The equation is here 
with Forecasts here the next 21 days (444-464) 
reflecting possible anomalies in the future.
The equation is here with Forecasts here the next 21 days (444-464) reflecting possible anomalies in the future.
The equation is here with Forecasts here the next 21 days (444-464) reflecting possible anomalies in the future.
You should entitle it "How to use daily integer data that collectively may have a "fat tailed distribution" or more precisely a non
EDITED AFTER RECEIPT OF DATA:
I took your first product (AR) and blank-normal distribution in order to to predict daily data taking into accountfilled the missing dates and obtained 443 daily effects/weekly effectshistorical values (1/monthly effects4/day-of-the16-month3/21/17 ) 
. Since the series is short I disabled Holiday effects detection along with Monthly Indicators (although there was some evidence of this) and introduced the data to AUTOBOX ,week-of-the month et al as needed while my tool of choice. If one were to naively simulate simply based on the histogram then one would draw samples from here 
essentially showing no discimination for the day being awarepredicted/simualted. A more nuanced approach would be to model the data and partition historical variability to signal and noise with the noise being the conditional distribution as the basis for randomness/simulation 
. This is the histogram of trendserrors from a model which used DAILY EFFECTS as a predictor while isolating exceptional values and a level shifts and outliersshift. A summary of the descriptive statistics by day is here 
If your data may be affected by holidays, please so stateHere is the Actual and provideCleansed graph 
and the country information alongActual/Fit/Forecast graph 
The equation is here with Forecasts here the starting date. I suggest that you select just one of your series to present my analysisnext 21 days (444-464) reflecting possible anomalies in the future.
To illustrate , this is the forecast distribution/simulation for day 444 ( 1 period out ) 3/22/17 a Monday 
while this is for day 445 
. So simulating the future requires a prediction for the future as all days are possibly different in their expectations and an estimate of the uncertainty(randomness) around that prediction . Forecasts are made and then integerized because all of the history is reported as integers . Here is a pix of the output showing history and projections 
You should entitle it "How to use daily integer data that collectively may have a "fat tailed distribution" or more precisely a non-normal distribution in order to to predict daily data taking into account daily effects/weekly effects/monthly effects/day-of-the-month,week-of-the month et al as needed while being aware of trends and level shifts and outliers.
If your data may be affected by holidays, please so state and provide the country information along with the starting date. I suggest that you select just one of your series to present my analysis.
EDITED AFTER RECEIPT OF DATA:
I took your first product (AR) and blank-filled the missing dates and obtained 443 daily historical values (1/4/16-3/21/17 ) . Since the series is short I disabled Holiday effects detection along with Monthly Indicators (although there was some evidence of this) and introduced the data to AUTOBOX , my tool of choice. If one were to naively simulate simply based on the histogram then one would draw samples from here essentially showing no discimination for the day being predicted/simualted. A more nuanced approach would be to model the data and partition historical variability to signal and noise with the noise being the conditional distribution as the basis for randomness/simulation . This is the histogram of errors from a model which used DAILY EFFECTS as a predictor while isolating exceptional values and a level shift. A summary of the descriptive statistics by day is here
Here is the Actual and Cleansed graph and the Actual/Fit/Forecast graph
The equation is here with Forecasts here the next 21 days (444-464) reflecting possible anomalies in the future.
To illustrate , this is the forecast distribution/simulation for day 444 ( 1 period out ) 3/22/17 a Monday while this is for day 445 . So simulating the future requires a prediction for the future as all days are possibly different in their expectations and an estimate of the uncertainty(randomness) around that prediction . Forecasts are made and then integerized because all of the history is reported as integers . Here is a pix of the output showing history and projections