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I have an hourly data which records how many customers visited to a restaurant. The part of it is like the below image: enter image description here

I'd like to predict visitors in next one or two hours using the previous data.

My question is

  • what do you think of my approach below?
  • what is the basic and promising approach for this problem?

(I know Box-Jenkins approach, but hope to know better approach.)

My approach is:

  1. Generate 'base function' representing basic trend which is common for all day
  2. Estimate the parameters of the 'base function' using previous data on that day

The bell curve (normal distribution) can be utilized as 'base function' and its mean and variance are estimated with previous data on the day.

I imagine the result of my approach is the red and green lines in the below figure: enter image description here

I think the limitation of my idea is

  • the bell curve might be too simple model to fit
  • difficulty to estimate the parameter of normal distribution (mu and sigma) with the data of the first several hours.

Edit (following @jdcaballerov's suggestion)

In my preliminary analysis. I've found the following tendency in my data:

  • The days different is tiny fluctuation and peak hour (not always 12pm) and the number of customers.
  • I could not find regularity for weekday vs weekend or Monday Tuesday,....
  • I've already plot hourly visitors (and I've shown in my question) and compared weekday and weekend. (I could not find regurarity on days different)
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    $\begingroup$ I think the question is too open. Anyway. It all depends on the number of data points and other considerations. I suggest before jumping over the problem try to understand the data with questions such as: How are the days different. Fridays, mondays, etc. Plot by visitors by hour, Plot by hour conditional on the day or weekday vs weekend,etc. Then you can select a model $\endgroup$ – jdcaballerov Nov 18 '15 at 15:53
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    $\begingroup$ You could try a seasonal arima (with weekdays as "seasons") $\endgroup$ – kjetil b halvorsen Nov 18 '15 at 16:03
  • $\begingroup$ @jdcaballerov Thank you for suggesting preliminary analysis. In my observation, the days different is tiny fluctuation and peak hour (not always 12pm) and the number of customers. I could not find regularity for weekday vs weekend or Monday Tuesday,.... I've already plot hourly visitors (and I've shown in my question) and compared weekday and weekend. $\endgroup$ – rkjt50r983 Nov 19 '15 at 2:40
  • $\begingroup$ @kjetilbhalvorsen Thank you for suggesting a specific technique. I'll try seasonal ARIMA later. If you have another idea seems better than Box-Jenkins such as ARIMA, plz let me know. (I mentioned that "I know Box-Jenkins approach, but hope to know better approach." in my question) $\endgroup$ – rkjt50r983 Nov 19 '15 at 2:52

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