Deterministic vs stochastic trends

This video explains the difference between stochastic and deterministic trends. A simulation is provided at the end of the video, demonstrating the graphical difference between these two types of stochastic process.

I also provide code below in Matlab/Octave for anyone wanting to run these simulations.

clear; close all; clc;



n=10000; % Number of time periods
b=1;
rho=1; %The parameter on the lagged value of x
alpha=0.05; % The slope parameter

% Initialise x and y
x=zeros(n,1);
x(1)=0;
y=zeros(n,1);
y(1)=0;
% Generate the x and y series
for i = 2:n
x(i)=alpha+rho*x(i-1)+b*randn();
y(i)=alpha*i+b*randn();
end

% Plot the x and y series
zoom=1.0;
FigHandle = figure('Position', [750, 300, 1049*zoom, 895*zoom]);
plot(x, 'LineWidth', 1.4)
hold on

[abheeksinha]

Thanks a lot for the explanation. Here the the simulated R code if anyone needs it.

n=10000
b=1
rho=1
alpha=0.05


#Initialise x and y

x <- rep(0, n)
y <- rep(0, n)

for (i in 2:n)
{
x[i] = alpha+rho*x[i-1]+b*rnorm(1)
y[i]=alpha*i+b*rnorm(1)
}


# Plot the x and y series
plot(x, type="l", col="red")
lines(y, col="green")

[frankthetank]

Is there a video which explains te concepts that lead to stochastic/deterministic models?I also don't understand the error parameter. Is this a constant value? If it's a variable, on what is it dependent? What does iid mean?

[ivotavares]

+Ben Lambert, when you do the variance of the r.w. with drift, you're assuming that Var(X_0)=0, i.e. that the series has an initial fixed value? Otherwise, with an infinite past it would just diverge. Am I right?

[MFpermance]

Just to be sure (I may have skipped some important part), the deterministic trend is still a stochastic process right?

[odiseeacarmen]

homoskedastic and conditional and non-conditiional heteroskeastic nonstationarity means actually the stochastic trend? or am i wrong?

[smsm]

Hello sir, good job, good luck
Please, I have a series it is DS (of model 3: with constant and trend) at the level, and TS at the first difference; are we going to the second difference or not?
Ie is this series integer of order 2 or 1?
Cordially

[StephenGillie]

These videos are good, but very hard to hear. At maximum volume, this video is much quieter than most music videos. Can you increase the loudness?

[littlerainyone]

I can't read the Matlab code. Do you offer a download elsewhere?

[dunwantoknow]

Thanks a lot, it help to clarify my confusion (:

[tiggersmith]

I was with you for the first two think your brain is a different shape to mine.