Underlying model for prediction using different prediction variables

Question

I have time-series energy consumption data for a duration of one-month. The frequency of data is half-hourly. The features of dataset are

• temperature - temperature value at particular time instant
• humidity - humidity value at particular time instant
• timeofday - this corresponds to 48 half-hourly durations of a day.
• weekday - day of the week (value between 1 - 7)
• prevday1 - energy consumption at the same time-instant on previous day
• prevday2 - energy consumption at the same time-instant on a day before the previous day
• prev_instant1 - energy consumption at the previous time instant. For example, for 7 pm, previous_instant1 is 6:30 pm
• prev_2_hour - average energy consumption during the last two hours

Using these variable I need to forecast power (energy) consumption. The pairs plot of these variables is

I started with a linear model, but it seems that the model is performing very badly. I want to know is there any automatic technique, which can check all possible combinations of predictor variables and output the best fitted model. I can check all models (linear combinations, non-linear, splines etc) manually, but it will take huge time.

UPDATE

I am forecasting in real-time at a half-hourly rate (very short term forecasting). Also, I use separate models corresponding to different half-hours of the day. For example, In a day we have 48 half-hours so corresponding to each half-hour I have a separate model. For the whole process, I use following approach:

1. Create a training data set with above mentioned features. This training data set is of one month duration (30 days)
2. In the next step, I forecast for the next day (testing day) using specific models for each of 48 half-hour durations
3. At the end of the day, I retrain all my 48 models with recently updated data (recent historical 30 days)

Steps 2 and 3 continue till stopping condition. Stopping condition used is the no. of testing days. A screenshot of my training data is as:

head(training_data)

tail(training_data)

Answer 1

Have had the same problem before. Used Weka tool (http://www.cs.waikato.ac.nz/ml/weka/).

The approach:
• convert time of day into a nominal (non-numeric), eg bins numbered 0-47
• convert day of week into a nominal (non-numeric)
• use M5Tree to construct a model

The rules in the tree will pop out things like "if 0 < bin < 5:30am_bin" then ... which discriminates start of day

It is better with more than 1 month of data. There will only be 4 samples for certain days of the week, for example. So more months would be better. And in such case again converting month to a nominal value (non-numeric) lets the rules pick up seasonal and monthly changes.