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Is this picture below indicating a form of heteroscedasticity? According to the definition of heteroscedasticity, heteroscedasticity exists when the variance is not the same. But here the variance is the same but the average increases.

enter image description here

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    $\begingroup$ The conditional variance is not constant at the left hand end of that display - between 0 and 0.05 on the x-axis the spread of the residuals increases quite clearly. $\endgroup$
    – Glen_b
    Commented Feb 15, 2015 at 9:52
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    $\begingroup$ Jdging variance from scatter plots is often difficult. In addition to edge problems as mentioned by @Glen_b, overplotted points can be consistent with inconstant variance, even when the pattern looks the same. You should calculate and plot variance too. All that said, your most obvious problem is the overall tilt of the residual plot. It appears also that you have many tied values in the response. For better advice, you would need to tell us much more about the data and your model, but you may be fitting a linear model when the observed response cannot be negative. Log or logit link? $\endgroup$
    – Nick Cox
    Commented Feb 15, 2015 at 9:59

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Non-constant variance in the residuals can arise as the result of different Gaussian violations. For example if the residual series has Pulses/Seasonal Pulses/Level Shifts or Local Time trends the variance of the errors can exhibit non-constancy. If there is auto-correlation in the residuals then this will lead to a non-constant error variance . If the model parameters vary over time this can lead to non-constant error variance. If the error variance is proportional to the expected value then this leas to non-constant error variance. If the error variance changes deterministically at different points in time this also is a de facto case of non-constant variance. If the variance of the errors can be represented by an ARIMA model this is also a case of non-const variance. The conclusion is that one needs to evaluate some of the alternative states-of-nature in order to determine that approach that is minimally sufficient. As @nick states one might need to actually have more information and nearly always in my opinion the raw data.

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  • $\begingroup$ Glad we agree on the general points. This assumes that the data are time series; that is not mentioned either way. The Gaussian is unlikely to be a reference distribution for this thread as the data appear to be bounded as necessarily positive. Again, the absence of a full description inhibits a really good response. $\endgroup$
    – Nick Cox
    Commented Feb 16, 2015 at 0:54
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The fact that your residuals are trending might suggest an issue of autocorrelation rather than heteroskedasticity (whether they are heteroskedastic or not, which they may well be and which could be tested by, say, White's test),

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