# Why SARIMA has better accuracy on weekly dataset than on daily one?

I am studying time series right now. So, I have this dataset. My aim is temperature prediction.

I've found out that ARIMA can't work with long period seasonality. So, I've resampled daily dataset into weekly. Than I create an ARIMA with S = 52 and fit it. Here is a code (python):

import statsmodels.api as sm
import pandas as pd

df = df.resample('W').mean()

model=sm.tsa.statespace.SARIMAX(
df.meantemp,
order=(1, 1, 1),
seasonal_order=(2, 1, 0, 52)
).fit()


And here is the prediction and the test data (blue - test data, red - predictions):

As you see, the MSE is 6.08.

Later, I decided to use daily format with S = 365.25. I didn't find solution in python, but I found a fourier approximation in R. So, here my daily model (R):

require(forecast)
require(data.table)

y_train = ts(train[, 2], freq=365.25)

fit <- auto.arima(y_train, seasonal=FALSE, xreg=fourier(y_train, K=15))


And for some reason this works much worse:

I'm really sorry for such long introduction. My question is: why daily prediction works much worse than weekly?

• I'm not sure, but looks like the models you showed were fitted on test dataset. Perhaps I didn't make myself clear. I fit my models on Train.csv and both screenshots in my question - are models' evaluation on Test.csv. May 4, 2020 at 12:55