# 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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### How random are financial data series?

Pseudorandom number generators are often tested using e.g. a test suite like Diehard tests or Dieharder. If one would run these tests e.g. on stock market time series or other financial data, would ...
75 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 ...
30 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?
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% ...
1 vote
216 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 ...
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 ...
52 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 ...
83 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 ...
267 views

### How to see if a set of asset returns corresponds to a known correlation matrix?

Let's say I have an arbitrary set of $n$ period returns for $k$ assets, and a given $k \times k$ correlation matrix (of asset returns), which is known a priori. Does it makes sense, or is it even ...
1 vote
437 views

### How to obtain annualized IR from t-monthly IC?

When we checking the relation between some factors and Stock price, we could use Information Coefficient(IC) to meausre. And then I already have t-monthly IC for each factor, and I need to calculate ...
446 views

### bayes theorem probability Jar [closed]

I am trying to come up with different theoretical answers below. I believe the standard one is based on Bayes theorem, but I am struggling to prove it. A jar has 1000 coins, of which 999 are fair ...
142 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 ...
589 views

### Where to get Tobin's Q by country

I am trying to rank countries based on Tobin's Q ratio. US data can be easily gathered from FED's report and is available on multiple website. I want get data on other countries with high Index of ...
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, $\mu$ ...
154 views

### How to apply derived beta to daily change?

I've taken three months of price return data for two instruments and calculated a $\beta$ between the two using the formula $\beta = \frac{Cov(x,y}{Var(y)}$ with the goal of estimating what the ...
172 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 ...
180 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?
8k views

### How do you evaluate a covariance forecast?

Suppose you have two sources of covariance forecasts on a fixed set of $n$ assets, method A and method B (you can think of them as black box forecasts, from two vendors, say), which are known to be ...
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 ...
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 ...
521 views

### Impulse response function interpretation

I would need a quick help with Impulse response function interpretation which I have done after Vector autoregression model in stata. I need to understand how to interpret IRF graph or table values ...
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 ...
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 ...
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, ...
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 ...
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 $v_\pi(s)$ ...
24k views

### Kalman Filter Equity Example

I am looking out for some material where I can study about Kalman Filter applied to Equity using Excel or R?
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 ...
826 views

### What machine learning method is more suitable for prediction of financial time series?

I have time series data for various assets and which I transform to create various features. I have framed the problem as a classification task where I attempt to predict either a positive or negative ...
1 vote
150 views

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 ...
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 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 ...
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,...
65k views

### How to fit ARMA+GARCH Model In R?

I am currently working on ARMA+GARCH model using R. I am looking out for example which explain step by step explanation for fitting this model in R. I have time series which is stationary and I am ...
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 $M_j$ ...
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
429 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 ...
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 (...
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 ...
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 ...
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 ...