mul',seasonal='mul',seasonal_periods = 6).fit()
predict = model.forecast(6)

However, when I see the predicted value its all are Nans. I am not sure where I'm making the mistake. Could anyone help in rectifying the issue?

Answer 1

Looking at the documentation, seasonal_periods is the number of periods in a seasonal cycle.

If you look at the equation for Holt-Winters (e.g., here), it includes a term for seasonality which is shifted by m steps (where m is equal to seasonal_periods). This means, that to make a prediction where seasonal_periods=6, you need to have the input value in the data 6 timesteps earlier.

Since the data only contains 6 data points there is no way to make any prediction.

Possible solutions:

• Is the data really seasonal with a period of 6? If not, remove the seasonal_periods argument or change it.
• Add more data to the dataframe. If you have just one more timestep with data then you will obtain actual predictions.