Dear friends: I have a myriad of small time-series data sets, which are normally distributed (example: Daily electricity demand in a location by hours 1 thru 24. You could clearly observe that during peak hours there is high demand for electricity, and then it dies out during evening and night hours). If I plot the demand curves under normal distribution, I need to mathematically find a way to find the most-like shapes of the curves. My initial thought was to use Maximum Likelihood Function (MLE) to find the most like shapes because we know Mean and Standard Deviation of each data set. Is there any other commonly used methods within the quant community to solve mathematically this problem. Please note I am not a big fan of using Least Squares method (LSE) because it is prone to errors - i found data sets with similar sum of least squared error but their shapes were NOT similar. I appreciate your advise.
The curve does not represent a normal distribution, which is a random sample of observations, the peak representing the most likely value and the tails less and less likely value drawn from a random sample. A Normal distribution is probability model. Your data is an oscillation of values driven ultimately by the sun.
The question is not at all clear to me. The previous answers confirm that some clarification is needed.
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