ARMA(1,1) processes - introduction and examples

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In this video I explain what is meant by an ARMA(1,1) process, and provide a couple of examples of processes which could be modelled as thus.

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Thanks a lot. Im currently doing my master degree in economics. Your videos saved my life a couple of times during my studies.

pierre-oliviermathieu

For an assignment I was asked to write some R code to simulate an ARMA(p, q) process given the AR and MA coefficients. Working solely from the expression of the model in terms of Xt I came up with the following code in about an hour. Hopefully someone finds it useful -- or better! can point out any mistakes before I have to hand it in.

#!/usr/bin/Rscript --vanilla

# The code is simplified when we build {Xt} in reverse then return it re-reverse.
# Otherwise this ARMA simulation function is straight forward.

ARMA = function(phi, theta, n=100, init=0, burn=0)
{
m = n + burn # Optional burn-in
z = rnorm(m) # White noise sample

x = init
for (i in 2:m) # Generate the time series
{
# Autoregression component

p = min(length(x), length(phi)) # Prevent out-of-bounds
AR = sum(phi[1:p] * x[1:p])

# Moving-average component

q = min(i-1, length(theta)) # Prevent out-of-bounds
MA = sum(theta[1:q] * z[(i-1):(i-q)])

# Combined AR+MA component

new = AR + MA + z[i]
x = c(new, x) # x is built in reverse
}

# Truncate the burn-in
# Re-reverse x vector
# Return time series

ts(rev(x[1:n]))
}

JesseMaurais

I have a question. It is obvious that at time t, we have a shock due to E(t), but in the next time step and for the second example, can we strongly say that the curve goes up and then goes down by exponential decay? I mean in the next time step there are two different forces, rho and teta which are forcing in the opposite directions, so can't we say that the behavior of the curve depends on the relative amount of these two parameters? Thanks

rareclassicmovies

Does this not disregard the effect of E_t in the previous period (contained in pho*x_t-1)?

lastua

the ARMA model is explained differently for each different source i looked at. So confusing

marchern

thank you for your explanation, but I have a question please .i want to model my time series ( stock returns) with ARMA-GARCH. IN residual analysis, I found some p-values for the Q test (Ljung-Box), are significant and others not, should I consider or reject H0? It's normal ??? I continue my work ?? I must differentiate the series? to pass to the GARCH modeling. THANK YOU

guiriamine

Great video series about TS! Question: the y-axes of the two plots in the video are both the first order difference of the sales? or are they just sales? TIA!

charliean

if rho < 1, then why the chart line just decrease to what it was instead of keeping decreasing(rho<1 implies the decreasing trend line)

napolnzo

MA contains the error term, how come you assigned it another parameter ?

sudiptabanerjee

Thank you for this amazing video. I finally have an idea why ARMA is a good process to model ocean waves. Now JONSWAP is another model but it can be fitted with CARMA. I am reading this paper on it and I am very confused. Could you make a video about CARMA and how it expands on ARMA? And if I want to model something as a CARMA process, like say stochastic friction, where do I start? Do I start, like you did here by deciding what my rho and theta is? Can I then just write them in state space format and do normal calculations on them!

hediyehb

Thanks very much. Very helpful videos.... Could u please in next videos demonstrate ARFIMA and MS-ARFIM models?

Thanks

aq

HI Ben, thank you so much for this great video. I just have a question:
I'm using this model :
Y(t)=ρY(t-1)+β0+∑βi*X(i, t)+ε(t)
Which model is most appropriate to estimate it ?
Emergency ! and THANK YOU :)

lamineoussama

Would you kind also doing an video to explain what is arch and garch please?-?

chrislam

What is exactly (roh) ¶ in AR and theta in MA? Correlation coefficient? Slope?If yes how is it caluclated for each lagged values ?

adithyapai

Hi Ben, what do you think it would mean if roe and theta were equal? I saw it on a past exam paper and I didn't know the answer, so I came to this video.

MyMpc

I have an assignment on this which is proving painful, is there anyway i can email you for some assistance please

adeyinkaojedokun

Need practical lessons through Excel or by showing data.

ArunKumar-ybjn

Drop the frequent use of "sort of."

milescooper

i thought u were discussing arma game lol

exiled

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