How to run a regression of lognrnd?

I have a vector with random data log-norm distributed and I need to run a regression of this.

[the cyclist]

Do you just have one variable that you want to fit a lognormal distribution to, or do you have two variables where you need to fit a regression line between them?

[Fernanda Suarez Jaimes]

Thank you for your promnt reply!

I have two time series, one normally distributed (normrnd) and the second one log-norm distributed (lognrnd)

I need to run a regression model for both of them X over Y

This is my dataset

%Time Vector
xtime1= [1:1:42000]'; %daily
xtime2= [1:1:6000]'; %weekly

%Time Series 1- daily entries
%comand randn generats 42000 random numbers that are normaly distributed. 
rng('default')
time_series1=normrnd(0,1,42000,1);

%generating time series with 6000 entries log-normal distributed
%the code for this distribution is based on the code available at
%mathworks.com

rng('default');  % So that numbers can be repeated
time_series2 = lognrnd(0,0.25,6000,1); %generating time series with mu set to zero and sigma 0.25

[the cyclist]

You are using the word "regression", which suggests that you are trying to find the relationship between two variables. Usually, that would mean that you have

y = f(x) + error

and you would have the same number of elements in your x vector and your y vector.

But that doesn't seem right, in your example. Are you actually just trying to fit two different distributions (one a normal, and the other a lognormal)?

[Fernanda Suarez Jaimes]

Yes, correct. The thing is that I transformed the time_series1 into a new "weekly" time series with 6,000 elements as well. So I can fit the two distributions together. Like this

%Converting the 'daily' ts to a  to a 'weekly' one
arrayts1 = padarray (time_series1, [ceil(numel (time_series1) / 7) * 7 - numel(time_series1) 0], 0, 'post' );
time_series3 = mean (reshape (arrayts1, 7, []), 1);

Then in the Y axis are the random valued and in the X axis are the time values.

I need to get a regression of X over Y.

This is what I have so far:

scatter(time_series2,time_series3,'.') % plot the data points
hAx=gca; hAx.XScale='log'; % on semilog x axis
b=polyfit(log(time_series2),Y,1); % fit response to log(independent) Y is the meanleast square value given by the fit for the above specific dataset
yHat=polyval(b,log([min(time_series2) max(time_series2)]))  % remember, it's log in X
hold on
plot([min(time_series2) max(time_series2)],yHat,'r-')

[Fernanda Suarez Jaimes]

This is another option I have. The issue is that we need to do a regression of a time series. Therefore, the result of the model is not significant as it is near 0,05.

logarithms_ts2=log(time_series2); %calculating logarithm of the values in order to use GLM fuction
[regression2,dev,stats] = glmfit(xtime2,logarithms_ts2,'normal');
regression2=fitglm(xtime2,time_series2) %regression of time series 2

Answer 1

[Steven Lord]

It sounds like you want the lognfit function.

[Fernanda Suarez Jaimes]

You mean something as this?

rng ( 'default' );  % So that numbers can be repeated
time_series2 = lognrnd (0,0.25,6000,1); % generating time series with mu set to zero and sigma 0.25
[pHat,pCI] = lognfit(time_series2,0.01)

The result I get is this:

pHat =

    0.0017    0.2494

pCI =

   -0.0066    0.2437
    0.0100    0.2554