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I have a time series data with the date and temperature records of a city. Following are my observations from the time series analysis:

  1. By plotting the graph of date vs temperature seasonality is observed.
  2. Performing adfuller test we find that the data is already stationary, so d=0.
  3. Perform Partial Autocorrelation and Autocorrelation with First Seasonal Difference and found p=2 and q=10 respectively.

Code to Train Model

model=sm.tsa.statespace.SARIMAX(df['temperature'],order=(1, 1, 1),seasonal_order=(2,0,10,12))
results=model.fit()

This fit function runs indefinitely and does not reach an output. I am running on a on Google Colab CPU.

How to fix this issue?

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  • $\begingroup$ Unless you have a really good reason for using stats models I suggest you to change to FB Prophet, it is an amazing and well documented library for advance time series forecasting. neuralprophet.com $\endgroup$ – Julio Jesus Mar 7 at 2:17
  • $\begingroup$ Statsmodels is very slow, you could try pmdarima: pypi.org/project/pmdarima or as suggested you could try fb prophet if you just want some time series fit reasonably well although it also can be quite slow when compared to other time series methods. $\endgroup$ – Tylerr Mar 7 at 22:50
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Assuming you have multiple cities in the dataframe. you can create some new features in the dataframe . For example , I created a few features below to try and match you PACF and ACF graphs .

df['lag_1'] = df.groupby(['city'])['temperature'].transform(lambda x: x.shift(1))

d=1

df['d_1'] = df['temperature'] - df['lag_1']

p = 1:

df['p_1'] = df.groupby(['city'])['d_1'].transform(lambda x: x.shift(1))

q = 1:

df['ma_1'] = df.groupby(['city'])['d_1'].transform(lambda x: x.shift(1).rolling(1).mean())

P=2 (and other terms)

df['lag_t12'] = df.groupby(['city'])['temperature'].transform(lambda x: x.shift(12))

df['lag_t24'] = df.groupby(['city'])['temperature'].transform(lambda x: x.shift(24))

.

.

.

df['lag_t120'] = df.groupby(['city'])['temperature'].transform(lambda x: x.shift(120))

Q=10 :

df['Q_10'] = df[col for col in df if col.startswith('lag_t')].mean()

After this try using LightGBM , XGBoost or other regression packages to regress against these newly created features with temprature as your target variable.

Alternatively , you can forego the ACF/PCF approach altogether and instead create bunch of commonly used features using :

  • shift
  • rolling mean
  • rolling standard deviations
  • max() , min() within groups

and regress against those and check which features minimize RMSE/AIC/BIC in your Regression Hyperparameters.

Since Cross validation is different in cases of Time Series,consider using TimeSeriesSplit in scikit-learn . Check-out this post in case you want to do grouped time series cross validation .

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