# Questions tagged [statistics]

The study of the collection, organization, analysis, and interpretation of data. Questions may deal with descriptive statistics, probability distributions, random variables, sampling, regression, density estimation, filtering, inference, estimation theory, or computational statistics.

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10 views

### Is the portfolio return distribution a weighted combination of individual asset return distributions?

We know that the portfolio expected return is a weighted sum of the individual assets' expected returns (asset means). We also know that the portfolio variance is a weighted combination of the ...
36 views

### Why are discrete moment estimators used more than continuous estimators for financial data?

The discrete sample estimator of a random variable's variance is σ2 = ∑ (Xi – μ)2 / N which is always used when calculating financial risk/volatility of prices, returns etc. There is also the ...
26 views

### Hierarchical copula vs. vine copula

Vine copulas are a sequential cascade of bivariate copulas meant to capture the hierarchical structure in the dependence structure of random variables. How does this relate or differ from the concept ...
153 views

### Imperfect Competition among Informed Traders - Back, Chao and Willard

The following assumptions are part of the paper of Back, Chao and Willard and I can not solve for the statistic that is denoted as $\phi$ in the sequel. I would be glad if anyone could help me. Below ...
67 views

### What should degrees of freedom $\nu$ be set to when modeling financial returns that follow the t-distribution?

The closer the t-distribution degrees of freedom ($\nu$) is to 0, the more heavy are the tails, whereas high degrees of freedom recovers the normal distribution. In finance, what value is usually used ...
39 views

### How to prove that the portfolio mean $\mu_P$ is biased in the presence of skewness in the portfolio return distribution?

Portfolio returns are a vector that have a statistical distribution, which in turn has moments. $$s_P = w^\top M_3 (w\otimes w)$$ is the formula for portfolio skewness, where $M_3$ is the coskewness ...
52 views

### Alternative low-moment measure of skewness

$$\widehat{\text {Skew}}_{i, t}=\frac{3 \cdot\left[\hat{\mu}_{i, t}-\operatorname{median}\left(r_{i, d, t}\right)\right]}{\hat{\sigma}_{i, t}}$$ is called Low Moment Skewness by Baltas and Salinas (...
27 views

### How to understand the results of the Johansen test?

So I now there are numerous pages on the johansen test, and what the results mean. Though I am confused as to what it is doing exactly. So my understanding is that it will find the spread of 2 ...
57 views

### sub-Gaussian random variables in financial economics

Unlike financial time series that typically possess fat tails, sub-Gaussian random variables have strong decay in the tails of their distribution. do sub-Gaussian random variables or processes appear ...
31 views

### Comparing curve fits

I am experimenting with building a forward curve. I have a piece of code which constructs my prototype curve. I've got a curve sample which was constructed manually and I use it as the baseline - the &...
45 views

### Escape Dynamics in financial economics or time series

These slides describe escape dynamics to be a type of, or having some relation to, rare event(s). Black swan events in business cycles was also included under the definition of rare events. My guess ...
114 views

### Large deviations theory in finance

In probability theory, the theory of large deviations concerns the asymptotic behavior of remote tails of sequences of probability distributions. A related post says: Large deviations theory is ...
48 views

### garch(1,1) Annualised Volitility with python

I am trying to calculate the annualized Volatility of given returns for a stock with Garch(1,1) on python using a code I found online. The value I should be getting is around 27, but the value I am ...
64 views

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### Issues making series stationary

I am trying to run some ARIMA forecasts and I switched recently from R to Python. I am struggling for some reason to make this series stationary . I try to take the log returns of stock prices as such ...
67 views

### How to use autocorrelation plot to interpret time series data?

how can we use auto correlation plot or correlogram to interpret time series data? I have 6 different acf plots (a,b,c,d,e,f), from this 6 plots what kind of informations and patterns can I identify? ...
75 views

### Creating a standard Gaussian model on stock market data

One of the big problems in creating good statistical models in the stock market is because of the long tails that deviate from Gauss' [regular] bell model, is there a way to create a synthetic Gauss ...
56 views

### The distribution of mean reversion time from the OU process

I was reading the paper Statistical Arbitrage in the US Equity Market and I couldn't understand the figure that plots the histogram of the empirical distribution of characteristic time to mean ...
82 views

### How to annualize skewness and kurtosis of a forecasted distribution

I have a (non-normal) distribution of expected cumulative returns 10 quarters in the future, from which I have calculated mean, standard deviation, skewness and kurtosis. I would like to annualize ...
76 views

### Cointegration stationary test yields different results if the pairs are swapped

I've been backtesting on a spread mean reversion strategy on certain stock pairs. I observe the stationarity via scatterplot and plotting a histogram. Then I verify it using Augmented Dickey Fuller ...
129 views

### What are important statistical concepts used as a quant?

I'm interviewing for some quantitative researcher positions at some hedge funds, and I've been told that there will be one interview session focused on stats, and one focused on ML, among others. This ...
82 views

### Is there a way to formulate a Martingale series that will never explode?

Martingale's betting method can be seen here:https://www.investopedia.com/articles/forex/06/martingale.asp My question is if there is a way to put a non-exploding martingale, [There is one attempt to ...
83 views

### Proof of variance reduction of bagging

In Lecture 4 of the following course: Advances in Financial Machine Learning: 10 Lectures by Marcos Lopez de Prado link in the proof of variance reduction for a ...
47 views

### Mutual fund performance over time

I am a little bit stuck with my dissertation thesis, so help will be greatly appreciated. I am trying to analyze the performance of different mutual funds, which I have classified according to ...
52 views

### Does the default rate follow normal distribution or binomial distribution?

I'm quite confused about the distribution of default rate. I understand the default can be seen as from binomial distribution
119 views

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### Unbalanced Panel Data in Excel and Stata

We have unbalanced panel data (columns for date and firm identifier as well as other variables) that is heavily unbalanced involving several thousand firms. We would like to turn it into what ...
605 views

### Forecasting Volatility using GARCH in Python - Arch Package

Disclaimer: Posted this on stackoverflow, but maybe here should be the right place to ask something about GARCH I'm testing ARCH package to forecast the Variance (Standard Deviation) of two series ...