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

Question

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 = pd.read_csv('data/DailyDelhiClimateTrain.csv', parse_dates=['date'], index_col='date')
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)

train <- read.csv("data/DailyDelhiClimateTrain.csv")
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?

Answer 1

I have examined your 2 data sets ... DAILY and WEEKLY and found that your model specification for DAILY is WAYOVERCOMPLICATED while your automatic arima approach was inadequate/deficient. Both data sets benefit from having level/step shifts and anomalies empirically identified with model

The Weekly series is here with model

IN general the results are VERY SIMILAR insofar as memory (arima structure) is omitted as it was found unnecessary to adequately characterize the series being analyzed.