In this question you will consider properties of sample estimators in time series context and perform inference and testing. You may use R to assist you in calculations, but you should state the formula of any estimator you are calculating as well as the value you obtain for the estimator, and if R is used, the R command utilised. You can either obtain the solution by calculator or by R. 15 samples from a time series: You are given T {y₁,..., y15} = = {-0.92, 1.08, 0.20, -0.63, 1.36, 1.33, -1.06, 0.11, -1.00, -0.68, 1.81, 1.71, 0.93,-0.75, -2.16}
In this question you will consider properties of sample estimators in time series context and perform inference and testing. You may use R to assist you in calculations, but you should state the formula of any estimator you are calculating as well as the value you obtain for the estimator, and if R is used, the R command utilised. You can either obtain the solution by calculator or by R. 15 samples from a time series: You are given T {y₁,..., y15} = = {-0.92, 1.08, 0.20, -0.63, 1.36, 1.33, -1.06, 0.11, -1.00, -0.68, 1.81, 1.71, 0.93,-0.75, -2.16}
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:In this question you will consider properties of sample estimators
in time series context and perform inference and testing. You
may use R to assist you in calculations, but you should state the
formula of any estimator you are calculating as well as the value
you obtain for the estimator, and if R is used, the R command
utilised. You can either obtain the solution by calculator or by R.
You are given T = 15 samples from a time series:
{y₁,..., y15}
= {-0.92, 1.08, 0.20, -0.63, 1.36, 1.33, -1.06,
0.11, -1.00, -0.68, 1.81, 1.71, 0.93,-0.75, -2.16}
(c) Calculate a 95% confidence interval for estimator r(2) and
determine if the estimator is statistically different from 0.
You may assume that the Central Limit Theorem applies and
therefore the estimator has an asymptotic Gaussian distribu-
tion and you may use Bartlett's formula for the evaluation of
the finite sample standard error. Finally state the outcome
of your findings. Remark on the effect of such a small sample
size on this conclusion.
Expert Solution
Step 1
In this question, we are given a time series data set of size T=15. We are asked to calculate a confidence interval for the estimator r(2) and determine if the estimator is statistically different from 0.
Given:
Time series is given as,
{y1,..., Y15} = {-0.92, 1.08, 0.20, -0.63, 1.36, 1.33, -1.06, 0.11, -1.00, -0.68, 1.81, 1.71, 0.93, -0.75, -2.16}
T = 15 samples
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