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Predict binary employment vector from history vectors

I have a set of binary vectors where each vector represents one day of employment in the house and consists of 48 elements (each element for 30 minutes a day). Each element can be 1, which means that the house was occupied and 0 for an unoccupied house.

My task is to predict the next day based on the history of the same days (Monday from Monday's history, etc.). So far, I have been using the hamming distance to find the 5 most similar days in history, and from these I calculate the employment probabilities as the average of these 5 numbers. When the probability is higher than some X, in my case 0.4, I predict that it is busy.

But is there a definitely more efficient way to do this, any algorithms that would capture the trend in history?

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Your approach sounds reasonable enough (it's called K-nearest neighbors or KNN), although I'm not sure if you are using the correct distance label (the distance is still in this day). Your method is quite sensitive to the exact structure of the day, and it will probably take a long time to adapt to things like the holidays, being perhaps hypersensitive in the first few hours of the day.

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