## Archive for ARMA models

Posted in Books, Kids, Statistics, University life with tags , , , , , , , , , , , , , , on December 9, 2013 by xi'an

This week, thanks to a lack of clear instructions (from me) to my students in the Reading Classics student seminar, four students showed up with a presentation! Since I had planned for two teaching blocks, three of them managed to fit within the three hours, while the last one nicely accepted to wait till next week to present a paper by David Cox…

The first paper discussed therein was A new look at the statistical model identification, written in 1974 by Hirotugu Akaike. And presenting the AIC criterion. My student Rozan asked to give the presentation in French as he struggled with English, but it was still a challenge for him and he ended up being too close to the paper to provide a proper perspective on why AIC is written the way it is and why it is (potentially) relevant for model selection. And why it is not such a definitive answer to the model selection problem. This is not the simplest paper in the list, to be sure, but some intuition could have been built from the linear model, rather than producing the case of an ARMA(p,q) model without much explanation. (I actually wonder why the penalty for this model is (p+q)/T, rather than (p+q+1)/T for the additional variance parameter.) Or simulation ran on the performances of AIC versus other xIC’s…

The second paper was another classic, the original GLM paper by John Nelder and his coauthor Wedderburn, published in 1972 in Series B. A slightly easier paper, in that the notion of a generalised linear model is presented therein, with mathematical properties linking the (conditional) mean of the observation with the parameters and several examples that could be discussed. Plus having the book as a backup. My student Ysé did a reasonable job in presenting the concepts, but she would have benefited from this extra-week in including properly the computations she ran in R around the glm() function… (The definition of the deviance was somehow deficient, although this led to a small discussion during the class as to how the analysis of deviance was extending the then flourishing analysis of variance.) In the generic definition of the generalised linear models, I was also reminded of the
generality of the nuisance parameter modelling, which made the part of interest appear as an exponential shift on the original (nuisance) density.

The third paper, presented by Bong, was yet another classic, namely the FDR paper, Controlling the false discovery rate, of Benjamini and Hochberg in Series B (which was recently promoted to the should-have-been-a-Read-Paper category by the RSS Research Committee and discussed at the Annual RSS Conference in Edinburgh four years ago, as well as published in Series B). This 2010 discussion would actually have been a good start to discuss the paper in class, but Bong was not aware of it and mentioned earlier papers extending the 1995 classic. She gave a decent presentation of the problem and of the solution of Benjamini and Hochberg but I wonder how much of the novelty of the concept the class grasped. (I presume everyone was getting tired by then as I was the only one asking questions.) The slides somewhat made it look too much like a simulation experiment… (Unsurprisingly, the presentation did not include any Bayesian perspective on the approach, even though they are quite natural and emerged very quickly once the paper was published. I remember for instance the Valencia 7 meeting in Teneriffe where Larry Wasserman discussed about the Bayesian-frequentist agreement in multiple testing.)

## Approximate Bayesian computational methods on-line

Posted in R, Statistics, University life with tags , , , , , , on October 25, 2011 by xi'an

Fig. 4 – Boxplots of the evolution [against ε] of ABC approximations to the Bayes factor. The representation is made in terms of frequencies of visits to [accepted proposals from] models MA(1) and MA(2) during an ABC simulation when ε corresponds to the 10,1,.1,.01% quantiles on the simulated autocovariance distances. The data is a time series of 50 points simulated from a MA(2) model. The true Bayes factor is then equal to 17.71, corresponding to posterior probabilities of 0.95 and 0.05 for the MA(2) and MA(1) models, resp.

The survey we wrote with Jean-Michel Marin, Pierre Pudlo, and Robin Ryder is now published in [the expensive] Statistics and Computing (on-line). Beside recycling a lot of Og posts on ABC, this paper has the (personal) appeal of giving us the first hint that all was not so rosy in terms of ABC model choice. I wonder whether or not it will be part of the ABC special issue.

## Time series

Posted in Books, R, Statistics with tags , , , , , , on March 29, 2011 by xi'an

(This post got published on The Statistics Forum yesterday.)

The short book review section of the International Statistical Review sent me Raquel Prado’s and Mike West’s book, Time Series (Modeling, Computation, and Inference) to review. The current post is not about this specific book, but rather on why I am unsatisfied with the textbooks in this area (and correlatively why I am always reluctant to teach a graduate course on the topic). Again, I stress that the following is not specifically about the book by Raquel Prado and Mike West!

With the noticeable exception of Brockwell and Davis’ Time Series: Theory and Methods, most time-series books seem to suffer (in my opinion) from the same difficulty, which sums up as being unable to provide the reader with a coherent and logical description of/introduction to the field. (This echoes a complaint made by Håvard Rue a few weeks ago in Zurich.) Instead, time-series books appear to haphazardly pile up notions and techniques, theory and methods, without paying much attention to the coherency of the presentation. That’s how I was introduced to the field (even though it was by a fantastic teacher!) and the feeling has not left me since then. It may be due to the fact that the field stemmed partly from signal processing in engineering and partly from econometrics, but such presentations never achieve a Unitarian front on how to handle time-series. In particular, the opposition between the time domain and the frequency domain always escapes me. This is presumably due to my inability to see the relevance of the spectral approach, as harmonic regression simply appears (to me) as a special type of non-linear regression with sinusoidal regressors and with a well-defined likelihood that does not require Fourier frequencies nor periodogram (nor either spectral density estimation). Even within the time domain, I find the handling of stationarity  by time-series book to be mostly cavalier. Why stationarity is important is never addressed, which leads to the reader being left with the hard choice between imposing stationarity and not imposing stationarity. (My original feeling was to let the issue being decided by the data, but this is not possible!) Similarly, causality is often invoked as a reason to set constraints on MA coefficients, even though this resorts to a non-mathematical justification, namely preventing dependence on the future. I thus wonder if being an Unitarian (i.e. following a single logical process for analysing time-series data) is at all possible in the time-series world! E.g., in Bayesian Core, we processed AR, MA, ARMA models in a single perspective, conditioning on the initial values of the series and imposing all the usual constraints on the roots of the lag polynomials but this choice was far from perfectly justified…