Midterm One
Statistics 153, Spring 2017
March 7, 2017
The exam is out of 37 points.
US Wind Power Generation
20000
15000
10000
5000
MegawattHours (1000)
2002
2004
2006
2008
2010
Time
1. The figure abo
Introduction to Time Series Analysis. Lecture 11.
Peter Bartlett 1. Review: Time series modelling and forecasting 2. Parameter estimation 3. Maximum likelihood estimator 4. Yule-Walker estimation 5. Y
Homework 2 solutions
Joe Neeman
September 22, 2010
1. (a) We compute three cases: since the Wt are uncorrelated, we can ignore
any cross-terms of the form EWs Wt when s = t. Then
9
19
25
EWt2 1 + EWt2
Spring 2013 Statistics 153 (Time Series) : Lecture Six
Aditya Guntuboyina
06 February 2014
1
Backshift Notation
A convenient piece of notation avoids the trouble of writing huge expressions in the seq
Stat153 Assignment 5 (due Tuesday, November 23)
1. In this question, well show that a polynomial p with real coecients has p(z )p() = |p(z )|2 .
z
(a) Show that, for any complex z , z z = |z |2 . Draw
Homework 4 solutions
Joe Neeman
October 27, 2010
1. We began by looking at the ACF of the original data sequence (Figure 1),
which seems to decay very slowly. In particular, the process is probably no
Introduction to Time Series Analysis. Lecture 1.
Peter Bartlett 1. Organizational issues. 2. Objectives of time series analysis. Examples. 3. Overview of the course. 4. Time series models. 5. Time ser
Introduction to Time Series Analysis. Lecture 5.
Peter Bartlett
www.stat.berkeley.edu/bartlett/courses/153-fall2010
Last lecture: 1. ACF, sample ACF 2. Properties of the sample ACF 3. Convergence in m
Homework 3 solutions
Joe Neeman
September 22, 2010
1. Recall that the best linear predictor of Y given Z is and linear function
of Z (say, P (Y |Z ) = aZ + b) that satises (by the projection theorem)
STAT 758, Spring 2012
Key solution for Home Work 4
Prepared by Tracy Backes
MA(q )
Below we assume that Zt W N (0, 2 ).
4.1 Consider MA(1) process Xt = a Zt + b Zt1 . Find the white noise Wt such that
Stat153 Assignment 4 (due October 29, 2010)
1. (ARIMA models)
Shumway and Stoer problem 3.31.
The annual global temperature deviations data for 1880-2004 is available at
http:/www.stat.pitt.edu/stoer/
Homework 1 solutions
Joe Neeman
September 10, 2010
1. To check that cfw_Xt is white noise, we need to compute its means and
covariances. For the means, EXt = EWt (1 Wt1 )Zt = (EWt )(1
EWt1 )(EZt ) =
Introduction to Business
Introduction to Business
Business Defined
What is a business?
-All activities engaged in or caused to be engaged in with the object of gain,
benefit or advantage, direct or in
STAT 758, Spring 2012
Key solution for Home Work 1
Prepared by Tracy Backes
Dierencing, backshift operator
All notations are from lectures.
1.1 Show that the dierence operators and 12 are commutative,
STAT 758, Spring 2012
Key solution for Home Work 3
Prepared by Tracy Backes
ACF, iid sequence, white noise, random walk
3.1 Give two examples (specify distributions) of each:
a) iid sequence:
(a.1) Xt
STAT 758, Fall 2014
Home Work 1
Due date: Sep. 10
Dierencing, backshift operator
All notations are from lectures.
1.1 Show that the dierence operators
and
12
are commutative, that is
12
=
12 .
1.2 Sho
STAT 758, Spring 2012
Key solution for Home Work 2
Prepared by Tracy Backes
ACF, stationarity
2.1 Let cfw_Xt be a sequence of uncorrelated random variables, each with mean 0 and
variance 2 . For each
STAT 758, Fall 2014
Home Work 9
Spectral analysis
2
We assume below that Zt is a white noise with mean 0 and variance Z .
6.1 [similar to Chateld, Ex. 6.2] Find the power spectrum (spectral density) o
Statistics 758, Fall 2014
University of Nevada Reno
Homework 7 Solutions
Problem 1: The rvs Y and X are related as Y 10 20 X , ~ N 0, 42
a) Find the conditional distribution of Y given X x
Y | X x ~ N
We assume below that Zt W N (0, 2 ), B is a backshift operator.
1. Construct 1, 2, and 3-step forecasts for AR(2) process Xt = 1 Xt1 + 2 Xt2 + Zt and calculate the
forecast errors. Find the values of
We assume below that Zt W N (0, 2 ), B is a backshift operator.
6.1 For the model (1 B)(1 0.2B)Xt = (1 0.5B)Zt :
a) Classify the model as an ARIMA(p, d, q) process (i.e. nd p, d, q). ARIMA(1,1,1)
b) D
STAT 758, Fall 2014
Home Work 6
SARIMA
2
We assume below that Zt is a white noise with mean 0 and variance Z .
Problem 1
For the model (1 B)(1 0.2 B)Xt = (1 0.5 B)Zt :
a) Classify the model as an ARIM
STAT 758, Fall 2014
Home Work 7
Conditional expectation, Second-order forecasting
Problem 1
The rvs Y and X are related as
Y = 10 + 20 X + ,
N (0, 42 ).
a) Find the conditional distribution of Y give
STAT 758, Fall 2014
Home Work 4
MA(q)
Below we assume that Zt W N (0, 2 ).
4.1 Consider MA(1) process Xt = a Zt + b Zt1 . Find the white noise Wt such that
the process Xt is presented as Xt = Wt + Wt1
STAT 758, Fall 2014
Home Work 5
MA(q) processes, invertibility
Below we assume that Zt W N (0, 2 ), B is a backshift operator.
Problem 1
Find the operator inverse to
a) 1+2B
b) 1=0.3B
c) 2+0.6B
Proble
STAT 758, Fall 2014
Home Work 3 (due Sep 24)
ACF, iid sequence, white noise, random walk
3.1 Give two examples (specify distributions) of each: a) iid sequence, b) white noise,
c) random walk.
3.2 Giv
STAT 758, Spring 2012
Solution key for Home Work 5
Prepared by Tracy Backes
MA(q ), invertibility
Below we assume that Zt W N (0, 2 ), B is a backshift operator.
5.1 Find the operator inverse to
a) 1
STAT 758, Fall 2014
Home Work 2 (due Sep. 24)
ACF, stationarity
2.1 Let cfw_Xt be a sequence of uncorrelated random variables, each with mean 0 and
variance 2 . For each of the following processes, n
STAT 758, Fall 2014
Home Work 8
Second-order forecasting, Prediction operator
2
We assume below that Zt is a white noise with mean 0 and variance Z .
Problem 1 Construct 1, 2, and 3-step forecasts for
STAT 153 Fall 2015, Midterm 2 Exam
Nov 12, 2015
Name:
SID:
Person on left:
Person on right:
If you are stuck in one question of a problem, you can move to the following questions.
Partial credit wil
Fiscal Policy
Full Length Text Part: 3
Macro Only Text Part: 3
Chapter: 12
Chapter: 12
To Accompany Economics: Private and Public Choice 11th ed.
James Gwartney, Richard Stroup, Russell Sobel, & David
The Structure of the Atom
The Quantum Atom
Linus Course Mascot
Ernest Rutherford
http:/en.wikipedia.org/wiki/Ernest_Rutherford (3-05-12)
http:/en.wikipedia.org/wiki/Thomas_Young_%28scientist%29
(acces
International Business
Introduction (cont.)
International trade, as old as the nation-state,
has evolved because nations are efficient at
producing certain things. International trade
allows for speci
MATH 141, 2nd Examination
Prof. Jonathan Rosenberg
Monday, October 8, 2007
Instructions. Answer each question on a separate answer sheet, labeled with the problem number. Do not put the
answers to two
Practice Half-Exam 2
1. Short Answer:
a. Draw the shape of the sp2 orbital?
b. What is the hybridization on C in CO? How many pi bonds?
c. What is the electronic and molecular geometry in XeF 2?
d. Ar