The Error Bars of Forecasts in Time Series

[Former Member]

Hi,

The error bars are equal to twice the standard deviation computed on the Validation data set.

From above second record in my Forecasts Report, I could imply twice the standard deviation being (12718.944 - 8654.944) = 4064 and the standard deviation of error in the Validation data set being 4064/2 = 2032.

But in my Signal Anomaly Report,

The Error Standard Deviation is 1839.  It is not the same as the value  implied by the upper limit.

Could you help to explain me the reason that the two values of the error standard deviation are not consistency?

Thank you.

Max

[achab]

Hi Max,

Can you please share a little bit more details on where you are reading these values, as well as the underlying dataset?

Thanks & regards

Antoine

[Former Member]

Hi Antoine,

You could try the sample dataset R_ozone for time series and find the same situation.  The "Error Standard Deviation" in Other Performance Indicators section of Statistical Reports is not consistent with the implied error standard deviation from the View Forecasts.

Therefore, I would like to guess the situation not related with dataset.

Thank you for your asking.

Best regards,

Max

[achab]

Hi Max,

Update for you!

While the product is consistent, we will need to improve our documentation on this specific aspect.

In the product:

• Error bar should be considered as you said as either [Error_Max-Forecast] or [Forecast-Error_Min].
• Error bar is not equal to twice the standard deviation, it is equal to twice the mean square error (MSE).
• Mean square error value for each forecast is found in Performance Indicators/Forecasts Error Bars. I've done the maths on the ozone example and this matches.

The documentation here says on page 39:

Note - The error bars are equal to twice the standard deviation computed on the Validation data set.

while it should say

Note - The error bars are equal to twice the mean square error computed on the Validation data set.

Good catch, we'll change this.

Thanks for raising this point, best regards,

Antoine