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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1answer
110 views

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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1answer
32 views

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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1answer
93 views

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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1answer
83 views

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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0answers
51 views

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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0answers
36 views

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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0answers
66 views

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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0answers
80 views

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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0answers
36 views

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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0answers
126 views

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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0answers
42 views

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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1answer
79 views

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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2answers
64 views

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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1answer
143 views

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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1answer
60 views

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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0answers
36 views

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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0answers
94 views

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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0answers
79 views

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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0answers
38 views

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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0answers
62 views

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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1answer
84 views

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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0answers
23 views

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 ...
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2answers
120 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 ...
2
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0answers
79 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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0answers
40 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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0answers
46 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
43 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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0answers
43 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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0answers
33 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
30 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
90 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
65 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
80 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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0answers
72 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
146 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
120 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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0answers
45 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 ...
2
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1answer
167 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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0answers
81 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 ...
1
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1answer
57 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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0answers
40 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 ...
1
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1answer
94 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
37 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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0answers
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
165 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
70 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
93 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 ...
1
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1answer
48 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
146 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
406 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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