PSTAT 174/274 Practice Midterm 1
Instructions: i Closed books and notes. ii One cheat sheet and one calculator
are allowed. iii Answer all questions, write them clearly/neatly. iv Need extra
space, write answers back. iv. Topics from the first class to la

Time Series Analysis and Its Applications: With R Examples
http:/www.stat.pitt.edu/stoffer/tsa3/
(click the above textbook link on-campus and/or the click the link Springer's Site for the Text
and download the free e-text on to desktop/notebook)
Third Edi

PSTAT 174/274 Midterm1 Answers
2
Q1 (15pts). Consider the time series Xt = t + Wt , where Wt WN(0, w ).
(a)(5pts) Show that Xt is not stationary.
(b)(5pts) Consider the rst dierence, Yt = Xt Xt1 . Is Yt stationary? Why?
(c)(5pts) Derive the mean and autoc

PSTAT 174/274 HW2, due 3:30pm Tuesday Nov 4th at Teachers podium
Instructions:
(1) Write clearly your firstname and lastname in capitals, 174 or 274 hw #, perm
id on top of your answers. Write your TA name (Ling/Filip/Sergio) on the top
right corner of th

PSTAT 174/274 HW1, due 2pm Wednesday April 8th in class at Teachers
podium
Instructions:
(1) Write clearly your firstname and lastname in capitals, 174 or 274 hw #, perm
id on top of your answers. Write your TA name (Ling or Michelle) on the top right
cor

ACF
Stock Overview:
Chevron is one of the worlds six supermajor oil companies, and manufactures fuels, lubricants, and
petrochemicals. As of 2013, Chevrons net income was $21.423 billion, and their total number of assets
are valued at $253753 billion.
I c

Question Q1 Q2 Q3 Q4 Q5 Q6
Total
Points
20 20
3
7
20 10 70/80(G)
PSTAT 174/274 Midterm II Answers, UCSB, Spring 2015
Q1 (20pts). Suppose we have 100 observations X1 , X2 , , X100 of a time series, and we
have chosen to estimate an AR(3) model: Xt = 1 Xt1

PSTAT 174/274 HW6answers (Total 40/50 for undergrads/grads)
1. Fit an ARIMA(p,d,q) model to US monthly percentage of savings to disposable income.
The saverate.txt on gauchospace includes the data. You may use the attached code to answer
the questions.
(a

PSTAT 174/274 hw1 answers
Q1:
x= rnorm(100,5,1)
x=ts(x,start=1,end=100,frequency=1)
plot.ts(x)
(a) Explain what each line in the code does briey in one or two sentences.
(b) Attach the graph and identify if there is any (i) global trend, (ii) periodic tre

PSTAT174/274 HW3 answers
Exercise 1.7
a. x(t) = w(t 1) + 2w(t) + w(t + 1) and x(t h) = w(t h 1) + 2w(t h) + w(t h + 1).
Not for grading: Note that this is 2-sided MA(1) process or 2-sided MA(1) filter.
(i) E(x(t) = 0.
(ii) Multiply LHSs of X(t) and X(t-h)

PSTAT 174/274 HW6, due 2pm June 3rd at Teachers podium
Instructions:
(1) Write your firstname and lastname clearly in capitals, 174 or 274 hw #, perm
id on top of your answers. Write your TA name (Ling/Michelle) on the top right
corner of the first page.

PSTAT 174/274 hw2 answers
10pts for each question; undergrads (grads) max is 40(50)pts
Q1: Run (execute) the following six lines code in R.
x= rnorm(2200)
acv = acf(x[1:200], type="cov", lag.max=20)
plot(acv$lag, acv$acf, type="l")
for(i in 1:10)cfw_
acv

PSTAT 174/274 HW4, due 2pm Monday May 11th at Teachers podium
Instructions:
(1) Write your firstname and lastname clearly in capitals, 174 or 274 hw #, perm
id on top of your answers. Write your TA name (Michelle or Ling) on the top right
corner of the fi

PSTAT 174/274 Practice Midterm2
Instructions: 0. all the topics after the midterm1 from Y-W equations to Spectral
density function. i Closed books and notes. ii one cheat sheet and a calculator
allowed. iii Be on time!
Q1 (20pts). Suppose we have 100 obse

Final project planning until the due date Friday 11am August 1st
By Sunday July 20th
(a) You should have your ts data ready
(b) You should have ts plot, acf/pacf plots ready.
Make sure that your ts plot does not show explosions, sudden very big jump(s) o

PSTAT 174/274 HW1, due 3:30pm Tuesday Oct 21st in class at Teachers
podium
Instructions:
(1) Write clearly your firstname and lastname in capitals, 174 or 274 hw #, perm
id on top of your answers. Write your TA name (Ling/Filip/Sergio) on the top
right co

PSTAT 174/274 HW4, due 3:30pm Tuesday Nov 25th at Teachers podium
Instructions:
(1) Write your firstname and lastname clearly in capitals, 174 or 274 hw #, perm
id on top of your answers. Write your TA name (Ling/Filip/Sergio) on the top
right corner of t

PSTAT 174/274 HW3, due 3:30pm Thursday Nov 13th at Teachers podium
Instructions:
(1) Write your firstname and lastname clearly in capitals, 174 or 274 hw #, perm
id on top of your answers. Write your TA name (Ling/Filip/Sergio) on the top
right corner of

PSTAT 174/274 Lecture 7, page 27 of Text
2-sided innite MA model Yt =
j= j Wtj with Wt WN(w =
2
0, w ) is always stationary because:
E(Yt ) = E(
j Wtj ) = w
j=
j
j=
E(Yt ) = 0
y (t, t + h) = E(Yt Yt+h )
= E
j Wtj
j
=
i Wt+hi
i
i j E (Wtj Wt+hi )
i
j
i j

PSTAT 174/274 Lectures 12 and 13
Sections 1.6, 3.6 and Appendix A
Descriptive or Sample Estimators
1. Moment estimators for , (h) and correlations (h)
2. MLE estimators for , (h) and correlations (h)
3. Simulate estimators in R (?)
(See Appendix A in Text

PSTAT 174/274 Lectures 3 and 4
To calculate autocovariances and autocorrelations for time series data,
we need the following two denitions:
Section 1.5 from Text
Denition lag : Consider two random variables Xr , Xs from a stochastic process Xt1 , Xt2 , Xt

PSTAT 174/274 Lectures 9 to 11
Sections 3.1 to 3.4
Chapter 3 Cont.
Working with Backshift operator to get ACVF/ACF
Finding ACVF and ACF of ARMA(p, q)
Dierence equations(Review Text page 97,98)
Review :
Suppose Yt =
y (h) =
y (h) =
j Wtj ,
2
Wt W N (0,

PSTAT 174/274 Lectures 19 and 20
Chapter 4 pages 173-200 in Text
Spectral Analysis or Fourier Analysis
Review of Trigonometric and Complex Exponential
functions
sin2 + cos2 = 1
sin = cos( ) and cos = sin( )
2
2
cos( ) = cos cos
sin sin
sin( ) = sin

# Section 2 R code
#
# Question No. 1
# Plot ACF for given values of theta
#
# ARMAacf is a R command which generates theoretical
# acf values using mathematical formulae
ARMAacf(ma=c(0.45,0.55)
# Setting maximum lag value
h.max <- 21
plot(x=0:h.max,y=ARM

Homework 2 solutions - for use by Fall 2015 PSTAT 174/274 students only
Problem 1. Let cfw_Xt be the moving-average process of order 2 given by Xt = Zt + Zt2 ,
where cfw_Zt is WN(0,1).
(a) If = 0.8 and if t is a fixed value of time index, find
E(Xt ),

Time Series and their ACFs
Lectures 4 and 5
1
200 simulated values of i.i.d Gaussian WN and its ACF
Stationary time series, very choppy.
Theoretical ACF = 0 for lags k > 0;
Observe: Sample ACF is within 95% confidence interval except for k=0.
2
100 sim

PSTAT174/274 Spring 2017
Week 5 Lecture Notes: SARIMA. Sample ACF and PACF. Yule-Walker Estimates for AR(p).
9. SARIMA models (Seasonal ARIMA) ([BD] 6.5)
Review. SARIMA is a modification of ARIMA to account for seasonal and non-stationary behavior: if
the

PSTAT174/274 Spring 2017
WEEK 4: Non-stationary models: Seasonality, ARIMA, Transformations. SARIMA
7. Non-stationary models: Seasonality, ARIMA, Transformations.
Review:
(i) The Classical Decomposition Model: It assumes that the data is a realization of

PSTAT174/274 Spring 2017
Week 6: Parameter estimation.
Innovation Algorithm. LS, MLE and Akaike Information Criterion
11. Parameter estimation. (Based on Appendix B and 5.1 and 5.2)
Problem: Assume that we have a stationary sample of observations (x1 , .

Examples of Time Series and ACFs
Lecture 2
What color are the
Pegai?
Check your graphical outputs carefully!
https:/www.tes.com/lessons/iez-dWediUSu6w/mc-escher-tessellations-various-artwork
Tessellations by M.C. Escher
1
White noise, 200 simulated values