# Q: Defining Markov-Chain Probability Matrix States | Specific Academic Paper

I am working on a uni project, for which i will model synthetic electricity consumption time series using Markov-Chains. I am reading through current academic literature on that topic and came across an interesting paper (link below).

The authors use a 24x24 probability matrix for the different states that a household can be in, in terms of energy consumption. This makes sense, as there are 24 hours within a day. I think the values of the matrix describe the probability that a certain household is going to move from the current state of a given hour to the mean state of all datasets in the next hour. I am not completely sure on this though. So the unit of the matrix elements should be probably in kWh.

My question is how did they generate the matrix? I am not sure if the next sentence has something to do with it: "Bin sizes for sampling were chosen based on standard deviation (0.0837) and mean electricity consumption (0.5525kW) for a sample of 4,500 Irish dwellings"

The filled out 24x24 Matrix is not given in the paper, only the final results of the model.

If you want to take a look within the paper, ctrl+f this phrase: "Markov chain model using a 24x24 probability" and it should lead you to the part of the paper on page 5.

Citation: Duffy, Aidan & McLoughlin, Fintan & Conlon, Michael. (2010). The Generation of Domestic Electricity Load Profiles through Markov Chain Modelling.

link to the paper