# Creating Random Numbers

How to create random number in Julia and R? The following table translates the most common Julia commands into R language.

# Creating Matrices

How to create matrices in Julia and R? The following table translates the most common Julia commands into R language.

# Creating Vectors

How to create vectors in Julia and R? The following table translates the most common Julia commands into R language.

The package ‘Seasonal’ facilitates seasonal adjustment in R. The R package provides an easy-to-handle wrapper around the X-13ARIMA-SEATS Fortran libraries provided by the US Census Bureau. X-13ARIMA-SEATS is the state-of-the-art seasonal adjustment software produced, distributed, and maintained by the Census Bureau. Continue reading Seasonal Adjustment in R

# R – Pros and Cons

Learning a new programming language is costly. Usually it takes a considerable amount of time to get acquainted with a new language. Especially the first phase can be painful and frustrating. The good thing is that with enough time and effort most of us will learn how to master a programming language eventually. However, note that, once we are comfortable with one language, we hardly want to change again. It turns out that the cost of abandoning on programming language and switch to another are even higher than at the beginning. Knowing this, we really want to make sure not to invest in the wrong language. There might be nothing worse than after finally mastering a programming language, recognizing that there is no use for this language anymore. While in a former post I highlighted reason why to use R, I concentrate on the Pros and Cons of R in this post.

# Why should you use R?

There exists several reasons why one should start using R. During the last decade R has become the leading tool for statistics, data analysis, and machine learning. By now, R represents a viable alternative to traditional statistical programs such as Stata, SPSS, SAS, and Matlab. The reasons for R’s success are manifold. Continue reading Why R?

Seasonal adjustment refers to a statistical technique that tries to quantify and remove the influences of predictable seasonal patterns to reveal nonseasonal changes in data that would otherwise be overshadowed by the seasonal differences. Seasonal adjustments provide a Continue reading Seasonal adjustment

# The Derivative of the Natural Logarithm

The derivative of the natural logarithm is defined the following way:

$f(x) = ln (x)$

$f'(x)=\frac{1}{x}$

The formal proof of the derivative is provided at the bottom of this post.

The following example further explains the derivative of the natural logarithm. Remember that Continue reading The Derivative of the Natural Logarithm

# Unbiased Estimator of Sample Variance – Vol. 2

Lately I received some criticism saying that my proof (link to proof) on the unbiasedness of the estimator for the sample variance strikes through its unnecessary length. Well, as I am an economist and love proofs which read like a book, I never really saw the benefit of bowling down a proof to a couple of lines. Actually, I hate it if I have to brew over a proof for an hour before I clearly understand what’s going on. However, in order to satisfy the need for mathematical beauty, I looked around and found the following proof which is way shorter than my original version.

# The Gauss Markov Theorem

When studying the classical linear regression model, one necessarily comes across the Gauss-Markov Theorem. The Gauss-Markov Theorem is a central theorem for linear regression models. It states different conditions that, when met, ensure that your estimator has the lowest variance among all unbiased estimators. More formally, Continue reading The Gauss Markov Theorem