Arima Forecasting - Presentation by Sera Cresta, Nora Alosaimi and Puneet Mahana. Presentation for CS 6212 final project in GWU during Fall 2015 (Prof. Arora's class)

1. ARIMA
FORECASTING
ALGORITHM
1
Team
Members:
Sera
Crasta
Nora
Alosaimi
Puneet
Mahana
SERA/NORA/PUNEET
CS6212/ARORA/FALL
2015

2. Defini5on
ARIMA
-­‐
(A)uto(R)egressive
(I)ntegrated
(M)oving
(A)verage
models.
• Auto
Regressive
–
dependency
of
a
value
of
a
dataset
on
combinaKon
of
previous
values
of
the
same
dataset
• Integrated
–
CombinaKon
• Moving
average
–
analysing
past
forecast
errors
to
predict
future
values
A
forecasKng
technique
thus
projects
the
future
values
of
a
series
based
enKrely
on
its
own
inerKa.
SERA/NORA/PUNEET
CS6212/ARORA/FALL
2015
2

3. Why
is
Arima
Forecas5ng
important?
• Businesses
need
to
adjust
with
changing
market
trends
and
thus
its
management
need
to
predict
what
may
happen
in
future
with
greater
accuracy
to
avoid
losses.
• TradiKonal
methods
–
expert
advice,
panel
discussions.
• QuanKtaKve
Method
–
Arima
ForecasKng.
• EsKmaKng
the
Kme
delays/
lags
in
the
ongoing
processes.
• ForecasKng
the
economic
growth.
• Models
relaKonships
using
data
collected
over
Kme
-­‐
prices,
GDP,
quanKKes,
sales.
SERA/NORA/PUNEET
CS6212/ARORA/FALL
2015
3

4. Algorithm
Outline
Arima
Forecas5ng
approach:
1. Choose
a
dataset
to
be
forecasted
and
plot
the
data
against
Kme.
2. Analyse
the
plot
to
see
if
it
is
staKonary
with
Kme.
3. If
necessary,
difference
the
data
unKl
it
appears
staKonary
4.
Plot
autocorrelaKon(ACF)
and
parKal
autocorrelaKon(PACF)
of
the
differenced
data
and
esKmate
possible
model
parameters
5. Calculate
AIC
values
for
all
model
parameters
to
search
for
be^er
model
6. Plot
the
residual
of
the
model
parameters
obtained
to
verify
that
no
lag
occurs
for
them.
7. If
lag
occurs
in
residual
plot,
try
another
esKmated
model
parameters
unKl
we
get
a
good
residual
plot.
8. Once
a
good
residual
is
obtained,
calculate
forecast.
SERA/NORA/PUNEET
CS6212/ARORA/FALL
2015
4

5. Algorithm
Pseudo
Code
1.Plot(dataset)
while(graph
is
non-­‐staKonary
=
True)
{smoothen
graph
to
make
it
staKonary}
2.
ACF/PACF(StaKonary
Graph)
3.
EsKmate
all
possible
model
parameters
4.
Calculate
AIC
values
of
all
model
parameters
5.
plot
(residual
of
model
parameters)
if(residual
graph
with
no
lag)
{Forecast
Dataset
with
these
parameters}
else
choose
other
esKmated
model
parameters
and
repeat
step
3
SERA/NORA/PUNEET
CS6212/ARORA/FALL
2015
5

6. Forecas5ng
Result
SERA/NORA/PUNEET
CS6212/ARORA/FALL
2015
6

7. Comparing
Arima
with
other
techniques
SERA/NORA/PUNEET
CS6212/ARORA/FALL
2015
7

8. Forecast Accuracy Results
SERA/NORA/PUNEET
CS6212/ARORA/FALL
2015
8
METHOD
Mean
error
Root
mean
square
error
Mean
absolute
error
Mean
absolute
scaled
error
Mean
9.128060
756.3431
619.3957
1.739531
Naive
11.2086
495.6456
356.0705
1.000000
Drie
-­‐2.002087
496.345
358.0791
1.005641
Arima
6.649148
324.172
243.8181
0.7016939

9. Conclusions
Arima
Algorithm:
•
Arima
technique
is
more
accurate
than
tradiKonal
forecasKng
techniques.
• PracKcal
and
useful.
LimitaKon:
• Require
historical
data
–
the
larger
the
dataset,
the
be^er
the
forecast
ApplicaKon:
• Manufacturing
Industry.
• Sales
department.
• Finance
Department.
SERA/NORA/PUNEET
CS6212/ARORA/FALL
2015
9

10. Appendix
Source
Code:
For
non-­‐seasonal
dataset
Arima
(p,
d,
q)
where
p,
d,
q
are
model
parameters
For
Seasonal
Dataset
Arima
(p,
d,
q)
(P,
D,
Q)
where
p,
d,
q
are
non
seasonal
parameters
and
P,
D,
Q
are
seasonal
parameters
SERA/NORA/PUNEET
CS6212/ARORA/FALL
2015
10

11. Appendix
Arima
Forecas5ng
in
R
library(forecast)
library(fpp)
#forecas5ng
plot(sunspotarea,
main=
"
Original
Dataset")
sunspotarea1=diff(sunspotarea)
plot(sunspotarea1)
acf(sunspotarea1)
acf(sunspotarea1,
plot=FALSE)
pacf(sunspotarea1)
pacf(sunspotarea1,
plot=FALSE)
fit<-­‐Arima(sunspotarea,
order=c(2,1,5))
tsdisplay(residuals(fit))
plot(forecast(fit,
h=25),
main="ARIMA
FORECASTING",
xlab="Kme",
ylab="sunspotarea")
#Accuracy
checking
sun
<-­‐
window(sunspotarea,
end=2000)
plot(sun,
xlim=c(1874,2015))
lines(meanf(sun,h=15)$mean,
col=4)
lines(rwf(sun,h=15)$mean,
col=2)
lines(rwf(sun,drie=TRUE,h=15)$mean,
col=3)
legend("toplee",
lty=1,
col=c(4,2,3),
legend=c("Mean
method","Naive
method","Drie
method"))
lines(sunspotarea)
SERA/NORA/PUNEET
CS6212/ARORA/FALL
2015
11

12. Thank
you
SERA/NORA/PUNEET
CS6212/ARORA/FALL
12