Other
STK320 / WST 321 time series analysis exercise 4 memo
- Course
- Institution
STK320 time series analysis exercise 4 memo
[Show more]
1 review
By: ritikchudasama101 • 1 year ago
Seller
Follow
bradleysmith1
Reviews received
Content preview
1EXERCISE 4 SUGGESTED SOLUTION
SAS Program
proc import out=sasuser.ts1to6 datafile='c:\exercise4.csv' dbms=csv replace;
getnames=yes;
datarow=2;
run;
data identify;
set sasuser.ts1to6;
dser1=dif(series1);
dser2=dif(series2);
dser3=dif(series3);
dser4=dif(series4);
dser5=dif(series5);
dser6=dif(series6);
run;
SERIES 1
(a) SAS Program
goptions reset=all;
title1 'SERIES 1: SCAN, ESACF & MINIC Methods';
proc arima data=identify plot=none;
identify var=series1 scan esacf minic p=(0:4) q=(0:4);
run;
SAS Output
SERIES 1: SCAN, ESACF & MINIC Methods
The ARIMA Procedure
Name of Variable = Series1
Mean of Working Series 620.7027
Standard Deviation 48.40734
Number of Observations 700
Squared Canonical Correlation Estimates
Lags MA 0 MA 1 MA 2 MA 3 MA 4
AR 0 0.9970 0.9969 0.9943 0.9917 0.9889
AR 1 0.2260 0.1692 0.0001 0.0014 0.0007
AR 2 0.0576 0.1613 0.0014 0.0013 0.0005
AR 3 0.1175 0.0446 0.0008 0.0006 0.0011
AR 4 0.0048 0.0419 <.0001 0.0003 0.0010
SCAN Chi-Square[1] Probability Values
Lags MA 0 MA 1 MA 2 MA 3 MA 4
AR 0 <.0001 <.0001 <.0001 <.0001 <.0001
AR 1 <.0001 <.0001 0.8244 0.4687 0.6084
AR 2 <.0001 <.0001 0.4750 0.4633 0.6396
AR 3 <.0001 <.0001 0.5911 0.5749 0.6139
AR 4 0.0679 <.0001 0.9522 0.7616 0.6315
WST321
, 2
Extended Sample Autocorrelation Function
Lags MA 0 MA 1 MA 2 MA 3 MA 4
AR 0 0.9930 0.9875 0.9808 0.9739 0.9673
AR 1 -0.4909 0.4037 -0.0224 0.0263 -0.0372
AR 2 0.3979 0.4011 0.1412 -0.0024 -0.0367
AR 3 -0.4941 0.3496 0.3571 0.1715 -0.0289
AR 4 -0.2004 0.3762 0.0390 -0.1416 0.1675
ESACF Probability Values
Lags MA 0 MA 1 MA 2 MA 3 MA 4
AR 0 <.0001 <.0001 <.0001 <.0001 <.0001
AR 1 <.0001 <.0001 0.6591 0.6046 0.4647
AR 2 <.0001 <.0001 0.0010 0.9607 0.4641
AR 3 <.0001 <.0001 <.0001 0.0030 0.5257
AR 4 <.0001 <.0001 0.4347 0.0032 0.0006
Minimum Information Criterion
Lags MA 0 MA 1 MA 2 MA 3 MA 4
AR 0 7.737892 7.721587 7.671024 7.636208 7.619054
AR 1 1.93244 1.694605 1.593823 1.501374 1.506337
AR 2 1.686847 1.695624 1.507065 1.51072 1.481473
AR 3 1.635156 1.523962 1.511512 1.519546 1.472633
AR 4 1.517152 1.521738 1.491085 1.471467 1.480764
Error series model: AR(4)
Minimum Table Value: BIC(4,3) = 1.471467
ARMA(p+d,q) Tentative Order Selection
Tests
SCAN ESACF
p+d q BIC p+d q BIC
1 2 1.593823 1 2 1.593823
(5% Significance Level)
The SCAN and ESACF methods both suggest that ~ p = p + d = 1 and q = 2 , whereas
~
the MINIC method suggests that p = p + d = 4 and that q = 3 (which is unlikely).
WST321
, 3
(b) SAS Program
goptions reset=all i=join;
axis1 label=(angle=90 'First Difference of Series 1');
symbol1 color=blue;
title1 'SERIES 1: ADF Test';
proc gplot data=identify;
plot dser1*t / vaxis=axis1;
run;
goptions reset=all i=join;
axis1 label=(angle=90 'Series 1');
symbol1 color=blue;
title1 'SERIES 1: ADF Test';
proc gplot data=identify;
plot series1*t / vaxis=axis1;
run;
proc arima data=identify plot=none;
identify var=series1(1) stationarity=(adf=(0,1,2));
identify var=series1 stationarity=(adf=(0,1,2));
run;
SAS Output
WST321
, 4
SERIES 1: ADF Test
The ARIMA Procedure
Name of Variable = Series1
Period(s) of Differencing 1
Mean of Working Series -0.27252
Standard Deviation 2.610582
Number of Observations 699
Observation(s) eliminated by differencing 1
Augmented Dickey-Fuller Unit Root Tests
Type Lags Rho Pr < Rho Tau Pr < Tau F Pr > F
Zero Mean 0 -1029.70 0.0001 -44.33 <.0001
1 -630.103 0.0001 -17.72 <.0001
2 -250.290 0.0001 -10.28 <.0001
Single Mean 0 -1040.93 0.0001 -45.22 <.0001 1022.31 0.0010
1 -669.759 0.0001 -18.26 <.0001 166.76 0.0010
2 -272.431 0.0001 -10.65 <.0001 56.66 0.0010
Trend 0 -1040.94 0.0001 -45.19 <.0001 1020.90 0.0010
1 -669.797 0.0001 -18.25 <.0001 166.52 0.0010
2 -272.434 0.0001 -10.64 <.0001 56.58 0.0010
Name of Variable = Series1
Mean of Working Series 620.7027
Standard Deviation 48.40734
Number of Observations 700
Augmented Dickey-Fuller Unit Root Tests
Type Lags Rho Pr < Rho Tau Pr < Tau F Pr > F
Zero Mean 0 -0.3108 0.6122 -2.80 0.0051
1 -0.3031 0.6139 -4.66 <.0001
2 -0.3061 0.6132 -3.71 0.0002
Single Mean 0 -0.9667 0.8892 -0.68 0.8505 4.03 0.0847
1 -0.1766 0.9480 -0.21 0.9345 10.83 0.0010
2 -0.4089 0.9335 -0.39 0.9082 6.89 0.0010
Trend 0 -15.1695 0.1770 -2.75 0.2161 3.79 0.4145
1 -4.9038 0.8271 -1.50 0.8275 1.15 0.9465
2 -7.9882 0.5838 -1.95 0.6292 1.90 0.7962
We first determine whether Series 1 has 2 unit roots by testing H 0 : d = 1 against
H 1 : d = 0 with respect to the first difference of Series 1. The time plot indicates that
the first difference of Series 1 fluctuates around a zero mean, so Case 1 of the ADF test
is applicable.
WST321
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller bradleysmith1. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $2.99. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
77254 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now