Forecasting time series: Method Selection Im new to forecasting time series and Im looking for some advice on selecting the best method based on the analaysis of the graph.

I have the following data and based on the little knowledge I have, Im assuming it is a stationary time series because of the shape of the data and because of the result I got when performing a Dicker Fulley Test

Test Statistic                -6.560544e+00
p-value                        8.402824e-09
#Lags Used                     2.100000e+01
Number of Observations Used    1.164000e+03
Critical Value (5%)           -2.864026e+00
Critical Value (1%)           -3.435980e+00
Critical Value (10%)          -2.568094e+00
dtype: float64


That made me choose Arima with a p and q values of 1. However the result Im getting are pretty awful. Can anyone guide on how should I choose the adequeate method for forecasting and  if case ARIMA is a good choice, how should I tweak parameters to improve my results? The end goal is to predict the next month of data, so it might not be necessary to use all of the data.
You can try two different approaches:

1) Kalman filter, the method is battle-tested and has proven useful in many areas.

Resources:


Understanding the Basis of the Kalman Filter
kalman filter in pictures


2) Recurrent Neural Networks, the LSTM and GRU architectures are particularly interesting for time series predictions.

Resources:


RNN effectiveness
Understanding LSTMs


To do regression and predict future data points, you would need to build a training dataset consisting of a sequence of events. Let's say a value $x$ for every timestamp $t$.

Your data seems to have 1 dimension, so both the network input layer and the output layer would consist of 1 unit. You would then train your model to predict $(x_{t+1})$ given $(x_{t})$.

Let $M$ be our trained model and let's say you want to forecast a data point at time $k$ and you know the current value at time $t$.

$M(x_{t}) = (x_{t+1})$

$t = t+1$

$M(x_{t}) = (x_{t+1})$

$...$ increment $t$ and keep predicting until $t+1 = k-1$

$M(x_{t+1}) = (x_{k})$

Put in pictures this corresponds to:


(picture from Udacity lecture about Deep Learning)