The National Hurricane Center (NHC) collects datasets with all storms in North Atlantic, the North Atlantic Hurricane Database (HURDAT). For all sorms, we have the location of the storm, every six jours (at midnight, six a.m., noon and six p.m.). Note that we have also the date, the maximal wind speed – on a 6 … Continue reading Generating Hurricanes with a Markov Spatial Process→
Hier, sur Twitter, @JF_Godbout partageait un joli graphique relatif aux élections québécoises, avec les nombres de votes obtenus (ici en pourcentage des votes totaux) et le pourcentage de sièges que cela donne, Il faut dire qu’hier, c’était jour d’élection. Ce sont des élections à un tour, avec plusieurs partis (disons 4 grands partis si on se limite … Continue reading Elections Sans Bipartisme→
On the Monkey Cage blog, Baptiste Coulmont (a.k.a. @coulmont) recently uploaded a post entitled “You can vote twice ! The many political appeals of proxy votes in France“, coauthored with Joël Gombin (a.k.a. @joelgombin), and myself. The study was initially written in French as mentioned in a previous post. Baptiste posted additional information on his blog (http://coulmont.com/blog/…) and I also wanted to post … Continue reading Voting Twice in France→
La Vie des Idées a mis en ligne, ce matin, un court texte, écrit par Baptiste Coulmont (a.k.a. @coulmont) et Joël Gombin (a.k.a. @joelgombin), auquel j’ai très modestement contribué, intitulé “Un homme, deux voix. Le vote par procuration“. Alors que sur son blog, Baptiste a rajouté pas mal d’information sur le vote par procuration en France (et … Continue reading Le Vote par Procuration en France→
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) … Continue reading Inference for ARMA(p,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, … Continue reading Inference for MA(q) 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 … Continue reading Inference for AR(p) Time Series→
This week, I spend some time at the Workshop on Nonparametric Curve Smoothing conference at Concordia. Yesterday afternoon, Noël Veraverbeke show an interesting graph, to illustrate conditional copulas (and the derivation of conditional dependence measures, such as Kendall’s tau, or Spearman’s rho). A long time ago, in my PhD thesis (mainly on conditional copulas) I did … Continue reading Conditional dependence measures→
This morning, I was working with Julie, a student of mine, coming from Rennes, on mortality tables. Actually, we work on genealogical datasets from a small region in Québec, and we can observe a lot of volatiliy. If I borrow one of her graph, we get something like Since we have some missing data, we … Continue reading Smoothing mortality rates→
Let us continue our discussion on smoothing techniques in regression. Assume that . where is some unkown function, but assumed to be sufficently smooth. For instance, assume that is continuous, that exists, and is continuous, that exists and is also continuous, etc. If is smooth enough, Taylor’s expansion can be used. Hence, for which can also … Continue reading Some heuristics about spline smoothing→
In a standard linear model, we assume that . Alternatives can be considered, when the linear assumption is too strong. Polynomial regression A natural extension might be to assume some polynomial function, Again, in the standard linear model approach (with a conditional normal distribution using the GLM terminology), parameters can be obtained using least squares, … Continue reading Some heuristics about local regression and kernel smoothing→
I always claim that graphs are important in econometrics and statistics ! Of course, it is usually not that simple. Let me come back to a recent experience. A got an email from Sami yesterday, sending me a graph of residuals, and asking me what could be done with a graph of residuals, obtained from … Continue reading Residuals from a logistic regression→
Wednesday, in class, we’ve seen how to visualize a multiple regression model (with two continuous explanatory variables). Here, the goal is to predict the average cost of an insurance claim, using some covariates, e.g. the age of the driver, and the age of the car (recall that losses here are liability losses). The prediction obtained … Continue reading Multiple (smoothed) regression and portfolio exposure→
During the course, we have seen that it is natural to assume that not only the individual claims frequency can be explained by some covariates, but individual costs too. Of course, appropriate families should be considered to model the distribution of the cost , given some covariates .Here is the dataset we’ll use, > sinistre=read.table(“http://freakonometrics.free.fr/sinistreACT2040.txt”, … Continue reading Large claims, and ratemaking→
On http://www.bakadesuyo.com, there was recently an interesting discussion about infidelity, the key question being “at what ages are men and women most likely to have affairs?” The discussion is based on some graphs, e.g. The source is a paper by Donald Cox. Based on a sample of 36 men and 22 women 3,432 respondent (NHSLS … Continue reading Infidelity and econometrics→
"sendo l'intento mio scrivere cosa utile a chi la intende…"