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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43 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
47 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
42 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
31 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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57 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
100 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
74 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
64 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
69 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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53 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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33 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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73 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
118 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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79 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
81 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
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 ...
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1answer
39 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
114 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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33 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
90 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
65 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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43 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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12 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
74 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
73 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
63 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
36 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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1answer
63 views

Hurst Exponent and fractional differencing

I have a quick question. Currently I study daily OHLCVs of some stocks and find that many of them have the Hurst exponent not being equal to 0.5. I know that if it is less than 0.5 then it is a mean ...
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1answer
62 views

Predicting time series based on another

This is more of a generic question, but I'm sure it has a best answer/methodology which is what I'm trying to reach. I'm trying to figure out a solid line of thought when looking at a time series X ...
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36 views

Optimal Cash Deployment in a Bear Market

Assume: You can't time the market bottom You have a finite amount of cash to buy equities There are P dip/bear periods you're gonna purchase the equity 2 Problems: You deploy too much cash early, ...
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1answer
83 views

Can someone prove (or disprove) this assertion about the normal distribution? [closed]

Let $X$ be distributed as a $Normal (\mu, \sigma^2)$. Then for a fixed $\mu$ it is always the case that: \begin{equation} \frac{90th quantile-10th quantile}{\sigma}=constant \quad \forall \sigma>0 ...
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1answer
52 views

Why combining market share behaviours brings a different conclusion

Please check the following dummy example to explain the paradox. Both areas in the company keep the same market share during the years, but at the end company lost share in the market! Math is 100% ...
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19 views

Sample conditional multivariate random variable?

There's multivariate random variable, future prices of assets, 5 years from now: $$X = [Gold, Silver, SP500]$$ There's historical prices for $X$ available for last 50 years. It's possible to fit ...
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34 views

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 ...
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1answer
481 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 ...
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1answer
168 views

Two Probability Questions from Quantitative Finance Interview Book

I posted the two questions in math stack exchange one month ago but cannot get an answer, so I post it here and appreciate your advice:) I'm reading an interview book called A Practical Guide to ...
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1answer
88 views

how to I get the statistical significance of a backtested result

If I have a simple long/short value strategy (say long stocks with high e/p and short stocks low e/p or any other parameter) rebalanced monthly, and a look back window of say 15 years. How do I ...
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60 views

Why is SPY daily adjusted close negatively autocorrelated?

I took daily adjusted close prices (all history) from Yahoo Finance and ran the following code: ...
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0answers
29 views

Interpretation of $\alpha$ (confidence level) in mean CVaR optimization

How are an investors risk preferences related to $\alpha \in (0,1)$ in a mean CVaR optimization? Would a risk averse investor choose a higher value of $\alpha$, and if so why? My understanding is, ...
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110 views

Fama-Macbeth Regression: Weird Risk Premia

I just conducted a Fama-Macbeth regression where in the first step I calculated a time-series regression for each individual stock to get three betas (for mkt-rf, smb, hml) for each stock. Then I ran ...
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3answers
115 views

How to get know when CUSIP is changed

CUSIP code is not a constant, it could be changed. Does anybody know how to detect a CUSIP change? Is there any report with this info? Where can i find it? Thank you.
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1answer
90 views

Old codes for Companies (CUSIP/ISIN/SEDOL)

I found that for example ISIN have following rules: Merger and acquisition: Old ISINs for stock become inactive and are replaced by securities with a new ISIN. Bonds only need new ISINs if old ones ...
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0answers
33 views

Asset prices Boom,Bust and Recovery cycles

Is there any systematic way to detect the Boom, bust and Recovery cycles in Asset Prices ? Are there any good references about the Topic ? Thanks in advance.
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1answer
68 views

What does a regression of squared returns of stock on squared index returns and lags show?

We have a squared stock return at t regressed on 3 variables: squared index return, squared stock return at t-1, and squared index return at t-1. My two questions would be: 1. What does this test ...
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2answers
83 views

Cash flows regression on macroeconomic data

I'm looking into a research project and am struggling to find any existing work on this or whether I'm asking the right question. My question is to test the relationship between macroeconomic ...
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0answers
32 views

Average of R squared correct/allowed/useful?

I just conducted a Fama-Macbeth analysis to estimate the risk premia of Fama/French. In short, I estimated the betas on a company-individual basis first and then conducted a cross-section regression ...
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1answer
58 views

How to calculate R for strategies with dynamic exit points

Calculating risk-reward ratio R is easy when trading a straight forward strategy which has its entry and exit points clear: ...
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38 views

Markov Switching ARMA-GARCH

I am looking for R function for modelling Markov Switching ARMA-GARCH. I found package MSGARCH but that package can not accommodate mean model. Do you have an idea for my case?
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73 views

Classical Cramer Lundberg model - Ruin Theory Simple Question

I am trying to solve the following problem: 'An insurance company has an initial surplus of 150 and premium loading factor of 15%. Assume that claims arrive according to a compound Poisson process $(...

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