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For Saturday the seasonal effect is the average of For the second Saturday, the value of Use the table above to work out by how much the moving mean is changing each day. To predict the value of the fourth Saturday, assume that the moving mean will continue to decrease by about 1 each day as in the table.

Draw a graph of the moving means and insert a trend line. Use the gradient of the trend line to predict future values: The trend line has been extended to go to the next Saturday. In this tutorial, we will discuss how to implement moving average for numpy arrays in Python. Use the numpy. What is being done at each step is to take the inner product between the array of ones and the current window and take their sum.

The following code implements this in a user-defined function. It is assumed to be a little faster. Another way of calculating the moving average using the numpy module is with the cumsum function. It calculates the cumulative sum of the array. This is a very straightforward non-weighted method to calculate the Moving Average.

The following code returns the Moving Average using this function.

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The subsequent code is a bit more protracted and can be seen in the Jupyter Notebook file , but still entirely comprehensible! Lower value is smoother. If you are inclined to, please have a look at the mathematical proof for EWMA.

There are six different values of a, our tuning knob, and it should be possible to see the lag versus wiggliness tradeoff. Going Further There are of course hundreds of different filter algorithms to choose from, and they all have strengths and weaknesses. Both the simple and exponentially weighted moving averages are sensitive to large bogus values, or outliers. The simple average is only effected as long as the large value is in the moving window, but the EWMA sees the effect trailing off continuously, and perhaps slowly.

If you know a lot more about the dynamics of the system, a Kalman filter or similar first- or second-order filters might help, but at the expense of more calibration. It was also pretty hard to initialise the filter and sometimes it would just shoot off into infinity!

One last thing that I really wanted to solve was to get a filter working for polar coordinates. Naive averaging fails here. From the smoothed graph the upward trend of increasing sales can be clearly seen. Seasonally Adjusted Data When the data has been smoothed and trends analysed, each value can be looked at for seasonal effects.

This is to see if the values are significantly different from what might be expected and to help make predictions. As the data is for days of the week a moving mean of 7 is chosen. Seasonal effect The seasonal effect is the average of the individual seasonal effects for a particular day. For Saturday the seasonal effect is the average of

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