low_pass_filter.py

def low_pass_filter_anomaly_detection(df, 
                                      column_name, 
                                      number_of_stdevs_away_from_mean):
    """
    Implement a low-pass filter to detect anomalies in a time series, and save the filter outputs 
    (True/False) to a new column in the dataframe.
    Arguments:
        df: Pandas dataframe
        column_name: string. Name of the column that we want to detect anomalies in
        number_of_stdevs_away_from_mean: float. Number of standard deviations away from
        the mean that we want to flag anomalies at. For example, if 
        number_of_stdevs_away_from_mean=2,
        then all data points more than 2 standard deviations away from the mean are flagged as 
        anomalies.
    Outputs:
        df: Pandas dataframe. Dataframe containing column for low pass filter anomalies 
        (True/False)
    """
    #60-day rolling average
    df[column_name+'_Rolling_Average']=df[column_name].rolling(window=60, center=True).mean()
    #60-day standard deviation 
    df[column_name+'_Rolling_StDev']=df[column_name].rolling(window=60, center=True).std()
    #Detect anomalies by determining how far away from the mean (in terms of standard deviation)
    #each data point is
    df[column_name+'_Low_Pass_Filter_Anomaly']=(abs(df[column_name]-df[
                                column_name+'_Rolling_Average'])>(
                                number_of_stdevs_away_from_mean*df[
                                column_name+'_Rolling_StDev']))
    return df

##EXECUTE IN MAIN BLOCK

#APPLY LOW PASS FILTER (ROLLING AVERAGE+ 2 Z-SCORE FILTER) TO DETECT ANOMALIES
gasoline_price_df=low_pass_filter_anomaly_detection(df=gasoline_price_df, 
                                      column_name='Gasoline_Price', 
                                      number_of_stdevs_away_from_mean=3)
#Re-plot time series with color coding for anomaly column
scatterplot_with_color_coding(gasoline_price_df['Date'],
                                  gasoline_price_df['Gasoline_Price'], 
                                  gasoline_price_df['Gasoline_Price_Low_Pass_Filter_Anomaly'],
                                  'Date', 
                                  'Gasoline Price (Dollars Per Gallon)', 
                                  'Gasoline Prices, Color-Coded on Low-Pass Filter Anomalies')