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.

410 questions
Filter by
Sorted by
Tagged with
31 views

I want to calculate correlation with spread (which is often in dollar changes) and then a return but I want to make sure I get the most accurate result possible. What do y'all recommend?
77 views

How to implement rolling granger causality

I am investigating two time series where the first is the daily closing stock price changes and the other is the daily changes in the PCE index. I want to investigate how much the PCE index explains ...
79 views

Correlation with Differ Units of Measurement [closed]

I was wondering how to accurately get the correlation between a variable of percent change return and a variable of dollar change or basis points. Should I standardize both variables or will that lose ...
47 views

Reasons for negative autocorrelation of forward prices

I am working on each trade day's forward prices of gasoline. I noticed that the autocorrelation at lag 6 is significantly negative. I know how to interpret negative autocorrelation in a statistical ...
228 views

How can I measure returns such that the average is useful?

If I measure daily returns by simple percent change, a -50% day then a +50% day (or vice versa) results in a true -25% total change, but the average makes it look like you would expect a total 0% ...
32 views

Retail vs institutional percentage estimation in equity futures market (CME)

I am trying to find the most/least "popular with retail futures traders" instrument based on public data. I managed to estimate retail/institutional proportions by aggregating OI data from ...
53 views

Using the Fama-French 5 factor model in Panel Data

I have a question regarding the use of the FF5 Factors in an industry-fixed effects model. In order to clearify my question I'll post an example of my dataset Note that this is just an example, the ...
30 views

Particle Filter Importance Weight (SIR) Calculation for Price Series

I applied a particle filter on a price series but I am not sure if my maths checks out, especially at the update part. I've followed this tutorial and Kalman-and-Bayesian-Filters-in-Python from Roger ...
53 views

What is the Kurtosis of Returns in Geometric Brownian Motion?

Suppose that $dS_t=S_t(\mu\mathop{dt}+\sigma\mathop{dW_t})$ which has solution $$S_t=S_0\exp\left(t\left(\mu+\frac{\sigma^2}{2}\right)+\sigma W_t\right),$$ such that $W_t$ is a Wiener process, $\mu$ ...
• 110
181 views

Principal component analysis on a yield curve

When conducting principal component analysis on the yield curve, PC1 = constant (level shift), PC2 = Slope, PC3 = Curvature. How do you interpret PC>3, e.g. PC 4?
51 views

Average probability of varying input data

New to the quant finance exchange. I am stuck with a question maybe someone could help me. In the table below I have calculated if price is up/down w.r.t to the open shown in the 2nd column with ...
1 vote
68 views

Normalized statistical risk/reward measures to compare different quant trading strategy's returns, eg for backtesting

Want to select a metric or metrics to compare returns of different investment strategies, for quantitative backtesting, strategy selection, and forward measurement. Been reading different approaches ...
• 111
220 views

Interpreting the average correlation figure in Pozzi et al. (2013) paper

Has anyone read the paper "Spread of risk across financial markets:better to invest in the peripheries" by F. Pozzi, T. Di Matteo & T. Aste? If so, how do you interpret equation (1) in ...
85 views

What are the most common methods to model fat tails in the changes of asset prices?

I was wondering what the most common, or most popular, ways - in both academia, and industry - there were to model the fat tails of volatility in asset prices changes. I am presuming a basic Brownian ...
• 101
1 vote
132 views

Statistical metric to measure how well does the volatility surface fit the market

Suppose that I have a model for implied volatility surface and want to figure out required recalibration frequency based on historical quotes. Since I have a large range of strikes and tenors over a ...
• 440
1 vote
207 views

Is it safe to assume inflation rate and treasury yields are stationary?

I have YoY percent change in CPI and the nominal 10 year Treasury yield. I want to run some correlation analysis between them but worry they are not stationary. I ran a DF test and found that, ...
• 131
89 views

how to derive t-statistic for alpha (Eq. 15.29) in "quantitative equity portfolio management"?

I am reading "quantitative equity portfolio management: an active approach to portfolio construction and management" by Ludwig B. Chincarini, Daehwan Kim, and am confused by this derivation ...
• 181
87 views

Why do Monte-Carlo methods converge quadratically?

I'm reading Sutton's Reinforcemant Learning: An Introduction, and here's a part from page 93 of this book: In this case each return is an independent, identically distributed estimate of $v_\pi(s)$ ...
• 1
25 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 ...
1 vote
150 views

44 views

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 ...
133 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) ...
• 1
90 views

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,...
• 21
368 views

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?...
1 vote
95 views

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 $M_j$ ...
1 vote
161 views

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 ...
29 views

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 ...
1 vote
105 views

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 ...
• 11
1 vote
140 views

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 (...
• 11
1 vote
174 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 ...
• 11
68 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 ...
105 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 ...
93 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 ...
• 121
1 vote
55 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 ...
• 21
40 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....
132 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 ...
• 389
82 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 ...
41 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 ...
163 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 ...
66 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 ...
• 21
384 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 ...
71 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 ...
• 179
1 vote
163 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 ...
• 389
64 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 ...
• 1
1 vote
56 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 ...
115 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 ...
• 389
1 vote
89 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....
• 389
88 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 ...
131 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 (...
• 101
1 vote
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 ...