# 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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9 views

### Computing the average deviation range in a mean reverting series

Given a mean reverting time series, what's the appropriate measure to use to compute the range it deviates by before reversion? Assuming normal distribution, taking standard deviations of the actual ...
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### Which distribution has higher VaR?

Let say I have 2 distributions with cdf $F_1$ and $F_2$. And I know that $F_1 \leq F_2$. With this information I know that $F_1$ has bigger lower tail than $F_2$ but I don't think this right away ...
24 views

### [PYTHON - Create a For-loop for multiple regressions within the same/or different dataframe/s (Funds returns with fama french)

hopefully somebody can help me out, this is my first question on here. I have a dataframe with dates (Index) as the Y axis and the X axis (columns) hold all the dependent variables (target variables) ...
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### Fitting ARIMA + GARCH in R

I'm forecasting Electricity consumption Data. I have data for one year , so for every 15 minutes there is an observation. My data contains seasonality and I don't know how to fit SARIMA + GARCH into R,...
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### How can momentum trading strategies work if returns are not serially correlated?

Returns are demonstrably not serially correlated in most financial time series (Day 1 returns are uncorrelated to Day 2 returns etc.) . Since this is the case, how can momentum trading strategies work?...
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### Compare errors in estimating a probability

Let $X_t$ be a geometric Brownian motion: $dX_t = \mu(X_t,t)dt + \sigma(X_t,t)dW_t$ with $W_t$ a standard Brownian motion. Given the intervals $[t_{j-1}, t_{j}]$ for $j\in {1,...,U,...,N}$, let $M_j$ ...
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### How to conduct statistical test to see if certain factors impact trading streategy

Since the seminal paper by Fama and French(1993) that uses size, market, and value factors to explain extra market returns on the equity market, people have conducted tons of research on equity factor ...
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### Interpret interaction term between dummy and continues variable /bank risk (Beta and stock return)

I am using OLS regression to answer my research question.Well, I have two types of banks( Commercial banks and bank holding company's).My dependent variable is banks stock return in the first quarter ...
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### Hypothesis testing book

I am looking for a book that is focused on hypothesis testing. I read "Hypothesis Testing: An Intuitive Guide for Making Data Driven" by Jim Frost and I'm looking for similar book which is ...
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### How to annualize kurtosis of returns (in simple terms)?

I'm confused by this post on how to annualize kurtosis. I don't understand how to apply it to annualize the kurtosis for my data. In other words, if I evaluated the kurtosis of, say, monthly returns (...
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### Fat tailed can be estimated through a t-distributions?

I have a simple question that makes me doubt a bit. In a multiple choise exam I ecountered this question: "if the stocks returns are not normally distributed, the fat tail effect can be estimated ...
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### in time series analysis or finance people use log return for inference but returns can take negative value [closed]

in time series analysis or finance people use log return for inference but returns can take negative value. but log cant take negative values. so why we use it when log is not defined on most of ...
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### Statistical significance in the context of financial data?

I understand statistical significance in the general sense: we take a sample from a population and compute some parameter from the sample to infer what is the propulsion parameter to some degree of ...
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### Prediciting outperformance - choice of statistical design?

I want to predict relative outperformance between a stock and an associated benchmark index using statistical time-series models (e.g. ARIMA) and some exogenous variables (day of the week, corporate ...
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### Compare portfolio returns across time dimension

I've designed a trading strategy and would like to understand whether the return profile for it differs for the trades implemented before and after the Covid pandemic. Specifically I would like to ...
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### Portfolio variance over time vs. Portfolio variance from mix of two assets

Here are two facts about finance: 1. If stock returns are not independent, for example tomorrow's return equals today's return, then the variance over two days will be less than the variance of 1day*2....
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### Realized Volatility + GARCH - can I use hourly realized volatility?

I hav minute bar FX data and I am trying to fit a realized variance GARCH model using rugarch. This normally works by providing daily returns and daily realized volatility to the model. Realized ...
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### Completing the financial investment disclaimer platitude with statistics terminology

Take the typical disclaimer often seen where investment products can be found. Here is a sentence from the fine print of BlackRock's fundamental equity fund page: Performance data quoted represents ...
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### Real estate returns with incomplete dataset?

I have a dataset of real estate returns in markets A, B, and C. I also have national returns, denoted market N. I have 10 columns representing the time period for each data point. Market A only has ...
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### Contribution to Mahalanobis Distance

I am using Mahalanobis Distance to measure abnormal behavior within a portfolio consisting of a handful of general asset types, and am trying to figure out how to decompose this measurement into ...
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### Backtesting of outperformance of a benchmark using the Deflated Sharpe Ratio

I want to test whether, let's say, strategy A outperforms strategy B. In Marcos López de Prado's book Advances in Financial Machine Learning he presents the following statistics: The Probalistic ...
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### Covariance Shrinkage - Am I getting the right variances?

I am looking into a quite simple task: shrinking the sample covariance matrix of a minor sample of monthly returns data on 5 different assets. I am using Python to process my data and have been using ...
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### Creating a set of histories that satisfies certain statistics

I'm looking at a download of BlackRock's capital market assumptions, which gives a bunch of statistics, such as expected and quartiles for asset classes' returns for different timeframes, volatilities ...
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### Are return time series ergodic?

It seems intuitive to me that return time series would be ergodic. Is there a test statistic that I can use to check this? Would this be affected by sampling rate? One way I can think of checking ...
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### Topics for a 5 ECTS point project in a Msc Applied Math prorgram [closed]

I need 5 ECTS to complete my education (Msc in applied math, finance track). A statistics professor have agreed to do a project with me but I need to come up with the topic myself. Can you reccomend ...
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### Calculating performance decay of a strategy

Came across this thread which basically advises t-test for difference in means across periods to calculate whether our edge is deteriorating. The catch being that this test will probably not be ...
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### How skewed are FX returns? Does this look like a plausible histogram of EURUSD?

I'm reading about volatility. I've charted the histogram of EURUSD and I am wondering if this looks plausible? What I've charted are the 1-hour percent change returns (not log returns). I've removed 0 ...
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### Correct terminology - estimate or model?

I am doing some academic work and I'd like to summarise the picture around volatility models. As such, I'd like to refer to several ways of estimating volatility and I'd like to use proper terminology....
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### How to calculate the longest expected losing streak for a system that trades all the index members simultaneously?

For a trading system that trades only one security we can easily compute the longest expected losing streak using this formula: where: n is the number of trades, ln is natural logarithm, P is the ...
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### solve.QP in R doesn't give a solution satisfying the constraint

I've dealing with a quadratic programming problem as following, and my objective is to get a 49*1 vector. \widehat{\boldsymbol{w}}^{0}(\tau):=\underset{\boldsymbol{w}(\tau) \in \mathbb{W}}{\arg \min ...
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### CAPM alphas have unexpected p-value distribution

I am trying to "test" whether the EMH holds by testing for every stock in the S&P 500 whether it has a "significant" CAPM alpha. If the EMH is true, then the null-hypothesis (...
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### Statistical testing of out-of-time portfolio performance (measured via a custom metric)

I'm testing (out-of-time) my machine learning (ML) based strategy against a strong benchmark. As a performance metric, I'm using a custom rolling metric $M(t)$ which takes into account the portfolio ...
143 views

### How does trndbot generate buy/sell signals?

I was looking at trndbot and it's buy/sell signals are pretty good - what algorithm are they using to generate these signals? Although it maybe similar to bollinger bands, it algorithmically ...
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### 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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### 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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### 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 ...
44 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ...
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 ...
### 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 ...