negative values kernel density estimation

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ZHIMIN YAN 2022-12-20

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https://ww2.mathworks.cn/matlabcentral/answers/1881772-negative-values-kernel-density-estimation

评论： ZHIMIN YAN 2022-12-23

I have obtained the monthly temperature distribution using kernel density estimate. And using SVD(Singular Value Decomposition) and regression model, I forecast the monthly temperature distribution. But I found that some estimated kernel density values are negative. How to deal with these negative values?

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ZHIMIN YAN 2022-12-21

编辑：Torsten 2022-12-21

在 MATLAB Online 中打开

z.mat

This is z values. Thank you very much!!

zmat = load("z.mat");
z = zmat.z;
[U,S,V] = svd(z);
U1 = U(:,1);
Mdl = arima('Constant',0,'ARLags',1,'SARLags',12,'D',1,...
            'Seasonality',12,'MALags',1,'SMALags',12);
EstMdl = estimate(Mdl,U1);
 
    ARIMA(1,1,1) Model Seasonally Integrated with Seasonal AR(12) and MA(12) (Gaussian Distribution):
 
                 Value      StandardError    TStatistic      PValue   
                ________    _____________    __________    ___________

    Constant           0              0           NaN              NaN
    AR{1}        0.04126       0.054551       0.75636          0.44944
    SAR{12}      -0.1694       0.049563       -3.4179       0.00063099
    MA{1}       -0.81241       0.036031       -22.548      1.4186e-112
    SMA{12}     -0.78822       0.035602        -22.14      1.3097e-108
    Variance    0.003309     0.00019167        17.264        8.771e-67
numperiods = 11;
[Forecast,ForecastMSE] = forecast(EstMdl,numperiods,U(:,1));
Tempdiff_forecast = Forecast*S(1,1)*V(:,1)';

Adam Danz 2022-12-22

> So you mean that I should delete the negative values in z

No, I would take a step back and investigate. Do you expect there to be negative values in z? If not, then how did they get there? Perhaps something went wrong with your calculations of z or perhaps your expectations of what z should be aren't correct expectations. If you do expect there to be negative values in z or that negative values are possible, then I would re-think whether it is a problem that the forecast produces negative values.

If z isn't meaningful data and you're using z to poke around at the model, then it's completely fine to replace the negative values or use an entirely different set of data. But if z is meaningful data, you can't just delete some values because they are causing problems.

I don't know enough about what the data are or about the forecasting you're using to suggest the next steps.

ZHIMIN YAN 2022-12-23

z in my data is the difference between actual temperature kernel density distribution and average temperature kernel density distribution. So negative values in z are also meaningful data. And my purpose is to predict the temperature kernel distribution. Thank you very much!

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