An appropriate model for your data would require a remedy for the visually obvious change in error variance. 
Additionally there a few clear anomalies that need to be treated otherwise you are leaning on ARIMA and usually a bad ARIMA. There is agreement on the need for double differencinG but I suspect your AR(1) coefficient and MA(1) coefficient have nearly equal absolute value redundancy . Here is an alternative model 
with an AR polynomial that is "near" to a differencing factor (.8). Apologies to all for not precisely answering your question about the sign of the log-likelihood statistic.
EDITED to present the detection of the variance change , Here is a plot of the residuals before the variance change ( your model probably has a similar disappointing set of residuals ) 
leading to the following analysis 
. Since the data requires a Weighted Least Squares analysis summary statistics are not delivered as the metric has changed.