Inference for ARMA(p,q) Time Series

January 30, 2014
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Inference for ARMA(p,q) Time Series

As we mentioned in our previous post, as soon as we have a moving average part, inference becomes more complicated. Again, to illustrate, we do not need a two general model. Consider, here, some  process, where  is some white noise, and assume further that . > theta=.7 > phi=.5 > n=1000 > Z=rep(0,n) > set.seed(1) > e=rnorm(n) > for(t in 2:n) Z[t]=phi*Z[t-1]+e[t]+theta*e[t-1] > Z=Z[800:1000] > plot(Z,type="l") A two step procedure…

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GNU Screen

January 30, 2014
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GNU Screen

This is one of those things I picked up years ago while in graduate school that I just assumed everyone else already knew about. GNU screen is a great utility built-in to most Linux installations for remote session management. Typing 'screen' at t...

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Visualizing uneven distributions

January 30, 2014
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Visualizing uneven distributions

Jeff, a reader of the blog, asks for comment on this blog post of his (link). The highlight of the post is this chart, which shows an uneven distribution. The message of the chart is that a large amount of...

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History is too important to be left to the history professors, Part 2

January 30, 2014
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History is too important to be left to the history professors, Part 2

Completely non-gay historian Niall Ferguson, a man who we can be sure would never be caught at a ballet or a poetry reading, informs us that the British decision to enter the first world war on the side of France and Belgium was “the biggest error in modern history.” Ummm, here are a few bigger […]The post History is too important to be left to the history professors, Part 2…

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Machine Learning Lesson of the Day – Overfitting

Machine Learning Lesson of the Day – Overfitting

Any model in statistics or machine learning aims to capture the underlying trend or systematic component in a data set.  That underlying trend cannot be precisely captured because of the random variation in the data around that trend.  A model must have enough complexity to capture that trend, but not too much complexity to capture […]

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Free books on statistical learning

January 30, 2014
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Free books on statistical learning

Hastie, Tibshirani and Friedman’s Elements of Statistical Learning first appeared in 2001 and is already a classic. It is my go-to book when I need a quick refresher on a machine learning algorithm. I like it because it is written using the language and perspective of statistics, and provides a very useful entry point into the literature of machine learning which has its own terminology for statistical concepts. A free…

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Inference for MA(q) Time Series

January 30, 2014
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Inference for MA(q) Time Series

Yesterday, we’ve seen how inference for time series was possible.  I started  with that one because it is actually the simple case. For instance, we can use ordinary least squares. There might be some possible bias (see e.g. White (1961)), but asymptotically, estimators are fine (consistent, with asymptotic normality). But when the noise is (auto)correlated, then it is more complex. So, consider here some  time series for some white noise…

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Hastie-Tibshirani Statistical Learning Course Now Open

January 29, 2014
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Hastie-Tibshirani Statistical Learning Course Now Open

Machine learning is hot, hot, hot. I can't imagine better instructors (or scholars) in the area than H&T (great videos), and the course is also a fine way to learn R. It's happening now (started just last week) and runs through late March. Just go ...

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Stupid R Tricks: Random Scope

January 29, 2014
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Andrew and I have been discussing how we’re going to define functions in Stan for defining systems of differential equations; see our evolving ode design doc; comments welcome, of course. About Scope I mentioned to Andrew I would prefer pure lexical, static scoping, as found in languages like C++ and Java. If you’re not familiar […]The post Stupid R Tricks: Random Scope appeared first on Statistical Modeling, Causal Inference, and…

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Not teaching computing and statistics in our public schools will make upward mobility even harder

January 29, 2014
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In his book Average Is Over, Tyler Cowen predicts that as automatization becomes more common, modern economies will eventually be composed of two groups: 1) a highly educated minority involved in the production of  automated services and 2) a vast majority … Continue reading →

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“Questioning The Lancet, PLOS, And Other Surveys On Iraqi Deaths, An Interview With Univ. of London Professor Michael Spagat”

January 29, 2014
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“Questioning The Lancet, PLOS, And Other Surveys On Iraqi Deaths, An Interview With Univ. of London Professor Michael Spagat”

Mike Spagat points to this interview, which, he writes, covers themes that are discussed on the blog such as wrong ideas that don’t die, peer review and the statistics of conflict deaths. I agree. It’s good stuff. Here are some of the things that Spagat says (he’s being interviewed by Joel Wing): In fact, the […]The post “Questioning The Lancet, PLOS, And Other Surveys On Iraqi Deaths, An Interview With…

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Sample with replacement in SAS

January 29, 2014
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Sample with replacement in SAS

Randomly choosing a subset of elements is a fundamental operation in statistics and probability. Simple random sampling with replacement is used in bootstrap methods (where the technique is called resampling), permutation tests and simulation. Last week I showed how to use the SAMPLE function in SAS/IML software to sample with [...]

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Data mining with R course in the Netherlands taught by Luis Torgo

January 29, 2014
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In the course of this year, Dr. Luis Torgo will teach a Data Mining with R course together with the DIKW Academy in Nieuwegein, The Netherlands. Dr. Torgo is an Associate Professor at the department of Computer Science at the… See more ›

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What do I do? How do I apply statistics in my job? How did I get started?

January 29, 2014
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I've been invited to a panel discussion by the UCLA undergraduate statistics club. Some of the questions I was told to expect are down below. By answering the questions here, there's a chance of a more literate answer and other students will be able to...

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Applied Statistics Lesson of the Day – Blocking and the Randomized Complete Blocked Design (RCBD)

Applied Statistics Lesson of the Day – Blocking and the Randomized Complete Blocked Design (RCBD)

A completely randomized design works well for a homogeneous population - one that does not have major differences between any sub-populations.  However, what if a population is heterogeneous? Consider an example that commonly occurs in medical studies.  An experiment seeks to determine the effectiveness of a drug on curing a disease, and 100 patients are recruited […]

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The Mirrored Line Chart Is A Bad Idea

January 29, 2014
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The Mirrored Line Chart Is A Bad Idea

The mirrored line chart is a pet peeve of mine. It’s very common close to elections when there are two parties or candidates: one’s gains are at the other’s expense. But it becomes even more egregious when there are two categories that have to sum up to 100% by their very definition. In her coverage […]

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BOSTON COLLOQUIUM FOR PHILOSOPHY OF SCIENCE: Revisiting the Foundations of Statistics

January 29, 2014
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BOSTON COLLOQUIUM FOR PHILOSOPHY OF SCIENCE:  Revisiting the Foundations of Statistics

BOSTON COLLOQUIUM FOR PHILOSOPHY OF SCIENCE 2013–2014 54th Annual Program Download the 54th Annual Program REVISITING THE FOUNDATIONS OF STATISTICS IN THE ERA OF BIG DATA: SCALING UP TO MEET THE CHALLENGE Cosponsored by the Department of Mathematics & Statistics at Boston University. Friday, February 21, 2014 10 a.m. – 5:30 p.m. Photonics Center, 9th Floor Colloquium […]

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Inference for AR(p) Time Series

January 29, 2014
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Inference for AR(p) Time Series

Consider a (stationary) autoregressive process, say of order 2, for some white noise with variance . Here is a code to generate such a process, > phi1=.25 > phi2=.7 > n=1000 > set.seed(1) > e=rnorm(n) > Z=rep(0,n) > for(t in 3:n) Z[t]=phi1*Z[t-1]+phi2*Z[t-2]+e[t] > Z=Z[800:1000] > n=length(Z) > plot(Z,type="l") Here, we have to estimate two sets of parameters: the autoregressive coefficients, and the variance of the innovation process . Several techniques…

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cut, baby, cut!

January 28, 2014
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cut, baby, cut!

At MCMSki IV, I attended (and chaired) a session where Martyn Plummer presented some developments on cut models. As I was not sure I had gotten the idea [although this happened to be one of those few sessions where the flu had not yet completely taken over!] and as I wanted to check about a […]

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Time series data in R

January 28, 2014
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Time series data in R

There is no shortage of time series data available on the web for use in student projects, or self-learning, or to test out new forecasting algorithms. It is now relatively easy to access these data sets directly in R. M Competition data The 1001 series from the M-competition and the 3003 series from the M3-competition are available as part of the Mcomp package in R. DataMarket and Quandl Both DataMarket…

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Binomial testing with buttered toast

January 28, 2014
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Binomial testing with buttered toast

Rasmus' post of last week on binomial testing made me think about p-values and testing again. In my head I was tossing coins, thinking about gender diversity and toast. The toast and tossing a buttered toast in particular was the most helpful thought experiment, as I didn't have a fixed opinion on the probabilities for a toast to land on either side. I have yet to carry out some real…

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Context Matters When Modeling Human Judgment and Choice

January 28, 2014
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Context Matters When Modeling Human Judgment and Choice

Herbert Simon was succinct when he argued that judgment and choice "is shaped by a scissor whose two blades are the structure of the task environment and the computational capabilities of the actor" (Simon, 1990, p.7). As a marketing researcher, I take...

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Bias of Hill Estimators

January 28, 2014
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Bias of Hill Estimators

In the MAT8595 course, we’ve seen yesterday Hill estimator of the tail index. To be more specific, we did see see that if , with , then Hill estimators for are given by for . Then we did say that satisfies some consistency in the sense that if , but not too fast, i.e. (under additional assumptions on the rate of convergence, it is possible to prove that ). Further,…

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