Quasi-Maximum Likelihood (QML) beauty
Beauty.. really? well, beauty is in the eye of the beholder. One of the most striking features of using Maximum Likelihood (ML) method is that by merely applying the method, conveniently provides you...
View ArticlePCA as regression (2)
In a previous post on this subject, we related the loadings of the principal components (PC’s) from the singular value decomposition (SVD) to regression coefficients of the PC’s onto the X matrix. This...
View ArticleHow regression statistics mislead experts
This post concerns a paper I came across checking the nominations for best paper published in International Journal of Forecasting (IJF) for 2012-2013. The paper bears the annoyingly irresistible...
View ArticleMultivariate volatility forecasting (1)
Introduction When hopping from univariate volatility forecasts to multivariate volatility forecast, we need to understand that now we have to forecast not only the univariate volatility element, which...
View ArticleCorrelation and correlation structure (1); quantile regression
Given a constant speed, time and distance are fully correlated. Provide me with the one, and I’ll give you the other. When two variables have nothing to do with each other, we say that they are not...
View ArticleMultivariate volatility forecasting (2)
Last time we showed how to estimate a CCC and DCC volatility model. Here I describe an advancement labored by Engle and Kelly (2012) bearing the name: Dynamic equicorrelation. The idea is nice and the...
View ArticleCorrelation and correlation structure (2), copulas
This post is about copulas and heavy tails. In a previous post we discussed the concept of correlation structure. The aim is to characterize the correlation across the distribution. Prior to the global...
View ArticleMultivariate volatility forecasting (3), Exponentially weighted model
Broadly speaking, complex models can achieve great predictive accuracy. Nonetheless, a winner in a kaggle competition is required only to attach a code for the replication of the winning result. She is...
View ArticleMultivariate volatility forecasting (4), factor models
To be instructive, I always use very few tickers to describe how a method works (and this tutorial is no different). Most of the time is spent on methods that we can easily scale up. Even if...
View ArticleCorrelation and correlation structure (3), estimate tail dependence using...
What is tail dependence really? Say the market had a red day and saw a drawdown which belongs with the 5% worst days (from now on simply call it a drawdown): One can ask what is now, given that the …...
View ArticleMultivariate volatility forecasting (5), Orthogonal GARCH
In multivariate volatility forecasting (4), we saw how to create a covariance matrix which is driven by few principal components, rather than a complete set of tickers. The advantages of using such...
View ArticlePresent-day great statistical discoveries
Some time during the 18th century the biologist and geologist Louis Agassiz said: “Every great scientific truth goes through three stages. First, people say it conflicts with the Bible. Next they say...
View ArticleCurse of dimensionality part 1: Value at Risk
The term ‘curse of dimensionality’ is now standard in advanced statistical courses, and refers to the disproportional increase in data which is needed to allow only slightly more complex models. This...
View ArticleLinear regression assumes nothing about your data
We often see statements like “linear regression makes the assumption that the data is normally distributed”, “Data has no or little multicollinearity”, or other such blunders (you know who you are..)....
View ArticleCurse of dimensionality part 2: forecast combinations
In a previous post we discussed the term ‘curse of dimensionality’ and showed how it manifests itself, in practice. Here we give another such example. Forecast combinations Here is another situation...
View ArticleMultivariate volatility forecasting, part 6 – sparse estimation
First things first. What do we mean by sparse estimation? Sparse – thinly scattered or distributed; not thick or dense. In our context, the term ‘sparse’ is installed in the intersection between...
View ArticleASA statement on p-values
There are many problems with p-values, and I too have chipped in at times. I recently sat in a presentation of an excellent paper, to be submitted to the highest ranked journal in the field. The...
View ArticleThe case for Regime-Switching GARCH
GARCH models are very responsive in the sense that they allow the fit of the model to adjust rather quickly with incoming observations. However, this adjustment depends on the parameters of the model,...
View ArticleMeasurement error bias
What is measurement error bias? Errors-in-variables, or measurement error situation happens when your right hand side variable(s); your in a model is measured with error. If represents the price of a...
View ArticleForecast averaging example
Especially in economics/econometrics, modellers do not believe their models reflect reality as it is. No, the yield curve does NOT follow a three factor Nelson-Siegel model, the relation between a...
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