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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73 views

Did annual Sharpe ratio follows T distribution?

Under some special condition, Sharpe ratio can be annualized by multiply $\sqrt{252}$, Since daily Sharpe ratio ($\frac{mean(r)}{std(r)}*\sqrt{T}$) follows student T distribution with degree of ...
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33 views

What does p-value adjustment under FWER do?

The background is I am predicting a time series with three strategies, the hypotheses is the strategies have a non-zero Sharpe ratio. I am reading Backtesting, by Campbell Harvey and Yan Liu paper in ...
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39 views

What's a sensible way to measure correlation in the volatility surface?

Lets say I construct a parametrisation of the volatility surface that lets me infer dynamics i.e correlation between strike vol. Is computing the sample correlation (after controlling for spot-vol ...
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1answer
40 views

Can I dynamically change hyper-parameters of a model?

Question Can I apply different hyper-parameters for different training sets? I can see the point of using the shared parameters but I cannot see the point of using shared hyper-parameters. The ...
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37 views

How do I deal with nonexistant data in a time series with an irregular frequency?

I am trying to do some time series analysis on the margin resulting from three specific commodity futures contracts and ultimately forecast the margin. The margin is calculated as M = F1 + F2 - F3. I ...
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31 views

Examining individual portfolio allocation changes over time

I am currently working with a pretty large panel dataset containing the investment holdings of many individuals over time (i.e., for each individual I know the positions per stock over time). I was ...
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0answers
25 views

Computing statistics from historical returns

I'm reading age 35 of "Advances in Machine Learning" by de Prado. Consider an IID multivariate Gaussian process characterized by a vector of means μ, of size Nx1, and a covariance matrix V, ...
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2answers
78 views

Best method to determine future success or to determine best linearity?

Long time viewer, but first time poster, so excuse me if i'm in the wrong place please. Anyway, I am working on a project that is pretty interesting. Through data mining, I am able to gather a ton of ...
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2answers
54 views

Estimating the variance of returns with aggregated data

Say I have an asset return time series: Jan2020: -5% Feb2020: +5% Mar2020: -5% Apr2020: +5% May2020: -5% Jun2020: +5% Q3 2020: +20% Oct2020: +5 Nov2020: -5 Dec2020: +5 Note that 3 months of data is an ...
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1answer
71 views

Why is a smaller portfolio norm better?

If the norm of the portfolio weight vector, $\frac{1}{p}\sum_{i=1}^n |w_i|^p$ for $p=1,2$, of portfolio A is 0.6, and the norm of portfolio B is 0.4, then portfolio B is considered more attractive ...
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70 views

Martingale stochastic processes

Does anyone know how to do this question? A player whose initial holding is $N$ bets 1 on each game of a series of independent identical parts. He loses his bet whether he loses or he wins but, if he ...
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2answers
142 views

Forecasts for the S&P 500?

Would anyone know of any monthly forecasts for the S&P 500, historical over a long time periods. Websites like estimize provide forecasts of all sorts of things likes stocks and the balance of ...
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1answer
107 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 ...
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38 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 ...
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1answer
161 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 ...
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70 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 ...
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1answer
55 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 (...
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32 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 ...
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1answer
72 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 ...
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0answers
34 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 &...
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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 ...
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0answers
136 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 ...
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0answers
54 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 ...
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1answer
90 views

question about significance level

A case study in a exam material goes like this: "Assume that the bank reports a daily VAR of \$100 million at the 99% level of confidence. Under the null hypothesis that the VAR model is ...
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1answer
44 views

Pearson correlation significance : Issue with $t$-statistic increasing with $N$

I have two assets which seem not correlated (correlation coefficient = 6.3% using monthly frequency and 48 data points). I want to test the significance of the correlation. Null hypothesis is that ...
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1answer
76 views

How to extract p-value from ur.df package of urca in R? [closed]

I want to extract the p-value from the below output. How do i get it? ...
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0answers
184 views

Why does the Hurst exponent pseudo code not match the Python implementation?

I am working on understanding the Hurst exponent calculation by Ernest Chan; however, the description of the algorithm does not match the Python implementation. Chan [Algorithmic Trading: Winning ...
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1answer
291 views

How to calculate a position's contribution to its portfolio's tracking error?

Say we have assets X (with weight $w_a$) and Y (with weight $w_y$) in a portfolio. X and B returns are correlated: $Cov(R_x, R_y)\neq 0$. The portfolio's tracking error is: $std(R_p - R_b) = std((w_x*(...
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1answer
146 views

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 ...
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2answers
75 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? ...
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1answer
91 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 ...
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0answers
61 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 ...
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0answers
153 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 ...
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83 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 ...
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2answers
195 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 ...
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2answers
85 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 ...
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0answers
85 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 ...
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1answer
48 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 ...
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1answer
70 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
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1answer
129 views

How to test signifcance of a sharpe ratio

Let say you have measured a Sharpe Ratio of $S^*$. What is the simplest way (ie no fancy distributions) to do a hypothesis that this is different from $0$? So $H_0: \text{ The sharpe ratio is equal ...
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0answers
39 views

Backtesting conditional VaR

I'm writing a thesis about conditional VaR of Standard & Poor's 500 index. I have fitted my log-returns with GARCH(1,1)-proces and then made some conditional VaR-forecast (500 observations) with ...
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2answers
144 views

What's the difference between Statistics and Econometrics? [closed]

I can't really grasp the similarities and differences between Statistics and Econometrics. Is Econometrics includes every Statistical models inside it? or is there areas of Statistics outside of the ...
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0answers
109 views

Are intraday volatility estimators useful for close-to-close predictions

I am interested in predicting the PnL of a gamma scalping strategy which trades only once per day. For simplicity, let's say we can always trade at the daily close. So, what I need to predict are the ...
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0answers
59 views

Understanding output from Johansen Cointegration test

I have a VECM model that Im using to determine the revenues for a firm, based on factors like Interest rates, S&P 500 and company specific variables, as follows: Stage 1: $$z_t= a+ bX_t+e_t$$ ...
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13 views

A bounded random variable is sub-Gaussian, thus financial returns are not bounded?

Bounded random variables are sub-Gaussian, yet I, intuitively, assume financial returns are bounded random variables; however, they are not sub-Gaussian. Am I wrong to assume financial returns are ...
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1answer
158 views

Determining Value at Risk of a Poisson distribution

If my discrete random variable had a poisson distribution with both moments say equal to 10, how can I find the Value at Risk for a 95 percent confidence interval? I have seen that I need to ...
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0answers
75 views

Why doesn't the first principal component maximize the standard deviation of returns

I am trying to apply PCA to portfolio of securities. My understanding is that the first principal component can be used to evaluate weights for portfolio of maximum variance and each next principal ...
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1answer
31 views

What should basic statistical analysis of different price forecasts contain

we have set of historical data of different price forecasts and the real prices. When assessing "which forecasts are best", what parts of the analysis should one never miss out? We are at a very ...
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1answer
77 views

What's the meaning of linearity in classical statistics in Prado's book?

I am reading Prado's new book, Machine Learning for Asset Managers. In the page1 of his book, there is this sentence. To a greater extent than other mathematical disciplines, statistics is a ...
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1answer
43 views

Performance attribution of indices to their sector weights

Is it possible to attribute performance of indices (monthly returns and risk measures - Sharpe ratio, etc.) to their sector weights (if I know them)? Example: I know the monthly performance of ...

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