import pandas as pd

import numpy as np

import matplotlib.pyplot as plt

from statsmodels.tsa.ar_model import AutoReg

df=pd.read_csv('min_temp_data.csv',index_col=0,parse_dates=True)

X=df.values

print("shape of data",df.shape)

print("original dataset\n",df.head())

print('After extracting only temperature:\n',X)

shape of data (3650, 1)

original dataset

Temp

Date

1981-01-01 20.7

1981-01-02 17.9

1981-01-03 18.8

1981-01-04 14.6

1981-01-05 15.8

After extracting only temperature:

[[20.7]

[17.9]

[18.8]

...

[13.5]

[15.7]

[13. ]]

df.plot()

#df[:200].plot()

<AxesSubplot:xlabel='Date'>

check for stationarity

from statsmodels.tsa.stattools import adfuller

dftest=adfuller(df['Temp'],autolag='AIC')

#dftest

print('1. ADF',dftest[0])

print('2. P value',dftest[1])

print('3. Number of Lag',dftest[2])

print('4. Number of observations used for ADF Regression and Critical values Calculation',dftest[3])

print('critical values')

for key,val in dftest[4].items():

print('\t',key,":",'\t',val)

1. ADF -4.444804924611684

2. P value 0.0002470826300361156

3. Number of Lag 20

4. Number of observations used for ADF Regression and Critical values Calculation 3629

critical values

1% : -3.4321532327220154

5% : -2.862336767636517

10% : -2.56719413172842

dftest

(-4.444804924611684,

0.0002470826300361156,

20,

3629,

{'1%': -3.4321532327220154,

'5%': -2.862336767636517,

'10%': -2.56719413172842},

16642.822304301197)

from statsmodels.graphics.tsaplots import plot_pacf,plot_acf

pacf=plot_pacf(df['Temp'],lags=25)

acf=plot_acf(df['Temp'],lags=25)

split the dataset into train and test: testing: last 7 days

train=X[:len(X)-7]

#train

test=X[len(X)-7:]

#test

model=AutoReg(train,lags=10,old_names=False).fit()

print(model.summary())

AutoReg Model Results

==============================================================================

Dep. Variable: y No. Observations: 3643

Model: AutoReg(10) Log Likelihood -8375.514

Method: Conditional MLE S.D. of innovations 2.427

Date: Thu, 19 May 2022 AIC 1.780

Time: 11:36:47 BIC 1.800

Sample: 10 HQIC 1.787

3643

==============================================================================

coef std err z P>|z| [0.025 0.975]

------------------------------------------------------------------------------

const 0.9350 0.142 6.603 0.000 0.657 1.213

y.L1 0.6103 0.017 36.795 0.000 0.578 0.643

y.L2 -0.0832 0.019 -4.289 0.000 -0.121 -0.045

y.L3 0.0631 0.019 3.246 0.001 0.025 0.101

y.L4 0.0512 0.019 2.632 0.008 0.013 0.089

y.L5 0.0547 0.019 2.810 0.005 0.017 0.093

y.L6 0.0422 0.019 2.166 0.030 0.004 0.080

y.L7 0.0590 0.019 3.032 0.002 0.021 0.097

y.L8 0.0324 0.019 1.664 0.096 -0.006 0.070

y.L9 0.0502 0.019 2.585 0.010 0.012 0.088

y.L10 0.0360 0.017 2.175 0.030 0.004 0.069

Roots

==============================================================================

Real Imaginary Modulus Frequency

------------------------------------------------------------------------------

AR.1 1.0275 -0.0000j 1.0275 -0.0000

AR.2 0.9811 -0.7934j 1.2617 -0.1082

AR.3 0.9811 +0.7934j 1.2617 0.1082

AR.4 0.4192 -1.3007j 1.3665 -0.2004

AR.5 0.4192 +1.3007j 1.3665 0.2004

AR.6 -0.4338 -1.3906j 1.4567 -0.2981

AR.7 -0.4338 +1.3906j 1.4567 0.2981

AR.8 -1.3012 -0.8676j 1.5639 -0.4064

AR.9 -1.3012 +0.8676j 1.5639 0.4064

AR.10 -1.7501 -0.0000j 1.7501 -0.5000

------------------------------------------------------------------------------

print(len(train))

3643

pred=model.predict(start=len(train),end=len(X)-1,dynamic=False)

plt.plot(pred)

plt.plot(test,color='red')

print(pred)

[11.47679312 12.63726604 13.0574664 13.03378918 12.8259307 12.65767226

12.43273596]

calculate Error

from math import sqrt

from sklearn.metrics import mean_squared_error

rmse=sqrt(mean_squared_error(test,pred))

print(rmse)

1.563819622086097

making future prediction

pred_future=model.predict(start=len(X)+1,end=len(X)+7,dynamic=False)

print("The future prediction for the next week")

print(pred_future)

print('Number of prediction made:\t',len(pred_future))

The future prediction for the next week

[12.28608804 12.20309536 12.24915916 12.30618875 12.31199689 12.27225975

12.21843712]

Number of prediction made: 7