How do I create a Linear regression model for a time series data?

Question

How do I create a Linear Regression Model for a time series data?

I've removed the datetime, and proceeded as the normal regression method but that showed an r-squared of -7. I have data from 13H1 to 17H2.

df:

UID BaselineHalf    Metric_Type Segment rateadj_amount_usd  CPI_Inflation    
Exports Fixed_Invstment GDP Govt_Growth Imports Industrial_Production    
Merchandise_Exports Merchandise_Imports Nominal_Retail_Sales     
Private_Consumption Real_Retail_Sales   WPI_Inflation
100130_Print HW 2013-12-31  Print HW    CANADA_PRINT_NAMED  2212.060000  
3.036892    5.99463 -1.890996   3.885646    2.970826    3.762586    4.716683     
-3.32253    -2.444949   10.148924   5.35529 7.001484    2.402204

    df1 = df[df['UID']== '100130_Print HW']
    x = df1[['CPI_Inflation', 'Exports', 'Fixed_Invstment', 'GDP', 
    'Govt_Growth',
   'Imports', 'Industrial_Production', 'Merchandise_Exports',
   'Merchandise_Imports', 'Nominal_Retail_Sales', 'Private_Consumption',
   'Real_Retail_Sales', 'WPI_Inflation']]
    y = df1['rateadj_amount_usd']
    X_train, X_test, y_train, y_test = train_test_split(x, y, test_size=0.2, 
    random_state=101)
    lm = LinearRegression()
    lm.fit(X_train,y_train)
    predictions = lm.predict(X_test)
    from sklearn.metrics import r2_score
    coefficient_of_determination = r2_score(y_test,predictions)

Answer 1

I see a general problem in your approach: you are trying to regress a time series but removed the time data and pulled a randomized sample from the data (with train_test_split()). However, the data points are stochastically dependent. Surely the data from a given year depends on the previous year to a very large extend. But the way you do it the model cannot use this information.

Therefore, your model performs very poorly as you can see from the R squared. Try it out using the time series data.