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I'm new to this forum and I'm quite new to forecasting.
Currently I'm trying to learn the basics about exponential smoothing, ARIMA etc. Now I want to forecast the total energy consumption of a rather small company at the end of the month. You can see a typical power load profile for a full week in this image.

Power load profile for a complete week

The consumed energy of a month would be the integral over the entire load profile of a month. The weekdays have a strong correlation but the weekend is totally different. I have historical data for more than a year. Also there might be a small long term upwards trend. Every month the goal is to forecast the energy at the end of the month by means of the already passed days in this month and any data from previous (complete) months.

My question: Which forecasting method(s) do you consider suitable for such a case? Which methods I should study?

Edit:

I should have stated that this is a research project for a software development. We have a software for data aquisition from proprietary measuring devices and a new software for visualization that we would like to equip with some forecasting functionalities.

During the coming year we want to investigate several forecasting methods/possibilities and learn as much as possible. The quality or accurateness is not the primary goal at the moment. At a later time we may surely want to use a product like Autobox. Currently we would like use R for analysis and try to implement some things in the software ourselves, most likely by using open source libraries for the algorithms.

It's not the goal to have the best solution from the start on but rather to encounter the shortcomings of easier methods and advance to better solutions.

So I should maybe rephrase my question: What are the forecasting methods to start with for these data? In which direction should we go? Should we handle weekdays and weekends completely separate?

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This data is very similar to passenger data on the Paris subways that I had previously studied. Hourly activity (aside from the lead and lag effects of holidays) is somwehat consistent for weekdays but quite different patterns emerge on the weekends. Trends and level shifts along with significant changes in day-of-the-week patterns also are opportunities for good software analytics. One needs to incorporate not only hour-of-the-day BUT day-of-the-week structure and sometimes week-of-the-month and month-of-the-year patterns. Simple minded techniques which include separate and totally independent analyses of data like this just don't work. I suggest that you contact the folks at Automatic Forecasting Systems who have developed very sophisticated approaches to this thorny but very common time series problem. You can get them via http://www.autobox.com/cms/ . I was one of the developers of this system. In closing one also has to deal with anomalies, possible changes in parameters over time and changes in error variance over time. AUTOBOX routinely deals with these vexing problems/opportunities. If you would like to share your data , I would be happy to show you the art of the possible.

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  • $\begingroup$ Wow, I have never received such a quick reply with that much information :-) Thanks for that. I edited my question with a little more information. Of course you can have the data. I have prepared three months of data as a csv but I don't know how to send it to you via StackExchange, any idea? $\endgroup$ – NicolasR Aug 14 '14 at 21:49
  • $\begingroup$ 36 months might be more appropriate to pick up seasonal factors i.e. weekly/monthly effects . You can post the data to dropbox dropbox.com/business/… . Please include a value for all hours for all days . If for some reason you don't have a full audit simply average values around the missing points. For example if you are missing day x use average the values for x-7 and x+7 $\endgroup$ – IrishStat Aug 14 '14 at 23:41
  • $\begingroup$ First of all: thanks for your help! I will try to get data for as many months as I can tomorrow. I am currently not sure how to guarantee that there are no missing values. We measure every 15 minutes, that makes almost 3000 values a month, so it's hard in a spreadsheed application to check whether the data are complete. Do you know of any way to automate the averaging for missing values? $\endgroup$ – NicolasR Aug 15 '14 at 2:22
  • $\begingroup$ I would suggest using hourly data and perhaps 1 year of data thus 365x24 total values should suffice. There is no easy way to deal with missing values. If it is a problem for you I might be able to write a script BUT it is important that you provide 0.0 for those missing points. In other words the file should have 24x365 records, hours within days. $\endgroup$ – IrishStat Aug 15 '14 at 9:10
  • $\begingroup$ on second thought if you can get multiple years (e.g. 3 years ) that would be better. Prepare an excel file with 24 columns and as many rows as you can ...oldest to newest . $\endgroup$ – IrishStat Aug 15 '14 at 9:35
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As @IrishStat states, it is important to model whole time series and not to try artificially subset these. Time series do exhibit linear and non-linear structures and time dependencies.

Whe have modeled hourly time series by transfer function methods which are also called ARIMAX methods. Our software is not so advanced as Autobox (IBM SPSS Modeler), but sometimes it gives almost same results.

Here is also a link to the study with hourly time series of district heating system which was modeled via Matlabs ARX-model (same as transfer function model).

http://www.diva-portal.org/smash/get/diva2:461661/FULLTEXT01.pdf

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  • $\begingroup$ Thanks for your reply and the link. Is it correct that ARIMAX/"Transfer function models" could also be used to include correlation of my electric load data with temperature (exogenous variable)? It seems plausible that there is a correlation so I would like to let this information enter the model (whatever model is suitable). $\endgroup$ – NicolasR Aug 18 '14 at 21:12
  • $\begingroup$ @NicolasR, yes it can be easily done. Text in my link implemented district heating load model as a function of past values of load, temperature and windiness. $\endgroup$ – Analyst Aug 20 '14 at 5:11
  • $\begingroup$ Am I correct that your solution did not automatically test for and detect changes in levels,changes in local time trends, changes in parameters and changes in error variance and the optimal lead/lag structures for your two input series. $\endgroup$ – IrishStat Aug 20 '14 at 13:57
  • $\begingroup$ @IrishStat , I doubt that Matlab does this automatically, though I do not personally use Matlab. It is most used engineering software in some industries. $\endgroup$ – Analyst Aug 26 '14 at 5:30

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