So here are some great news: **an awesome book chapter about time series analysis! **

And here is the link I used: http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc41.htm

And I’m going to explore the notes about the content here, the best part of the introduction is one of the applications of time series analysis:

- Fit a model and proceed to forecasting, monitoring or even feedback and feedforward control.

But I didn’t know what feedback or feedforward control were, and the best I could find was made on this Q&A. As it’s mentioned, and what I’ve found is this:

- Feedback control: Given some data points, I try to predict/forecast the time series and then compare it with actual data received from the future to measure error and improve the adjustements.
- Feedforward control: I got really lost on this one, so I’ll research further.

So I moved foward on the chapter and they already mention a simple technique to reveal underlying trend, seasonal and cyclic components, it’s called **smoothing**. And there are two groups of them:

- Averaging Methods
- Exponential Smoothing Methods (why exponential?)

It starts focusing on the first one, and gives the example of **mean** as a predictor, but we can see in our minds that it’s a poorly predictor for a time series where there are the concepts of trends and etc, so I won’t go further here on that. But next comes seemed interesting:

**Single Moving Average**

The process is simple taking small subsets of the data and take the average of them, these small subests being successive data points. So imagine the following data points:

x = [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]

and we select the step of m=3, I get the first three data points and avarage them. Then I’ll try to predict the one at the end of the “time window”, per example:

3 + 4 + 5 = 12/3 = 4,

the prediction would be 5 – 4. The next one would then be:

4 + 5 + 6 = 15 /3 = 5, then: 6-5.

so I built a python script to calculate that, let’s see how it works, this is the code:

from statistics import mean data = [20, 25, 33, 15, 8, 13, 18] errors = [] average_list = [] time_window = 3 for point in data: average_list.append(point) if len(average_list) == time_window: print(average_list) errors.append(point - mean(average_list)) average_list.pop(0) errors_mean = [(x-mean(errors))**2 for x in data] print("MSE: "+ str(mean([error**2 for error in errors]))) print("MSE by mean would be:" + str(mean(errors_mean)))

You can check the results for yourself and you’ll see the improvement is gigantic on MSE (which the smaller is the best, if you don’t what MSE is, here is a link).

Thus, today this is my contribution, I’ll try to explore more of the book and provide new stuff tomorrow. See you all.

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