auto_arima straight line prediction python

Question

I know this has been asked a lot but I have checked everything and still don't understand. To start, I have a dataset of global temperatures averaged over years. There is a trend in the series and I use pmdarima ndiffs to give me the number of differencing. I use pmdarima auto_arima to get the model with the lowest aic value. But when I plot the predictions, I get a straight line with a trend. The model I use is:

size = len(avg_temp)
cutoff = int(size*0.7)
train = avg_temp[:cutoff]
test = avg_temp[cutoff:]    
model = pm.auto_arima(train, start_p=1, start_q=1,
                     max_p=10, max_q=10,
                     seasonal=False,
                     d=1, trace=True,  
                     suppress_warnings=True)

The order of the model obtained by auto_arima is (1, 1, 3). I read in some answers that the forecast of ARIMA is only to the value of q. But I have seen people forecasting bigger ranges of values. I checked for seasonality by using statsmodels seasonal_decompose and there was no seasonality.

My questions are: Am I doing something wrong? What can I do to improve it? and if it can't be improved how do I explain it?

Answer 1

Maybe you need a slight change in your code as follows:

from matplotlib import pyplot
from sklearn.metrics import mean_squared_error
from statsmodels.tsa.arima.model import ARIMA
from pmdarima.arima import auto_arima


def ARIMA_Model(history,test,coeff):
    predictions = list()
    # walk-forward validation
    for t in range(len(test)):
        model = ARIMA(history, order=(coeff[0], coeff[1], coeff[2]))
        model_fit = model.fit()
        output = model_fit.forecast()
        yhat = output[0]
        predictions.append(yhat)
        obs = test[t]
        history.append(obs)
    rmse = sqrt(mean_squared_error(test, predictions))
    return (rmse, predictions)


size = len(avg_temp)
cutoff = int(size*0.7)
train = avg_temp[:cutoff]
test = avg_temp[cutoff:]    
coeff = auto_arima(y=train, seasonal=False, m=0,error_action="ignore", suppress_warnings=True, trace=True)

ARIMA_rmse,ARIMA_predictions=ARIMA_Model(train,test,coeff)
pyplot.plot(test, color='black',label='Original Data')    
pyplot.plot(ARIMA_predictions, color='blue',linestyle='dashed',label='ARIMA')