Modeling a time series with diminishing seasonality I have a time series data with its ACF shown below. The time unit is day(s).

What looks intriguing for me is that there seems to be a peaks at every 7 or 8 lags, and it looks like there is a seasonal trend but the trend diminishes as lags increase.  I use auto.arima() to select the best-fit ARIMA process according to information criteria, and below is an ACF of the residuals of a model with ARIMA(2,0,1) with non-zero mean:

While the pattern is weaker after ARIMA(2,0,1), it is still discernable and I wonder what would be the best way to model this trend. I have tried to  use dummies to address seasonality such as:
Week days
data$wday <- wday(dataset$time)
season <- lm(data$variable ~ factor(data$wday))
pacf(season$residuals)

Month
data$month <- month(data$time)
season <- lm(data$variable ~ factor(data$month))
pacf(season$residuals)

Quarters
data$quarter <- quarter(data$time)
season <- lm(data$variable ~ factor(data$quarter))
pacf(season$residuals)

But the pattern is still quite discernable in all cases. 
For time series practitioners on the forum, are there other ways that you would use to model this data? The ARIMA(2,0,1) passes the Box.test. But I am just not feeling satisfied as it looks like something associated with time is  still going on in the residual ACF.
Attachment: here is a link to a sample csv file.
 A: When you use a drug (or a piece of software like auto.arima you should read the warnings on the label ... for example auto.arima based upon my experience is very suspect when dealing with real world data that has outliers/anomalies or level shifts or deterministic time trends. Here is a plot of your data  . An additional warning is don't use if you have lots and lots of zeroes  . An additional warning is that it is assumed that there are no fixed effects like days-of-the-week , weeks of the month or monthly effects or Holiday Effects . Your data appears to have both monthly effects and Holiday Effects and a possibly spurious one-day-of-the-month effect .
New inexperienced time series analysts often with an econometric training usually know nothing or very little of these things (assumptions). You inadvertently are using the wrong analytical (although free) software in my opinion. Here is the model summary taking into account memory (non-existent) , monthly effects , holiday effects , one particular day of the month) and anomalies is here . 
In closing one might carefully look at https://www.quora.com/What-are-some-skills-nuances-that-software-engineer-turned-data-scientists-lack-that-statisticians-ML-PHDs-possess/answer/Daniel-Tunkelang?ref=fb_page .
The whole idea here is to educate new and old users on the complexities of real-world time series analysis and to shed light on solutions that may not be general enough to be routinely used. My experience tells me (withou seeing your coefficients) that your (3,0,3) or (2,0,1) are just artifacts of fitting versus modelling and most probably has self-cancelling structure i.e. redundant ARMA structure . 
In response to @Whuber's excellent question , asking for details (always a good idea !):
@whuber Identification of  daily seasonality is accomplished in two possible ways 1) by examining the ACF /PACF for significant structure (ARIMA seasonality) at lags 7.14 etc. or 2) by attempting to incorporate 6 seasonal /fixed dummies representing days-of-the-week . Neither was found to be useful /significant in this case. In terms of Monthly seasonality this was detected by simple trial and error, i.e. setting up the 11 monthly indicators and doing a step-down. The Holiday seasonal factors (lead, contemporaneous and lag) were also found via a heuristic data-based search process yielding two holiday/seasonal variables Christmas and Mardi Gras) . The day 14 effect was also found by a search/trial and error approach. Thus FOUR distinctly different "seasonal factors" were evaluated with only the ARIMA seasonality totally rejected. auto.arima in my experience only tries to find ARIMA seasonality by a list-based trial and error rather than a data-based trial and error.

