Univariate Time Series Models
(M.Sc. Finance - Exercise 4)

Walter Distaso
Imperial College Business School w.distaso@imperial.ac.uk

Question 1
Consider the following three models that a researcher suggests might be reasonable models of stock market prices. yt yt yt = yt−1 + ut = 0.5yt−1 + ut = 0.8yt−1 + ut

(a) What classes of models are these examples of? (b) What would the autocorrelation function for each of these processes look like? (not exactly, just the shape) (c) Which model is more likely to represent stock market prices from a theoretical perspective, and why? If any of the three models truly represented the way stock market prices move, which could potentially be used to make money? (d) Consider the extent of persistence of shocks in the series in each case.

Question 2

You obtain the following estimates for an AR(2) model of some returns data. yt = 0.803yt−1 + 0.682yt−2 + ut , where ut is a white noise error process. By examining the characteristic equation, check the estimated model for stationarity.

Question 3
A researcher is trying to determine the appropriate order of an ARMA model to describe some data, with 200 observations available. She has the following ﬁgures for the log of estimated residual variance (log(ˆ 2 )) for various candidate models. She has σ assumed that an order greater than (3,3) should not be necessary to model the dynamics of the data. What is the “optimal” model order? ARMA(p, q) model order log(ˆ 2 ) σ (0,0) 0.932 (1,0) 0.864 (0,1) 0.902 (1,1) 0.836 (2,1) 0.801 (1,2) 0.821 (2,2) 0.789 (3,2) 0.773 (2,3) 0.782 (3,3) 0.764

Question 4

“Given that the objective of any econometric modeling exercise is to ﬁnd the model that most closely ‘ﬁts’ the data, then adding more lags to an ARMA model will almost invariably lead to a better ﬁt. Therefore, a large model is best because it will ﬁt the data more closely.” Comment on the validity (or otherwise) of this statement.

....2.3 Timeseries models
Timeseries is an ordered sequence of values of a variable at equally spaced time intervals. Timeseries occur frequently when looking at industrial data. The essential difference between modeling data via timeseries methods and the other methods is that Timeseriesanalysis accounts for the fact...

...report on the time-seriesanalysis of continuously compounded returns for Ford and GM for the periods January 2002 till April 2007 using monthly stockprices. This analysis is aimed at estimating the ARIMA model that provides the best forecast for the series. This paper will be divided into 2 sections; the first section showing the Ford analysis and the second the GM...

...Analysis of Financial TimeSeries
Third Edition
RUEY S. TSAY
The University of Chicago Booth School of Business Chicago, IL
A JOHN WILEY & SONS, INC., PUBLICATION
Analysis of Financial TimeSeries
WILEY SERIES IN PROBABILITY AND STATISTICS Established by WALTER A. SHEWHART and SAMUEL S. WILKS Editors: David J. Balding, Noel A. C. Cressie, Garrett M. Fitzmaurice, Iain M....

...Timeseriesanalysis
(Session – I)
Commands and syntax for data analysis using STATA
1. Open and Run the STATA application
• Click on the Data on the task bar and open Data editor
• Copy the data from Excel sheet and paste it on the data editor
• Preserve the data
• Close Data Editor
2. Type “describe” in the command space- Software will show the description of the
data set....

...company is now listed on the NASDAQ stock exchange under the ticker symbol .
The company's mission statement from the outset was "to organize the world's information and make it universally accessible and useful”, and the company's unofficial slogan is "Don’t be evil”. In 2006, the company moved to its current headquarters in Mountain View, California.
Objectives
1. To fit a multiple regression model to a data set comprising the put, call and strike prices...

...Secondary Research TimeSeriesAnalysis
VARIABLE FACTOR THAT INCREASING MALAYSIA GDP
Prepared by:
Dina Maya Avinati
Wery Astuti
Faculty of Business
UNIVERSITAS SISWA BANGSA INTERNATIONAL
Mulia Business Park, JL. MT. Haryono Kav. 58-60 Pancoran- South Jakarta
Page | 1
CONTENT
I.
Introduction
1.1
Back Ground of Study
1.2
Problem
1.3
Research Problem
1.4
Research Objective
1.5
Scope and Limitation
1.6...

...Timeseries
In statistics, signal processing, econometrics and mathematical finance, a timeseries is a sequence of data points, measured typically at successive times spaced at uniform time intervals. Examples of timeseries are the daily closing value of the Dow Jones index or the annual flow volume of the Nile River at Aswan. Time...

...TIMESERIESANALYSIS
Chapter Three
Univariate TimeSeries Models
Chapter Three
Univariate timeseries models c WISE
1
3.1
Preliminaries
We denote the univariate timeseries of interest as yt.
• yt is observed for t = 1, 2, . . . , T ;
• y0, y−1, . . . , y1−p are available;
• Ωt−1 the history or information set at time t − 1....

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