Spring 2013 Statistics 153 (Time Series) : Lecture Three
Aditya Guntuboyina
29 January 2013
1
Dierencing for Trend Elimination
In the last class, we studied trend models: Xt = mt + Zt where mt is a deterministic trend function and
cfw_Zt is white noise.
Statistics 153 (Introduction to Time Series) Homework Three
Due on 3 April, 2013
13 March, 2013
1. Consider a dataset of size n generated according to the zero-mean AR(1) model with parameter
. We have seen in class that the Yule-Walker estimate of is app
Statistics 153 (Introduction to Time Series) Homework 2
Due on 27 February, 2013
16 February, 2013
1. Let cfw_Yt be a doubly innite sequence of random variables that is stationary with autocovariance
function Y . Let
Xt = (a + bt)st + Yt ,
where a and b
Statistics 153 (Introduction to Time Series) Homework 1
Due on 13 February, 2013
04 February, 2013
1. Download the google trends time series dataset for the query orkut.
(a) Estimate the trend function in the data by tting a parametric curve to the data.
Fall 2013 Statistics 151 (Linear Models) : Lecture Four
Aditya Guntuboyina
10 September 2013
1
Recap
1.1
The Regression Problem
There is a response variable y and p explanatory variables x1 , . . . , xp . The goal is understand the relationship between y
Fall 2013 Statistics 151 (Linear Models) : Lecture Eight
Aditya Guntuboyina
24 September 2013
1
Normal Regression Theory
We assume that e Nn (0, 2 In ). Equivalently, e1 , . . . , en are independent normals with mean 0 and
variance 2 . As a result of this
Fall 2013 Statistics 151 (Linear Models) : Lecture Five
Aditya Guntuboyina
12 September 2013
1
Least Squares Estimate of in the linear model
The linear model is
with Ee = 0 and Cov(e) = 2 In
Y = X + e
where Y is n 1 vector containing all the values of the
Statistics 153 (Introduction to Time Series) Homework Five
Due on 8 May, 2013
28 April, 2013
1. Consider the following seasonal AR model:
(1 B)(1 B s )Xt = Zt ,
where cfw_Zt is white noise and | < 1, | < 1.
(a) Calculate the spectral density of cfw_Xt .
Spring 2013 Statistics 153 (Time Series) : Lecture One
Aditya Guntuboyina
22 January 2013
A time series is a set of numerical observations, each one being recorded at a specic time. Time
series data arise everywhere. The aim of this course is to teach you
Fall 2013 Statistics 151 (Linear Models) : Lecture Six
Aditya Guntuboyina
17 September 2013
We again consider Y = X + e with Ee = 0 and Cov(e) = 2 In . is estimated by solving the normal
equations X T X = X T Y .
1
The Regression Plane
If we get a new sub
Spring 2013 Statistics 153 (Time Series) : Lecture Two
Aditya Guntuboyina
24 January 2013
1
Last Class
Data Examples
White noise model
Sample Autocorrelation Function and Correlogram
2
Trend Models
Many time series datasets show an increasing or decrea
Spring 2013 Statistics 153 (Time Series) : Lecture Ten
Aditya Guntuboyina
21 February 2013
1
Best Linear Prediction
Suppose that Y and W1 , . . . , Wm are random variables with zero means and nite variances.
cov(Y, Wi ) = i , i = 1, . . . , m and
cov(Wi ,
Fall 2013 Statistics 151 (Linear Models) : Lecture Seven
Aditya Guntuboyina
19 September 2013
1
Last Class
We looked at
1. Fitted Values: Y = X = HY where H = X(X T X)1 X T Y . Y is the projection of Y onto the
column space of X.
2. Residuals: e = Y Y = (
Fall 2013 Statistics 151 (Linear Models) : Lecture Nine
Aditya Guntuboyina
26 September 2013
1
Hypothesis Tests to Compare Models
Let M denote the full regression model:
yi = 0 + 1 xi1 + + p xip + ei
which has p explanatory variables.
Let m denote a sub-m